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class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Materials with magnetic moments that change properties at the Curie temperature subsection</span> </button> <ul id="toc-Materials_with_magnetic_moments_that_change_properties_at_the_Curie_temperature-sublist" class="vector-toc-list"> <li id="toc-Paramagnetic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Paramagnetic"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Paramagnetic</span> </div> </a> <ul id="toc-Paramagnetic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ferromagnetic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ferromagnetic"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Ferromagnetic</span> </div> </a> <ul id="toc-Ferromagnetic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ferrimagnetic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ferrimagnetic"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Ferrimagnetic</span> </div> </a> <ul id="toc-Ferrimagnetic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Antiferromagnetic_and_the_Néel_temperature" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Antiferromagnetic_and_the_Néel_temperature"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Antiferromagnetic and the Néel temperature</span> </div> </a> <ul id="toc-Antiferromagnetic_and_the_Néel_temperature-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Curie–Weiss_law" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Curie–Weiss_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Curie–Weiss law</span> </div> </a> <ul id="toc-Curie–Weiss_law-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Physics" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Physics</span> </div> </a> <button aria-controls="toc-Physics-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Physics subsection</span> </button> <ul id="toc-Physics-sublist" class="vector-toc-list"> <li id="toc-Approaching_Curie_temperature_from_above" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Approaching_Curie_temperature_from_above"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Approaching Curie temperature from above</span> </div> </a> <ul id="toc-Approaching_Curie_temperature_from_above-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Approaching_Curie_temperature_from_below" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Approaching_Curie_temperature_from_below"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Approaching Curie temperature from below</span> </div> </a> <ul id="toc-Approaching_Curie_temperature_from_below-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Approaching_absolute_zero_(0_kelvin)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Approaching_absolute_zero_(0_kelvin)"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Approaching absolute zero (0 kelvin)</span> </div> </a> <ul id="toc-Approaching_absolute_zero_(0_kelvin)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ising_model_of_phase_transitions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ising_model_of_phase_transitions"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Ising model of phase transitions</span> </div> </a> <ul id="toc-Ising_model_of_phase_transitions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Weiss_domains_and_surface_and_bulk_Curie_temperatures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Weiss_domains_and_surface_and_bulk_Curie_temperatures"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Weiss domains and surface and bulk Curie temperatures</span> </div> </a> <ul id="toc-Weiss_domains_and_surface_and_bulk_Curie_temperatures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Changing_a_material's_Curie_temperature" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Changing_a_material's_Curie_temperature"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6</span> <span>Changing a material's Curie temperature</span> </div> </a> <ul id="toc-Changing_a_material's_Curie_temperature-sublist" class="vector-toc-list"> <li id="toc-Composite_materials" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Composite_materials"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6.1</span> <span>Composite materials</span> </div> </a> <ul id="toc-Composite_materials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Particle_size" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Particle_size"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6.2</span> <span>Particle size</span> </div> </a> <ul id="toc-Particle_size-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pressure" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Pressure"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6.3</span> <span>Pressure</span> </div> </a> <ul id="toc-Pressure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Orbital_ordering" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Orbital_ordering"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6.4</span> <span>Orbital ordering</span> </div> </a> <ul id="toc-Orbital_ordering-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Curie_temperature_in_ferroelectric_materials" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Curie_temperature_in_ferroelectric_materials"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Curie temperature in ferroelectric materials</span> </div> </a> <button aria-controls="toc-Curie_temperature_in_ferroelectric_materials-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Curie temperature in ferroelectric materials subsection</span> </button> <ul id="toc-Curie_temperature_in_ferroelectric_materials-sublist" class="vector-toc-list"> <li id="toc-Ferroelectric_and_dielectric" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ferroelectric_and_dielectric"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Ferroelectric and dielectric</span> </div> </a> <ul id="toc-Ferroelectric_and_dielectric-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relative_permittivity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relative_permittivity"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Relative permittivity</span> </div> </a> <ul id="toc-Relative_permittivity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Applications</span> </div> </a> <ul id="toc-Applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Curie temperature</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 48 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-48" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">48 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%B1%D8%AC%D8%A9_%D8%AD%D8%B1%D8%A7%D8%B1%D8%A9_%D9%83%D9%88%D8%B1%D9%8A" title="درجة حرارة كوري – Arabic" lang="ar" hreflang="ar" data-title="درجة حرارة كوري" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/K%C3%BCri_n%C3%B6qt%C9%99si" title="Küri nöqtəsi – Azerbaijani" lang="az" hreflang="az" data-title="Küri nöqtəsi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8D%E0%A6%AF%E0%A7%81%E0%A6%B0%E0%A6%BF_%E0%A6%A4%E0%A6%BE%E0%A6%AA%E0%A6%AE%E0%A6%BE%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%BE" title="ক্যুরি তাপমাত্রা – Bangla" lang="bn" hreflang="bn" data-title="ক্যুরি তাপমাত্রা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D1%80%D0%BE%D0%BF%D0%BA%D0%B0_%D0%9A%D1%8E%D1%80%D1%8B" title="Кропка Кюры – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Кропка Кюры" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BC%D0%BF%D0%B5%D1%80%D0%B0%D1%82%D1%83%D1%80%D0%B0_%D0%BD%D0%B0_%D0%9A%D1%8E%D1%80%D0%B8" title="Температура на Кюри – Bulgarian" lang="bg" hreflang="bg" data-title="Температура на Кюри" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Curiejeva_ta%C4%8Dka" title="Curiejeva tačka – Bosnian" lang="bs" hreflang="bs" data-title="Curiejeva tačka" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Temperatura_de_Curie" title="Temperatura de Curie – Catalan" lang="ca" hreflang="ca" data-title="Temperatura de Curie" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Curieova_teplota" title="Curieova teplota – Czech" lang="cs" hreflang="cs" data-title="Curieova teplota" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Curietemperaturen" title="Curietemperaturen – Danish" lang="da" hreflang="da" data-title="Curietemperaturen" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Curie-Temperatur" title="Curie-Temperatur – German" lang="de" hreflang="de" data-title="Curie-Temperatur" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Curie_punkt" title="Curie punkt – Estonian" lang="et" hreflang="et" data-title="Curie punkt" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%98%CE%B5%CF%81%CE%BC%CE%BF%CE%BA%CF%81%CE%B1%CF%83%CE%AF%CE%B1_%CE%9A%CE%B9%CF%81%CE%AF" title="Θερμοκρασία Κιρί – Greek" lang="el" hreflang="el" data-title="Θερμοκρασία Κιρί" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Temperatura_de_Curie" title="Temperatura de Curie – Spanish" lang="es" hreflang="es" data-title="Temperatura de Curie" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Curie-punkto" title="Curie-punkto – Esperanto" lang="eo" hreflang="eo" data-title="Curie-punkto" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Curie_tenperatura" title="Curie tenperatura – Basque" lang="eu" hreflang="eu" data-title="Curie tenperatura" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D9%85%D8%A7%DB%8C_%DA%A9%D9%88%D8%B1%DB%8C" title="دمای کوری – Persian" lang="fa" hreflang="fa" data-title="دمای کوری" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Temp%C3%A9rature_de_Curie" title="Température de Curie – French" lang="fr" hreflang="fr" data-title="Température de Curie" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Teocht_Curie" title="Teocht Curie – Irish" lang="ga" hreflang="ga" data-title="Teocht Curie" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Temperatura_de_Curie" title="Temperatura de Curie – Galician" lang="gl" hreflang="gl" data-title="Temperatura de Curie" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%80%B4%EB%A6%AC_%EC%98%A8%EB%8F%84" title="퀴리 온도 – Korean" lang="ko" hreflang="ko" data-title="퀴리 온도" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B5%D5%B8%D6%82%D6%80%D5%AB%D5%AB_%D5%BB%D5%A5%D6%80%D5%B4%D5%A1%D5%BD%D5%BF%D5%AB%D5%B3%D5%A1%D5%B6" title="Կյուրիի ջերմաստիճան – Armenian" lang="hy" hreflang="hy" data-title="Կյուրիի ջերմաստիճան" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%AF%E0%A5%82%E0%A4%B0%E0%A5%80_%E0%A4%A4%E0%A4%BE%E0%A4%AA" title="क्यूरी ताप – Hindi" lang="hi" hreflang="hi" data-title="क्यूरी ताप" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Curiejeva_temperatura" title="Curiejeva temperatura – Croatian" lang="hr" hreflang="hr" data-title="Curiejeva temperatura" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Punto_di_Curie" title="Punto di Curie – Italian" lang="it" hreflang="it" data-title="Punto di Curie" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%98%D7%9E%D7%A4%D7%A8%D7%98%D7%95%D7%A8%D7%AA_%D7%A7%D7%99%D7%A8%D7%99" title="טמפרטורת קירי – Hebrew" lang="he" hreflang="he" data-title="טמפרטורת קירי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D1%8E%D1%80%D0%B8_%D1%82%D0%B5%D0%BC%D0%BF%D0%B5%D1%80%D0%B0%D1%82%D1%83%D1%80%D0%B0%D1%81%D1%8B" title="Кюри температурасы – Kazakh" lang="kk" hreflang="kk" data-title="Кюри температурасы" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Germahiya_Curie" title="Germahiya Curie – Kurdish" lang="ku" hreflang="ku" data-title="Germahiya Curie" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Curie-h%C5%91m%C3%A9rs%C3%A9klet" title="Curie-hőmérséklet – Hungarian" lang="hu" hreflang="hu" data-title="Curie-hőmérséklet" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%B8%D1%80%D0%B8%D0%B5%D0%B2%D0%B0_%D1%82%D0%B5%D0%BC%D0%BF%D0%B5%D1%80%D0%B0%D1%82%D1%83%D1%80%D0%B0" title="Кириева температура – Macedonian" lang="mk" hreflang="mk" data-title="Кириева температура" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%B0%E0%A5%80_%E0%A4%A4%E0%A4%BE%E0%A4%AA%E0%A4%AE%E0%A4%BE%E0%A4%A8" title="क्युरी तापमान – Marathi" lang="mr" hreflang="mr" data-title="क्युरी तापमान" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Suhu_Curie" title="Suhu Curie – Malay" lang="ms" hreflang="ms" data-title="Suhu Curie" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Curietemperatuur" title="Curietemperatuur – Dutch" lang="nl" hreflang="nl" data-title="Curietemperatuur" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AD%E3%83%A5%E3%83%AA%E3%83%BC%E6%B8%A9%E5%BA%A6" title="キュリー温度 – Japanese" lang="ja" hreflang="ja" data-title="キュリー温度" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Curie-temperatur" title="Curie-temperatur – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Curie-temperatur" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kyuri_nuqtasi" title="Kyuri nuqtasi – Uzbek" lang="uz" hreflang="uz" data-title="Kyuri nuqtasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Temperatura_Curie" title="Temperatura Curie – Polish" lang="pl" hreflang="pl" data-title="Temperatura Curie" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Temperatura_de_Curie" title="Temperatura de Curie – Portuguese" lang="pt" hreflang="pt" data-title="Temperatura de Curie" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Punct_Curie" title="Punct Curie – Romanian" lang="ro" hreflang="ro" data-title="Punct Curie" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%BE%D1%87%D0%BA%D0%B0_%D0%9A%D1%8E%D1%80%D0%B8" title="Точка Кюри – Russian" lang="ru" hreflang="ru" data-title="Точка Кюри" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Curieho_teplota" title="Curieho teplota – Slovak" lang="sk" hreflang="sk" data-title="Curieho teplota" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Curiejeva_temperatura" title="Curiejeva temperatura – Slovenian" lang="sl" hreflang="sl" data-title="Curiejeva temperatura" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Curien_piste" title="Curien piste – Finnish" lang="fi" hreflang="fi" data-title="Curien piste" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Curietemperaturen" title="Curietemperaturen – Swedish" lang="sv" hreflang="sv" data-title="Curietemperaturen" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%BF%E0%AE%AF%E0%AF%82%E0%AE%B0%E0%AE%BF_%E0%AE%B5%E0%AF%86%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%A8%E0%AE%BF%E0%AE%B2%E0%AF%88" title="கியூரி வெப்பநிலை – Tamil" lang="ta" hreflang="ta" data-title="கியூரி வெப்பநிலை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Curie_s%C4%B1cakl%C4%B1%C4%9F%C4%B1" title="Curie sıcaklığı – Turkish" lang="tr" hreflang="tr" data-title="Curie sıcaklığı" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BC%D0%BF%D0%B5%D1%80%D0%B0%D1%82%D1%83%D1%80%D0%B0_%D0%9A%D1%8E%D1%80%D1%96" title="Температура Кюрі – Ukrainian" lang="uk" hreflang="uk" data-title="Температура Кюрі" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Nhi%E1%BB%87t_%C4%91%E1%BB%99_Curie" title="Nhiệt độ Curie – Vietnamese" lang="vi" hreflang="vi" data-title="Nhiệt độ Curie" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" 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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Temperature above which magnetic properties change</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1273380762/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:204px;max-width:204px"><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Diagram_of_Ferromagnetic_Magnetic_Moments.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Diagram_of_Ferromagnetic_Magnetic_Moments.png/200px-Diagram_of_Ferromagnetic_Magnetic_Moments.png" decoding="async" width="200" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Diagram_of_Ferromagnetic_Magnetic_Moments.png/300px-Diagram_of_Ferromagnetic_Magnetic_Moments.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Diagram_of_Ferromagnetic_Magnetic_Moments.png/400px-Diagram_of_Ferromagnetic_Magnetic_Moments.png 2x" data-file-width="640" data-file-height="400" /></a></span></div><div class="thumbcaption"><b>Figure 1.</b> Below the Curie temperature, neighbouring magnetic spins align parallel to each other in a ferromagnet in the absence of an applied <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a>.</div></div></div><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Diagram_of_Paramagnetic_Magnetic_Moments.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Diagram_of_Paramagnetic_Magnetic_Moments.png/200px-Diagram_of_Paramagnetic_Magnetic_Moments.png" decoding="async" width="200" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Diagram_of_Paramagnetic_Magnetic_Moments.png/300px-Diagram_of_Paramagnetic_Magnetic_Moments.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Diagram_of_Paramagnetic_Magnetic_Moments.png/400px-Diagram_of_Paramagnetic_Magnetic_Moments.png 2x" data-file-width="640" data-file-height="400" /></a></span></div><div class="thumbcaption"><b>Figure 2.</b> Above the Curie temperature, the magnetic spins are randomly aligned in a paramagnet unless a magnetic field is applied.</div></div></div></div></div> <p>In <a href="/wiki/Physics" title="Physics">physics</a> and <a href="/wiki/Materials_science" title="Materials science">materials science</a>, the <b>Curie temperature</b> (<i>T</i><sub>C</sub>), or <b>Curie point</b>, is the temperature above which certain materials lose their <a href="/wiki/Magnet" title="Magnet">permanent magnetic</a> properties, which can (in most cases) be replaced by <a href="/wiki/Magnetization" title="Magnetization">induced magnetism</a>. The Curie temperature is named after <a href="/wiki/Pierre_Curie" title="Pierre Curie">Pierre Curie</a>, who showed that magnetism is lost at a critical temperature.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>The force of magnetism is determined by the <a href="/wiki/Magnetic_moment" title="Magnetic moment">magnetic moment</a>, a dipole moment within an atom that originates from the <a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a> and <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> of electrons. Materials have different structures of intrinsic magnetic moments that depend on temperature; the Curie temperature is the critical point at which a material's intrinsic magnetic moments change direction. </p><p>Permanent magnetism is caused by the alignment of magnetic moments, and induced magnetism is created when disordered magnetic moments are forced to align in an applied magnetic field. For example, the ordered magnetic moments (<a href="/wiki/Ferromagnetism" title="Ferromagnetism">ferromagnetic</a>, Figure 1) change and become disordered (<a href="/wiki/Paramagnetism" title="Paramagnetism">paramagnetic</a>, Figure 2) at the Curie temperature. Higher temperatures make magnets weaker, as spontaneous magnetism only occurs below the Curie temperature. <a href="/wiki/Magnetic_susceptibility" title="Magnetic susceptibility">Magnetic susceptibility</a> above the Curie temperature can be calculated from the <a href="/wiki/Curie%E2%80%93Weiss_law" title="Curie–Weiss law">Curie–Weiss law</a>, which is derived from <a href="/wiki/Curie%27s_law" title="Curie's law">Curie's law</a>. </p><p>In analogy to ferromagnetic and paramagnetic materials, the Curie temperature can also be used to describe the phase transition between <a href="/wiki/Ferroelectricity" title="Ferroelectricity">ferroelectricity</a> and <a href="/wiki/Dielectric#Paraelectricity" title="Dielectric">paraelectricity</a>. In this context, the <a href="/wiki/Phase_transition#Order_parameters" title="Phase transition">order parameter</a> is the <i>electric</i> <a href="/wiki/Dielectric#Dipolar_polarization" title="Dielectric">polarization</a> that goes from a finite value to zero when the temperature is increased above the Curie temperature. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Curie_temperatures_of_materials">Curie temperatures of materials</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=1" title="Edit section: Curie temperatures of materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable" style="float:right; clear:right; margin-left:1em;"> <caption>The Curie points of various materials<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-table_3.1_3-0" class="reference"><a href="#cite_note-table_3.1-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kitteltable_4-0" class="reference"><a href="#cite_note-Kitteltable-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </caption> <tbody><tr> <th rowspan="2">Material </th> <th colspan="3">Curie temperature in </th></tr> <tr> <th>K </th> <th>°C </th> <th>°F </th></tr> <tr> <td><a href="/wiki/Iron" title="Iron">Iron</a> (Fe) </td> <td>1043–1664 </td> <td>770 </td> <td>1418 </td></tr> <tr> <td><a href="/wiki/Cobalt" title="Cobalt">Cobalt</a> (Co) </td> <td>1400 </td> <td>1130 </td> <td>2060 </td></tr> <tr> <td><a href="/wiki/Nickel" title="Nickel">Nickel</a> (Ni) </td> <td>627 </td> <td>354 </td> <td>669 </td></tr> <tr> <td><a href="/wiki/Gadolinium" title="Gadolinium">Gadolinium</a> (Gd) </td> <td>293.2<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </td> <td>20.1 </td> <td>68.1 </td></tr> <tr> <td><a href="/wiki/Dysprosium" title="Dysprosium">Dysprosium</a> (Dy) </td> <td>88 </td> <td>−185.2 </td> <td>−301.3 </td></tr> <tr> <td><a href="/wiki/Bismanol" title="Bismanol">Manganese bismuthide</a> (MnBi) </td> <td>630 </td> <td>357 </td> <td>674 </td></tr> <tr> <td>Manganese antimonide (Mn<a href="/wiki/Antimony" title="Antimony">Sb</a>) </td> <td>587 </td> <td>314 </td> <td>597 </td></tr> <tr> <td><a href="/wiki/Chromium(IV)_oxide" title="Chromium(IV) oxide">Chromium(IV) oxide</a> (CrO<sub>2</sub>) </td> <td>386 </td> <td>113 </td> <td>235 </td></tr> <tr> <td>Manganese arsenide (Mn<a href="/wiki/Arsenic" title="Arsenic">As</a>) </td> <td>318 </td> <td>45 </td> <td>113 </td></tr> <tr> <td><a href="/wiki/Europium(II)_oxide" title="Europium(II) oxide">Europium(II) oxide</a> (EuO) </td> <td>69 </td> <td>−204.2 </td> <td>−335.5 </td></tr> <tr> <td><a href="/wiki/Iron(III)_oxide" title="Iron(III) oxide">Iron(III) oxide</a> (Fe<sub>2</sub>O<sub>3</sub>) </td> <td>948 </td> <td>675 </td> <td>1247 </td></tr> <tr> <td><a href="/wiki/Iron(II,III)_oxide" title="Iron(II,III) oxide">Iron(II,III) oxide</a> (FeOFe<sub>2</sub>O<sub>3</sub>) </td> <td>858 </td> <td>585 </td> <td>1085 </td></tr> <tr> <td>NiO–Fe<sub>2</sub>O<sub>3</sub> </td> <td>858 </td> <td>585 </td> <td>1085 </td></tr> <tr> <td><a href="/wiki/Copper" title="Copper">Cu</a>O–Fe<sub>2</sub>O<sub>3</sub> </td> <td>728 </td> <td>455 </td> <td>851 </td></tr> <tr> <td>MgO–Fe<sub>2</sub>O<sub>3</sub> </td> <td>713 </td> <td>440 </td> <td>824 </td></tr> <tr> <td>MnO–Fe<sub>2</sub>O<sub>3</sub> </td> <td>573 </td> <td>300 </td> <td>572 </td></tr> <tr> <td><a href="/wiki/Yttrium_iron_garnet" title="Yttrium iron garnet">Yttrium iron garnet</a> (Y<sub>3</sub>Fe<sub>5</sub>O<sub>12</sub>) </td> <td>560 </td> <td>287 </td> <td>548 </td></tr> <tr> <td><a href="/wiki/Neodymium_magnet" title="Neodymium magnet">Neodymium magnets</a> </td> <td>583–673 </td> <td>310–400 </td> <td>590–752 </td></tr> <tr> <td><a href="/wiki/Alnico" title="Alnico">Alnico</a> </td> <td>973–1133 </td> <td>700–860 </td> <td>1292–1580 </td></tr> <tr> <td><a href="/wiki/Samarium%E2%80%93cobalt_magnet" title="Samarium–cobalt magnet">Samarium–cobalt magnets</a> </td> <td>993–1073 </td> <td>720–800 </td> <td>1328–1472 </td></tr> <tr> <td><a href="/wiki/Strontium_ferrite" class="mw-redirect" title="Strontium ferrite">Strontium ferrite</a> </td> <td>723 </td> <td>450 </td> <td>842 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> That heating destroys magnetism was already described in <i><a href="/wiki/De_Magnete" title="De Magnete">De Magnete</a></i> (1600):</p><blockquote><p>Iron filings, after being heated for a long time, are attracted by a loadstone, yet not so strongly or from so great a distance as when not heated. A loadstone loses some of its virtue by too great a heat; for its humour is set free, whence its peculiar nature is marred. (Book 2, Chapter 23).</p></blockquote> <div class="mw-heading mw-heading2"><h2 id="Magnetic_moments">Magnetic moments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=3" title="Edit section: Magnetic moments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At the atomic level, there are two contributors to the <a href="/wiki/Magnetic_moment" title="Magnetic moment">magnetic moment</a>, the <a href="/wiki/Electron_magnetic_moment" title="Electron magnetic moment">electron magnetic moment</a> and the <a href="/wiki/Nuclear_magnetic_moment" title="Nuclear magnetic moment">nuclear magnetic moment</a>. Of these two terms, the electron magnetic moment dominates, and the nuclear magnetic moment is insignificant. At higher temperatures, electrons have higher thermal energy. This has a randomizing effect on aligned magnetic domains, leading to the disruption of order, and the phenomena of the Curie point.<sup id="cite_ref-Hall_6-0" class="reference"><a href="#cite_note-Hall-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Jullien136_7-0" class="reference"><a href="#cite_note-Jullien136-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Ferromagnetism" title="Ferromagnetism">Ferromagnetic</a>, <a href="/wiki/Paramagnetism" title="Paramagnetism">paramagnetic</a>, <a href="/wiki/Ferrimagnetism" title="Ferrimagnetism">ferrimagnetic</a>, and <a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">antiferromagnetic</a> materials have different intrinsic magnetic moment structures. At a material's specific Curie temperature (<span class="texhtml"><i>T</i><sub>C</sub></span>), these properties change. The transition from antiferromagnetic to paramagnetic (or vice versa) occurs at the <a class="mw-selflink-fragment" href="#Antiferromagnetic_and_the_Néel_temperature">Néel temperature</a> (<span class="texhtml"><i>T</i><sub>N</sub></span>), which is analogous to Curie temperature. </p> <table> <tbody><tr> <th>Below <span class="texhtml"><i>T</i><sub>C</sub></span></th> <th>Above <span class="texhtml"><i>T</i><sub>C</sub></span> </th></tr> <tr> <td>Ferromagnetic</td> <td>↔ Paramagnetic </td></tr> <tr> <td>Ferrimagnetic</td> <td>↔ Paramagnetic </td></tr> <tr> <th>Below <span class="texhtml"><i>T</i><sub>N</sub></span></th> <th>Above <span class="texhtml"><i>T</i><sub>N</sub></span> </th></tr> <tr> <td>Antiferromagnetic</td> <td>↔ Paramagnetic </td></tr></tbody></table> <ul class="gallery mw-gallery-packed"> <li class="gallerycaption">Orientations of magnetic moments in materials</li> <li class="gallerybox" style="width: 194px"> <div class="thumb" style="width: 192px;"><span typeof="mw:File"><a href="/wiki/File:Diagram_of_Ferromagnetic_Magnetic_Moments.png" class="mw-file-description" title="Ferromagnetism: The magnetic moments in a ferromagnetic material are ordered and of the same magnitude in the absence of an applied magnetic field."><img alt="Ferromagnetism: The magnetic moments in a ferromagnetic material are ordered and of the same magnitude in the absence of an applied magnetic field." src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Diagram_of_Ferromagnetic_Magnetic_Moments.png/288px-Diagram_of_Ferromagnetic_Magnetic_Moments.png" decoding="async" width="192" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Diagram_of_Ferromagnetic_Magnetic_Moments.png/432px-Diagram_of_Ferromagnetic_Magnetic_Moments.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Diagram_of_Ferromagnetic_Magnetic_Moments.png/576px-Diagram_of_Ferromagnetic_Magnetic_Moments.png 2x" data-file-width="640" data-file-height="400" /></a></span></div> <div class="gallerytext"><b><a href="/wiki/Ferromagnetism" title="Ferromagnetism">Ferromagnetism</a></b>: The magnetic moments in a ferromagnetic material are ordered and of the same magnitude in the absence of an applied magnetic field.</div> </li> <li class="gallerybox" style="width: 194px"> <div class="thumb" style="width: 192px;"><span typeof="mw:File"><a href="/wiki/File:Diagram_of_Paramagnetic_Magnetic_Moments.png" class="mw-file-description" title="Paramagnetism: The magnetic moments in a paramagnetic material are disordered in the absence of an applied magnetic field and ordered in the presence of an applied magnetic field."><img alt="Paramagnetism: The magnetic moments in a paramagnetic material are disordered in the absence of an applied magnetic field and ordered in the presence of an applied magnetic field." src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Diagram_of_Paramagnetic_Magnetic_Moments.png/288px-Diagram_of_Paramagnetic_Magnetic_Moments.png" decoding="async" width="192" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Diagram_of_Paramagnetic_Magnetic_Moments.png/432px-Diagram_of_Paramagnetic_Magnetic_Moments.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Diagram_of_Paramagnetic_Magnetic_Moments.png/576px-Diagram_of_Paramagnetic_Magnetic_Moments.png 2x" data-file-width="640" data-file-height="400" /></a></span></div> <div class="gallerytext"><b><a href="/wiki/Paramagnetism" title="Paramagnetism">Paramagnetism</a></b>: The magnetic moments in a paramagnetic material are disordered in the absence of an applied magnetic field and ordered in the presence of an applied magnetic field.</div> </li> <li class="gallerybox" style="width: 194px"> <div class="thumb" style="width: 192px;"><span typeof="mw:File"><a href="/wiki/File:Diagram_of_Ferrimagnetic_Magnetic_Moments.png" class="mw-file-description" title="Ferrimagnetism: The magnetic moments in a ferrimagnetic material have different magnitudes (due to the crystal containing two different types of magnetic ions[clarification needed]) which are aligned oppositely in the absence of an applied magnetic field."><img alt="Ferrimagnetism: The magnetic moments in a ferrimagnetic material have different magnitudes (due to the crystal containing two different types of magnetic ions[clarification needed]) which are aligned oppositely in the absence of an applied magnetic field." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Diagram_of_Ferrimagnetic_Magnetic_Moments.png/288px-Diagram_of_Ferrimagnetic_Magnetic_Moments.png" decoding="async" width="192" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Diagram_of_Ferrimagnetic_Magnetic_Moments.png/432px-Diagram_of_Ferrimagnetic_Magnetic_Moments.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Diagram_of_Ferrimagnetic_Magnetic_Moments.png/576px-Diagram_of_Ferrimagnetic_Magnetic_Moments.png 2x" data-file-width="640" data-file-height="400" /></a></span></div> <div class="gallerytext"><b><a href="/wiki/Ferrimagnetism" title="Ferrimagnetism">Ferrimagnetism</a></b>: The magnetic moments in a ferrimagnetic material have different magnitudes (due to the crystal containing two different types of magnetic ions<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (May 2022)">clarification needed</span></a></i>]</sup>) which are aligned oppositely in the absence of an applied magnetic field.</div> </li> <li class="gallerybox" style="width: 194px"> <div class="thumb" style="width: 192px;"><span typeof="mw:File"><a href="/wiki/File:Diagram_of_Antiferromagnetic_Magnetic_Moments.png" class="mw-file-description" title="Antiferromagnetism: The magnetic moments in an antiferromagnetic material have the same magnitudes but are aligned oppositely in the absence of an applied magnetic field."><img alt="Antiferromagnetism: The magnetic moments in an antiferromagnetic material have the same magnitudes but are aligned oppositely in the absence of an applied magnetic field." src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Diagram_of_Antiferromagnetic_Magnetic_Moments.png/288px-Diagram_of_Antiferromagnetic_Magnetic_Moments.png" decoding="async" width="192" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Diagram_of_Antiferromagnetic_Magnetic_Moments.png/432px-Diagram_of_Antiferromagnetic_Magnetic_Moments.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Diagram_of_Antiferromagnetic_Magnetic_Moments.png/576px-Diagram_of_Antiferromagnetic_Magnetic_Moments.png 2x" data-file-width="640" data-file-height="400" /></a></span></div> <div class="gallerytext"><b><a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">Antiferromagnetism</a></b>: The magnetic moments in an antiferromagnetic material have the same magnitudes but are aligned oppositely in the absence of an applied magnetic field.</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Materials_with_magnetic_moments_that_change_properties_at_the_Curie_temperature">Materials with magnetic moments that change properties at the Curie temperature</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=4" title="Edit section: Materials with magnetic moments that change properties at the Curie temperature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ferromagnetic, paramagnetic, ferrimagnetic, and antiferromagnetic structures are made up of intrinsic magnetic moments. If all the electrons within the structure are paired, these moments cancel out due to their opposite spins and angular momenta. Thus, even with an applied magnetic field, these materials have different properties and no Curie temperature.<sup id="cite_ref-Ibach_8-0" class="reference"><a href="#cite_note-Ibach-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Levy_9-0" class="reference"><a href="#cite_note-Levy-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Paramagnetic">Paramagnetic</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=5" title="Edit section: Paramagnetic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Paramagnetism" title="Paramagnetism">Paramagnetism</a></div> <p>A material is paramagnetic only above its Curie temperature. Paramagnetic materials are non-magnetic when a <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> is absent and magnetic when a magnetic field is applied. When a magnetic field is absent, the material has disordered magnetic moments; that is, the magnetic moments are asymmetrical and not aligned. When a magnetic field is present, the magnetic moments are temporarily realigned parallel to the applied field;<sup id="cite_ref-Dekker1_10-0" class="reference"><a href="#cite_note-Dekker1-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Levy4_11-0" class="reference"><a href="#cite_note-Levy4-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> the magnetic moments are symmetrical and aligned.<sup id="cite_ref-Fan_12-0" class="reference"><a href="#cite_note-Fan-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The magnetic moments being aligned in the same direction are what causes an induced magnetic field.<sup id="cite_ref-Fan_12-1" class="reference"><a href="#cite_note-Fan-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Dekker_13-0" class="reference"><a href="#cite_note-Dekker-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>For paramagnetism, this response to an applied magnetic field is positive and is known as <a href="/wiki/Magnetic_susceptibility" title="Magnetic susceptibility">magnetic susceptibility</a>.<sup id="cite_ref-Ibach_8-1" class="reference"><a href="#cite_note-Ibach-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The magnetic susceptibility only applies above the Curie temperature for disordered states.<sup id="cite_ref-Mendelssohn3_14-0" class="reference"><a href="#cite_note-Mendelssohn3-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Sources of paramagnetism (materials which have Curie temperatures) include:<sup id="cite_ref-Levy1_15-0" class="reference"><a href="#cite_note-Levy1-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <ul><li>All atoms that have unpaired electrons;</li> <li>Atoms that have inner shells that are incomplete in electrons;</li> <li><a href="/wiki/Radical_(chemistry)" title="Radical (chemistry)">Free radicals</a>;</li> <li>Metals.</li></ul> <p>Above the Curie temperature, the atoms are excited, and the spin orientations become randomized<sup id="cite_ref-Levy_9-1" class="reference"><a href="#cite_note-Levy-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> but can be realigned by an applied field, i.e., the material becomes paramagnetic. Below the Curie temperature, the intrinsic structure has undergone a <a href="/wiki/Phase_transition" title="Phase transition">phase transition</a>,<sup id="cite_ref-Cusack_16-0" class="reference"><a href="#cite_note-Cusack-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> the atoms are ordered, and the material is ferromagnetic.<sup id="cite_ref-Fan_12-2" class="reference"><a href="#cite_note-Fan-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The paramagnetic materials' induced magnetic fields are very weak compared with ferromagnetic materials' magnetic fields.<sup id="cite_ref-Cusack_16-1" class="reference"><a href="#cite_note-Cusack-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ferromagnetic">Ferromagnetic</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=6" title="Edit section: Ferromagnetic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ferromagnetism" title="Ferromagnetism">Ferromagnetism</a></div> <p>Materials are only ferromagnetic below their corresponding Curie temperatures. Ferromagnetic materials are magnetic in the absence of an applied magnetic field. </p><p>When a magnetic field is absent the material has <a href="/wiki/Spontaneous_magnetization" title="Spontaneous magnetization">spontaneous magnetization</a> which is a result of the ordered magnetic moments; that is, for ferromagnetism, the atoms are symmetrical and aligned in the same direction creating a permanent magnetic field. </p><p>The magnetic interactions are held together by <a href="/wiki/Exchange_interaction" title="Exchange interaction">exchange interactions</a>; otherwise thermal disorder would overcome the weak interactions of magnetic moments. The exchange interaction has a zero probability of parallel electrons occupying the same point in time, implying a preferred parallel alignment in the material.<sup id="cite_ref-Hall1_17-0" class="reference"><a href="#cite_note-Hall1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> The Boltzmann factor contributes heavily as it prefers interacting particles to be aligned in the same direction.<sup id="cite_ref-Palmer_18-0" class="reference"><a href="#cite_note-Palmer-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> This causes <a href="/wiki/Ferromagnetism" title="Ferromagnetism">ferromagnets</a> to have strong magnetic fields and high Curie temperatures of around 1,000 K (730 °C).<sup id="cite_ref-Hall3_19-0" class="reference"><a href="#cite_note-Hall3-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Below the Curie temperature, the atoms are aligned and parallel, causing spontaneous magnetism; the material is ferromagnetic. Above the Curie temperature the material is paramagnetic, as the atoms lose their ordered magnetic moments when the material undergoes a phase transition.<sup id="cite_ref-Cusack_16-2" class="reference"><a href="#cite_note-Cusack-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ferrimagnetic">Ferrimagnetic</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=7" title="Edit section: Ferrimagnetic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ferrimagnetism" title="Ferrimagnetism">Ferrimagnetism</a></div> <p>Materials are only ferrimagnetic below their corresponding Curie temperature. Ferrimagnetic materials are magnetic in the absence of an applied magnetic field and are made up of two different <a href="/wiki/Ions" class="mw-redirect" title="Ions">ions</a>.<sup id="cite_ref-Jullien158_20-0" class="reference"><a href="#cite_note-Jullien158-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>When a magnetic field is absent the material has a spontaneous magnetism which is the result of ordered magnetic moments; that is, for ferrimagnetism one ion's<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (May 2022)">clarification needed</span></a></i>]</sup> magnetic moments are aligned facing in one direction with certain magnitude and the other ion's magnetic moments are aligned facing in the opposite direction with a different magnitude. As the magnetic moments are of different magnitudes in opposite directions there is still a spontaneous magnetism and a magnetic field is present.<sup id="cite_ref-Jullien158_20-1" class="reference"><a href="#cite_note-Jullien158-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>Similar to ferromagnetic materials the magnetic interactions are held together by exchange interactions. The orientations of moments however are anti-parallel which results in a net momentum by subtracting their momentum from one another.<sup id="cite_ref-Jullien158_20-2" class="reference"><a href="#cite_note-Jullien158-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>Below the Curie temperature the atoms of each ion are aligned anti-parallel with different momentums causing a spontaneous magnetism; the material is ferrimagnetic. Above the Curie temperature the material is paramagnetic as the atoms lose their ordered magnetic moments as the material undergoes a phase transition.<sup id="cite_ref-Jullien158_20-3" class="reference"><a href="#cite_note-Jullien158-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Antiferromagnetic_and_the_Néel_temperature"><span id="Antiferromagnetic_and_the_N.C3.A9el_temperature"></span>Antiferromagnetic and the Néel temperature</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=8" title="Edit section: Antiferromagnetic and the Néel temperature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">Antiferromagnetism</a></div> <p>Materials are only antiferromagnetic below their corresponding <b>Néel temperature</b> or <b>magnetic ordering temperature</b>, <i>T</i><sub>N</sub>. This is similar to the Curie temperature as above the Néel Temperature the material undergoes a <a href="/wiki/Phase_transition" title="Phase transition">phase transition</a> and becomes paramagnetic. That is, the thermal energy becomes large enough to destroy the microscopic magnetic ordering within the material.<sup id="cite_ref-spaldin_21-0" class="reference"><a href="#cite_note-spaldin-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> It is named after <a href="/wiki/Louis_N%C3%A9el" title="Louis Néel">Louis Néel</a> (1904–2000), who received the 1970 <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> for his work in the area. </p><p>The material has equal magnetic moments aligned in opposite directions resulting in a zero magnetic moment and a net magnetism of zero at all temperatures below the Néel temperature. Antiferromagnetic materials are weakly magnetic in the absence or presence of an applied magnetic field. </p><p>Similar to ferromagnetic materials the magnetic interactions are held together by exchange interactions preventing thermal disorder from overcoming the weak interactions of magnetic moments.<sup id="cite_ref-Hall1_17-1" class="reference"><a href="#cite_note-Hall1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Jullien10_22-0" class="reference"><a href="#cite_note-Jullien10-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> When disorder occurs it is at the Néel temperature.<sup id="cite_ref-Jullien10_22-1" class="reference"><a href="#cite_note-Jullien10-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>Listed below are the Néel temperatures of several materials:<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable sortable"> <tbody><tr> <th>Substance </th> <th>Néel temperature (<a href="/wiki/Kelvin" title="Kelvin">K</a>) </th></tr> <tr> <td><a href="/wiki/Manganese(II)_oxide" title="Manganese(II) oxide">MnO</a> </td> <td>116 </td></tr> <tr> <td><a href="/wiki/Manganese(II)_sulfide" title="Manganese(II) sulfide">MnS</a> </td> <td>160 </td></tr> <tr> <td><a href="/wiki/Manganese(II)_telluride" title="Manganese(II) telluride">MnTe</a> </td> <td>307 </td></tr> <tr> <td><a href="/wiki/Manganese(II)_fluoride" title="Manganese(II) fluoride">MnF<sub>2</sub></a> </td> <td>67 </td></tr> <tr> <td><a href="/wiki/Iron(II)_fluoride" title="Iron(II) fluoride">FeF<sub>2</sub></a> </td> <td>79 </td></tr> <tr> <td><a href="/wiki/Iron(II)_chloride" title="Iron(II) chloride">FeCl<sub>2</sub></a> </td> <td>24 </td></tr> <tr> <td><a href="/wiki/Iron(II)_iodide" title="Iron(II) iodide">FeI<sub>2</sub></a> </td> <td>9 </td></tr> <tr> <td><a href="/wiki/Iron(II)_oxide" title="Iron(II) oxide">FeO</a> </td> <td>198 </td></tr> <tr> <td><a href="/wiki/Iron_oxychloride" title="Iron oxychloride">FeOCl</a> </td> <td>80 </td></tr> <tr> <td><a href="/wiki/Chromium(II)_chloride" title="Chromium(II) chloride">CrCl<sub>2</sub></a> </td> <td>25 </td></tr> <tr> <td><a href="/wiki/Chromium(II)_iodide" title="Chromium(II) iodide">CrI<sub>2</sub></a> </td> <td>12 </td></tr> <tr> <td><a href="/wiki/Cobalt(II)_oxide" title="Cobalt(II) oxide">CoO</a> </td> <td>291 </td></tr> <tr> <td><a href="/wiki/Nickel(II)_chloride" title="Nickel(II) chloride">NiCl<sub>2</sub></a> </td> <td>50 </td></tr> <tr> <td><a href="/wiki/Nickel(II)_iodide" title="Nickel(II) iodide">NiI<sub>2</sub></a> </td> <td>75 </td></tr> <tr> <td><a href="/wiki/Nickel(II)_oxide" title="Nickel(II) oxide">NiO</a> </td> <td>525 </td></tr> <tr> <td>KFeO<sub>2</sub> </td> <td>983<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Chromium" title="Chromium">Cr</a> </td> <td>308 </td></tr> <tr> <td><a href="/wiki/Chromium(III)_oxide" title="Chromium(III) oxide">Cr<sub>2</sub>O<sub>3</sub></a> </td> <td>307 </td></tr> <tr> <td>Nd<sub>5</sub>Ge<sub>3</sub> </td> <td>50 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Curie–Weiss_law"><span id="Curie.E2.80.93Weiss_law"></span>Curie–Weiss law</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=9" title="Edit section: Curie–Weiss law"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Curie%E2%80%93Weiss_law" title="Curie–Weiss law">Curie–Weiss law</a></div> <p>The Curie–Weiss law is an adapted version of <a href="/wiki/Curie%27s_law" title="Curie's law">Curie's law</a>. </p><p>The Curie–Weiss law is a simple model derived from a <a href="/wiki/Mean-field_theory" title="Mean-field theory">mean-field</a> approximation, this means it works well for the materials temperature, <span class="texhtml mvar" style="font-style:italic;">T</span>, much greater than their corresponding Curie temperature, <span class="texhtml"><i>T</i><sub>C</sub></span>, i.e. <span class="texhtml"><i>T</i> ≫ <i>T</i><sub>C</sub></span>; it however fails to describe the <a href="/wiki/Magnetic_susceptibility" title="Magnetic susceptibility">magnetic susceptibility</a>, <span class="texhtml mvar" style="font-style:italic;">χ</span>, in the immediate vicinity of the Curie point because of correlations in the fluctuations of neighboring magnetic moments.<sup id="cite_ref-Jullien153_25-0" class="reference"><a href="#cite_note-Jullien153-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>Neither Curie's law nor the Curie–Weiss law holds for <span class="texhtml"><i>T</i> < <i>T</i><sub>C</sub></span>. </p><p>Curie's law for a paramagnetic material:<sup id="cite_ref-Hall205_26-0" class="reference"><a href="#cite_note-Hall205-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi ={\frac {M}{H}}={\frac {M\mu _{0}}{B}}={\frac {C}{T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>M</mi> <mi>H</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>M</mi> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mi>B</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>C</mi> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi ={\frac {M}{H}}={\frac {M\mu _{0}}{B}}={\frac {C}{T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d931b8948eb5377dc7cd1cd6a8a9bc885cd55860" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:22.366ex; height:5.343ex;" alt="{\displaystyle \chi ={\frac {M}{H}}={\frac {M\mu _{0}}{B}}={\frac {C}{T}}}"></span> </p> <table> <tbody><tr> <th>Definition</th> <th> </th></tr> <tr> <td><span class="texhtml mvar" style="font-style:italic;">χ</span></td> <td>the magnetic susceptibility; the influence of an applied <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> on a material </td></tr> <tr> <td><span class="texhtml mvar" style="font-style:italic;">M</span></td> <td>the <a href="/wiki/Magnetic_moments" class="mw-redirect" title="Magnetic moments">magnetic moments</a> per unit volume </td></tr> <tr> <td><span class="texhtml mvar" style="font-style:italic;">H</span></td> <td>the macroscopic magnetic field </td></tr> <tr> <td><span class="texhtml mvar" style="font-style:italic;">B</span></td> <td>the magnetic field </td></tr> <tr> <td><span class="texhtml mvar" style="font-style:italic;">C</span></td> <td>the material-specific <a href="/wiki/Curie_constant" class="mw-redirect" title="Curie constant">Curie constant</a> </td></tr></tbody></table> <p>The Curie constant <span class="texhtml mvar" style="font-style:italic;">C</span> is defined as<sup id="cite_ref-Levy201_27-0" class="reference"><a href="#cite_note-Levy201-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C={\frac {\mu _{0}\mu _{\mathrm {B} }^{2}}{3k_{\mathrm {B} }}}N_{\text{A}}g^{2}J(J+1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msubsup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mn>3</mn> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> </msub> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>J</mi> <mo stretchy="false">(</mo> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\frac {\mu _{0}\mu _{\mathrm {B} }^{2}}{3k_{\mathrm {B} }}}N_{\text{A}}g^{2}J(J+1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2db88a1a0b0ffa063b0a11a90b983dcebd2d9bf" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:25.213ex; height:6.509ex;" alt="{\displaystyle C={\frac {\mu _{0}\mu _{\mathrm {B} }^{2}}{3k_{\mathrm {B} }}}N_{\text{A}}g^{2}J(J+1)}"></span> </p> <table> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{\text{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{\text{A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/037f8d054f445451d8fee1b440cddba989e66ea1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.331ex; height:2.509ex;" alt="{\displaystyle N_{\text{A}}}"></span> </td> <td>the <a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a> </td></tr> <tr> <td><span class="texhtml"><i>µ</i><sub>0</sub></span></td> <td>the <a href="/wiki/Permeability_of_free_space" class="mw-redirect" title="Permeability of free space">permeability of free space</a>. Note: in <a href="/wiki/CGS" class="mw-redirect" title="CGS">CGS</a> units is taken to equal one.<sup id="cite_ref-Kittel1996_28-0" class="reference"><a href="#cite_note-Kittel1996-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><span class="texhtml mvar" style="font-style:italic;">g</span></td> <td>the <a href="/wiki/Land%C3%A9_g-factor" title="Landé g-factor">Landé <i>g</i>-factor</a> </td></tr> <tr> <td><span class="texhtml"><i>J</i>(<i>J</i> + 1)</span></td> <td>the eigenvalue for eigenstate J<sup>2</sup> for the stationary states within the incomplete atoms shells (electrons unpaired) </td></tr> <tr> <td><span class="texhtml"><i>µ</i><sub>B</sub></span></td> <td>the <a href="/wiki/Bohr_magneton" title="Bohr magneton">Bohr magneton</a> </td></tr> <tr> <td><span class="texhtml"><i>k</i><sub>B</sub></span></td> <td>the <a href="/wiki/Boltzmann_constant" title="Boltzmann constant">Boltzmann constant</a> </td></tr> <tr> <td>total magnetism</td> <td>is <span class="texhtml mvar" style="font-style:italic;">N</span> number of magnetic moments per unit volume<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="This isn't a variable used in the above and N is also undefined. If it's the Avogadro number then first it should be N_A not N, second it's per mole (unit amount), not per "unit volume" (October 2024)">clarification needed</span></a></i>]</sup> </td></tr></tbody></table> <p>The Curie–Weiss law is then derived from Curie's law to be: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi ={\frac {C}{T-T_{\mathrm {C} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>C</mi> <mrow> <mi>T</mi> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi ={\frac {C}{T-T_{\mathrm {C} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e99ecd6744f4ce93d808db10f2fcd5fdee05c040" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.643ex; height:5.843ex;" alt="{\displaystyle \chi ={\frac {C}{T-T_{\mathrm {C} }}}}"></span> </p><p>where: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{\mathrm {C} }={\frac {C\lambda }{\mu _{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>C</mi> <mi>λ</mi> </mrow> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\mathrm {C} }={\frac {C\lambda }{\mu _{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb249ddceeb9c2768c5178b536cec61a78f71ad8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.833ex; height:5.843ex;" alt="{\displaystyle T_{\mathrm {C} }={\frac {C\lambda }{\mu _{0}}}}"></span> </p><p><span class="texhtml mvar" style="font-style:italic;">λ</span> is the Weiss molecular field constant.<sup id="cite_ref-Levy201_27-1" class="reference"><a href="#cite_note-Levy201-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Myers_29-0" class="reference"><a href="#cite_note-Myers-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p><p>For full derivation see <a href="/wiki/Curie%E2%80%93Weiss_law" title="Curie–Weiss law">Curie–Weiss law</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Physics">Physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=10" title="Edit section: Physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Approaching_Curie_temperature_from_above">Approaching Curie temperature from above</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=11" title="Edit section: Approaching Curie temperature from above"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As the Curie–Weiss law is an approximation, a more accurate model is needed when the temperature, <span class="texhtml mvar" style="font-style:italic;">T</span>, approaches the material's Curie temperature, <span class="texhtml"><i>T</i><sub>C</sub></span>. </p><p>Magnetic susceptibility occurs above the Curie temperature. </p><p>An accurate model of critical behaviour for magnetic susceptibility with <a href="/wiki/Critical_exponent" title="Critical exponent">critical exponent</a> <span class="texhtml mvar" style="font-style:italic;">γ</span>: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi \sim {\frac {1}{(T-T_{\mathrm {C} })^{\gamma }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo>∼</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi \sim {\frac {1}{(T-T_{\mathrm {C} })^{\gamma }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0546f98d041f75d8fa69c242b7653fed23626dc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:15.577ex; height:6.009ex;" alt="{\displaystyle \chi \sim {\frac {1}{(T-T_{\mathrm {C} })^{\gamma }}}}"></span> </p><p>The critical exponent differs between materials and for the <a href="/wiki/Mean-field_theory" title="Mean-field theory">mean-field</a> model is taken as <span class="texhtml mvar" style="font-style:italic;">γ</span> = 1.<sup id="cite_ref-Hall227_30-0" class="reference"><a href="#cite_note-Hall227-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>As temperature is inversely proportional to magnetic susceptibility, when <span class="texhtml mvar" style="font-style:italic;">T</span> approaches <span class="texhtml"><i>T</i><sub>C</sub></span> the denominator tends to zero and the magnetic susceptibility approaches <a href="/wiki/Infinity" title="Infinity">infinity</a> allowing magnetism to occur. This is a spontaneous magnetism which is a property of ferromagnetic and ferrimagnetic materials.<sup id="cite_ref-Kittel_31-0" class="reference"><a href="#cite_note-Kittel-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Approaching_Curie_temperature_from_below">Approaching Curie temperature from below</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=12" title="Edit section: Approaching Curie temperature from below"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Magnetism depends on temperature and spontaneous magnetism occurs below the Curie temperature. An accurate model of critical behaviour for spontaneous magnetism with critical exponent <span class="texhtml mvar" style="font-style:italic;">β</span>: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M\sim (T_{\mathrm {C} }-T)^{\beta }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>∼</mo> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> </msub> <mo>−</mo> <mi>T</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>β</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M\sim (T_{\mathrm {C} }-T)^{\beta }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/994ba84db20fd6e0ca41f49514cce580dcf758b6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.777ex; height:3.176ex;" alt="{\displaystyle M\sim (T_{\mathrm {C} }-T)^{\beta }}"></span> </p><p>The critical exponent differs between materials and for the mean-field model as taken as <span class="texhtml mvar" style="font-style:italic;">β</span> = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> where <span class="texhtml"><i>T</i> ≪ <i>T</i><sub>C</sub></span>.<sup id="cite_ref-Hall227_30-1" class="reference"><a href="#cite_note-Hall227-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>The spontaneous magnetism approaches zero as the temperature increases towards the materials Curie temperature. </p> <div class="mw-heading mw-heading3"><h3 id="Approaching_absolute_zero_(0_kelvin)"><span id="Approaching_absolute_zero_.280_kelvin.29"></span>Approaching absolute zero (0 kelvin)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=13" title="Edit section: Approaching absolute zero (0 kelvin)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The spontaneous magnetism, occurring in ferromagnetic, ferrimagnetic, and antiferromagnetic materials, approaches zero as the temperature increases towards the material's Curie temperature. Spontaneous magnetism is at its maximum as the temperature approaches <a href="/wiki/Absolute_zero" title="Absolute zero">0 K</a>.<sup id="cite_ref-Hall4_33-0" class="reference"><a href="#cite_note-Hall4-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> That is, the magnetic moments are completely aligned and at their strongest magnitude of magnetism due to lack of thermal disturbance. </p><p>In paramagnetic materials thermal energy is sufficient to overcome the ordered alignments. As the temperature approaches 0 K, the <a href="/wiki/Entropy" title="Entropy">entropy</a> decreases to zero, that is, the disorder decreases and the material becomes ordered. This occurs without the presence of an applied magnetic field and obeys the <a href="/wiki/Third_law_of_thermodynamics" title="Third law of thermodynamics">third law of thermodynamics</a>.<sup id="cite_ref-Hall1_17-2" class="reference"><a href="#cite_note-Hall1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>Both Curie's law and the Curie–Weiss law fail as the temperature approaches 0 K. This is because they depend on the magnetic susceptibility, which only applies when the state is disordered.<sup id="cite_ref-Mendelssohn1_34-0" class="reference"><a href="#cite_note-Mendelssohn1-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p><a href="/w/index.php?title=Gadolinium_sulfate&action=edit&redlink=1" class="new" title="Gadolinium sulfate (page does not exist)">Gadolinium sulfate</a> continues to satisfy Curie's law at 1 K. Between 0 and 1 K the law fails to hold and a sudden change in the intrinsic structure occurs at the Curie temperature.<sup id="cite_ref-Mendelssohn2_35-0" class="reference"><a href="#cite_note-Mendelssohn2-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ising_model_of_phase_transitions">Ising model of phase transitions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=14" title="Edit section: Ising model of phase transitions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Ising_model" title="Ising model">Ising model</a> is mathematically based and can analyse the critical points of <a href="/wiki/Phase_transition" title="Phase transition">phase transitions</a> in ferromagnetic order due to spins of electrons having magnitudes of ±<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span>. The spins interact with their neighbouring <a href="/wiki/Dipole" title="Dipole">dipole</a> electrons in the structure and here the Ising model can predict their behaviour with each other.<sup id="cite_ref-Bertoldi_36-0" class="reference"><a href="#cite_note-Bertoldi-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Brout_37-0" class="reference"><a href="#cite_note-Brout-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p><p>This model is important for solving and understanding the concepts of phase transitions and hence solving the Curie temperature. As a result, many different dependencies that affect the Curie temperature can be analysed. </p><p>For example, the surface and bulk properties depend on the alignment and magnitude of spins and the Ising model can determine the effects of magnetism in this system. </p><p>One should note, in 1D the Curie (critical) temperature for a magnetic order phase transition is found to be at zero temperature, i.e. the magnetic order takes over only at <span class="texhtml mvar" style="font-style:italic;">T</span> = 0. In 2D, the critical temperature, e.g. a finite magnetization, can be calculated by solving the inequality: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M=(1-\sinh ^{-4}(2\beta J))^{1/8}>0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>sinh</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>4</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>β</mi> <mi>J</mi> <mo stretchy="false">)</mo> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>8</mn> </mrow> </msup> <mo>></mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M=(1-\sinh ^{-4}(2\beta J))^{1/8}>0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9a483794a98d1353f532129ac9024bf0a6eb102" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.215ex; height:3.343ex;" alt="{\displaystyle M=(1-\sinh ^{-4}(2\beta J))^{1/8}>0.}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Weiss_domains_and_surface_and_bulk_Curie_temperatures">Weiss domains and surface and bulk Curie temperatures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=15" title="Edit section: Weiss domains and surface and bulk Curie temperatures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Weiss_domains_in_a_ferromagnetic_material.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/e/e8/Weiss_domains_in_a_ferromagnetic_material.png/220px-Weiss_domains_in_a_ferromagnetic_material.png" decoding="async" width="220" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e8/Weiss_domains_in_a_ferromagnetic_material.png/330px-Weiss_domains_in_a_ferromagnetic_material.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e8/Weiss_domains_in_a_ferromagnetic_material.png/440px-Weiss_domains_in_a_ferromagnetic_material.png 2x" data-file-width="640" data-file-height="400" /></a><figcaption><b>Figure 3.</b> The Weiss domains in a ferromagnetic material; the magnetic moments are aligned in domains.</figcaption></figure> <p>Materials structures consist of intrinsic magnetic moments which are separated into domains called <a href="/wiki/Magnetic_domain" title="Magnetic domain">Weiss domains</a>.<sup id="cite_ref-Jullien160_38-0" class="reference"><a href="#cite_note-Jullien160-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> This can result in ferromagnetic materials having no spontaneous magnetism as domains could potentially balance each other out.<sup id="cite_ref-Jullien160_38-1" class="reference"><a href="#cite_note-Jullien160-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> The position of particles can therefore have different orientations around the surface than the main part (bulk) of the material. This property directly affects the Curie temperature as there can be a bulk Curie temperature <span class="texhtml"><i>T</i><sub>B</sub></span> and a different surface Curie temperature <span class="texhtml"><i>T</i><sub>S</sub></span> for a material.<sup id="cite_ref-Rau_39-0" class="reference"><a href="#cite_note-Rau-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>This allows for the surface Curie temperature to be ferromagnetic above the bulk Curie temperature when the main state is disordered, i.e. ordered and disordered states occur simultaneously.<sup id="cite_ref-Bertoldi_36-1" class="reference"><a href="#cite_note-Bertoldi-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>The surface and bulk properties can be predicted by the Ising model and electron capture spectroscopy can be used to detect the electron spins and hence the <a href="/wiki/Magnetic_moment" title="Magnetic moment">magnetic moments</a> on the surface of the material. An average total magnetism is taken from the bulk and surface temperatures to calculate the Curie temperature from the material, noting the bulk contributes more.<sup id="cite_ref-Bertoldi_36-2" class="reference"><a href="#cite_note-Bertoldi-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Skomski_40-0" class="reference"><a href="#cite_note-Skomski-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a> of an electron is either +<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><span class="texhtml mvar" style="font-style:italic;">ħ</span></span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> or −<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><span class="texhtml mvar" style="font-style:italic;">ħ</span></span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> due to it having a spin of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span>, which gives a specific size of magnetic moment to the electron; the <a href="/wiki/Bohr_magneton" title="Bohr magneton">Bohr magneton</a>.<sup id="cite_ref-Jullien138_41-0" class="reference"><a href="#cite_note-Jullien138-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> Electrons orbiting around the nucleus in a current loop create a magnetic field which depends on the Bohr magneton and <a href="/wiki/Magnetic_quantum_number" title="Magnetic quantum number">magnetic quantum number</a>.<sup id="cite_ref-Jullien138_41-1" class="reference"><a href="#cite_note-Jullien138-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> Therefore, the magnetic moments are related between angular and orbital momentum and affect each other. Angular momentum contributes twice as much to magnetic moments than orbital.<sup id="cite_ref-Hall1994_42-0" class="reference"><a href="#cite_note-Hall1994-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p><p>For <a href="/wiki/Terbium" title="Terbium">terbium</a> which is a <a href="/wiki/Rare-earth_element" title="Rare-earth element">rare-earth metal</a> and has a high orbital angular momentum the magnetic moment is strong enough to affect the order above its bulk temperatures. It is said to have a high <a href="/wiki/Anisotropy" title="Anisotropy">anisotropy</a> on the surface, that is it is highly directed in one orientation. It remains ferromagnetic on its surface above its Curie temperature (219 K) while its bulk becomes antiferromagnetic and then at higher temperatures its surface remains antiferromagnetic above its bulk Néel Temperature (230 K) before becoming completely disordered and paramagnetic with increasing temperature. The anisotropy in the bulk is different from its surface anisotropy just above these phase changes as the magnetic moments will be ordered differently or ordered in paramagnetic materials.<sup id="cite_ref-Rau_39-1" class="reference"><a href="#cite_note-Rau-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Changing_a_material's_Curie_temperature"><span id="Changing_a_material.27s_Curie_temperature"></span>Changing a material's Curie temperature</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=16" title="Edit section: Changing a material's Curie temperature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Composite_materials">Composite materials</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=17" title="Edit section: Composite materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Composite_material" title="Composite material">Composite materials</a>, that is, materials composed from other materials with different properties, can change the Curie temperature. For example, a composite which has <a href="/wiki/Silver" title="Silver">silver</a> in it can create spaces for oxygen molecules in bonding which decreases the Curie temperature<sup id="cite_ref-Hwang_44-0" class="reference"><a href="#cite_note-Hwang-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> as the crystal lattice will not be as compact. </p><p>The alignment of magnetic moments in the composite material affects the Curie temperature. If the material's moments are parallel with each other, the Curie temperature will increase and if perpendicular the Curie temperature will decrease<sup id="cite_ref-Hwang_44-1" class="reference"><a href="#cite_note-Hwang-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> as either more or less thermal energy will be needed to destroy the alignments. </p><p>Preparing composite materials through different temperatures can result in different final compositions which will have different Curie temperatures.<sup id="cite_ref-Paulsen_45-0" class="reference"><a href="#cite_note-Paulsen-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Doping_(semiconductor)" title="Doping (semiconductor)">Doping</a> a material can also affect its Curie temperature.<sup id="cite_ref-Paulsen_45-1" class="reference"><a href="#cite_note-Paulsen-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p><p>The density of nanocomposite materials changes the Curie temperature. <a href="/wiki/Nanocomposite" title="Nanocomposite">Nanocomposites</a> are compact structures on a nano-scale. The structure is built up of high and low bulk Curie temperatures, however will only have one mean-field Curie temperature. A higher density of lower bulk temperatures results in a lower mean-field Curie temperature, and a higher density of higher bulk temperature significantly increases the mean-field Curie temperature. In more than one dimension the Curie temperature begins to increase as the magnetic moments will need more thermal energy to overcome the ordered structure.<sup id="cite_ref-Skomski_40-1" class="reference"><a href="#cite_note-Skomski-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Particle_size">Particle size</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=18" title="Edit section: Particle size"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The size of particles in a material's crystal lattice changes the Curie temperature. Due to the small size of particles (<a href="/wiki/Nanoparticle" title="Nanoparticle">nanoparticles</a>) the fluctuations of electron spins become more prominent, which results in the Curie temperature drastically decreasing when the size of particles decreases, as the fluctuations cause disorder. The size of a particle also affects the <a href="/wiki/Anisotropy" title="Anisotropy">anisotropy</a> causing alignment to become less stable and thus lead to disorder in magnetic moments.<sup id="cite_ref-Bertoldi_36-3" class="reference"><a href="#cite_note-Bertoldi-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Lopez-Dominguez_46-0" class="reference"><a href="#cite_note-Lopez-Dominguez-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p><p>The extreme of this is <a href="/wiki/Superparamagnetism" title="Superparamagnetism">superparamagnetism</a> which only occurs in small ferromagnetic particles. In this phenomenon, fluctuations are very influential causing magnetic moments to change direction randomly and thus create disorder. </p><p>The Curie temperature of nanoparticles is also affected by the <a href="/wiki/Bravais_lattice" title="Bravais lattice">crystal lattice</a> structure: <a href="/wiki/Cubic_crystal_system" title="Cubic crystal system">body-centred cubic</a> (bcc), <a href="/wiki/Cubic_crystal_system" title="Cubic crystal system">face-centred cubic</a> (fcc), and a <a href="/wiki/Hexagonal_crystal_family" title="Hexagonal crystal family">hexagonal</a> structure (hcp) all have different Curie temperatures due to magnetic moments reacting to their neighbouring electron spins. fcc and hcp have tighter structures and as a results have higher Curie temperatures than bcc as the magnetic moments have stronger effects when closer together.<sup id="cite_ref-Bertoldi_36-4" class="reference"><a href="#cite_note-Bertoldi-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> This is known as the <a href="/wiki/Coordination_number" title="Coordination number">coordination number</a> which is the number of nearest neighbouring particles in a structure. This indicates a lower coordination number at the surface of a material than the bulk which leads to the surface becoming less significant when the temperature is approaching the Curie temperature. In smaller systems the coordination number for the surface is more significant and the magnetic moments have a stronger effect on the system.<sup id="cite_ref-Bertoldi_36-5" class="reference"><a href="#cite_note-Bertoldi-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>Although fluctuations in particles can be minuscule, they are heavily dependent on the structure of crystal lattices as they react with their nearest neighbouring particles. Fluctuations are also affected by the exchange interaction<sup id="cite_ref-Lopez-Dominguez_46-1" class="reference"><a href="#cite_note-Lopez-Dominguez-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> as parallel facing magnetic moments are favoured and therefore have less disturbance and disorder, therefore a tighter structure influences a stronger magnetism and therefore a higher Curie temperature. </p> <div class="mw-heading mw-heading4"><h4 id="Pressure">Pressure</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=19" title="Edit section: Pressure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pressure changes a material's Curie temperature. Increasing <a href="/wiki/Pressure" title="Pressure">pressure</a> on the <a href="/wiki/Bravais_lattice" title="Bravais lattice">crystal lattice</a> decreases the volume of the system. Pressure directly affects the <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> in particles as movement increases causing the vibrations to disrupt the order of magnetic moments. This is similar to temperature as it also increases the kinetic energy of particles and destroys the order of magnetic moments and magnetism.<sup id="cite_ref-Bose_47-0" class="reference"><a href="#cite_note-Bose-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>Pressure also affects the <a href="/wiki/Density_of_states" title="Density of states">density of states</a> (DOS).<sup id="cite_ref-Bose_47-1" class="reference"><a href="#cite_note-Bose-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> Here the DOS decreases causing the number of electrons available to the system to decrease. This leads to the number of magnetic moments decreasing as they depend on electron spins. It would be expected because of this that the Curie temperature would decrease; however, it increases. This is the result of the <a href="/wiki/Exchange_interaction" title="Exchange interaction">exchange interaction</a>. The exchange interaction favours the aligned parallel magnetic moments due to electrons being unable to occupy the same space in time<sup id="cite_ref-Hall1_17-3" class="reference"><a href="#cite_note-Hall1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> and as this is increased due to the volume decreasing the Curie temperature increases with pressure. The Curie temperature is made up of a combination of dependencies on kinetic energy and the DOS.<sup id="cite_ref-Bose_47-2" class="reference"><a href="#cite_note-Bose-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>The concentration of particles also affects the Curie temperature when pressure is being applied and can result in a decrease in Curie temperature when the concentration is above a certain percent.<sup id="cite_ref-Bose_47-3" class="reference"><a href="#cite_note-Bose-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Orbital_ordering">Orbital ordering</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=20" title="Edit section: Orbital ordering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Atomic_orbital" title="Atomic orbital">Orbital ordering</a> changes the Curie temperature of a material. Orbital ordering can be controlled through applied <a href="/wiki/Deformation_(physics)" title="Deformation (physics)">strains</a>.<sup id="cite_ref-Sadoc_48-0" class="reference"><a href="#cite_note-Sadoc-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> This is a function that determines the wave of a single electron or paired electrons inside the material. Having control over the <a href="/wiki/Probability" title="Probability">probability</a> of where the electron will be allows the Curie temperature to be altered. For example, the <a href="/wiki/Delocalized_electron" title="Delocalized electron">delocalised</a> electrons can be moved onto the same <a href="/wiki/Lattice_plane" title="Lattice plane">plane</a> by applied strains within the crystal lattice.<sup id="cite_ref-Sadoc_48-1" class="reference"><a href="#cite_note-Sadoc-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p><p>The Curie temperature is seen to increase greatly due to electrons being packed together in the same plane, they are forced to align due to the <a href="/wiki/Exchange_interaction" title="Exchange interaction">exchange interaction</a> and thus increases the strength of the magnetic moments which prevents thermal disorder at lower temperatures. </p> <div class="mw-heading mw-heading2"><h2 id="Curie_temperature_in_ferroelectric_materials">Curie temperature in ferroelectric materials</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=21" title="Edit section: Curie temperature in ferroelectric materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In analogy to ferromagnetic and paramagnetic materials, the term Curie temperature (<span class="texhtml"><i>T</i><sub>C</sub></span>) is also applied to the temperature at which a <a href="/wiki/Ferroelectricity" title="Ferroelectricity">ferroelectric</a> material transitions to being <a href="/wiki/Dielectric" title="Dielectric">paraelectric</a>. Hence, <span class="texhtml"><i>T</i><sub>C</sub></span> is the temperature where ferroelectric materials lose their spontaneous polarisation as a first or second order phase change occurs. In case of a second order transition, the Curie Weiss temperature <span class="texhtml"><i>T</i><sub>0</sub></span> which defines the maximum of the dielectric constant is equal to the Curie temperature. However, the Curie temperature can be 10 K higher than <span class="texhtml"><i>T</i><sub>0</sub></span> in case of a first order transition.<sup id="cite_ref-Webster_49-0" class="reference"><a href="#cite_note-Webster-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1273380762/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:204px;max-width:204px"><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Ferroelectric_polarisation.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Ferroelectric_polarisation.svg/200px-Ferroelectric_polarisation.svg.png" decoding="async" width="200" height="201" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Ferroelectric_polarisation.svg/300px-Ferroelectric_polarisation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Ferroelectric_polarisation.svg/400px-Ferroelectric_polarisation.svg.png 2x" data-file-width="160" data-file-height="161" /></a></span></div><div class="thumbcaption"><b>Figure 4.</b> (Below <span class="texhtml"><i>T</i><sub>0</sub></span>) Ferroelectric polarisation <span class="texhtml"><b>P</b></span> in an applied electric field <span class="texhtml"><b>E</b></span></div></div></div><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Paraelectric_polarisation.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Paraelectric_polarisation.svg/200px-Paraelectric_polarisation.svg.png" decoding="async" width="200" height="201" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Paraelectric_polarisation.svg/300px-Paraelectric_polarisation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/27/Paraelectric_polarisation.svg/400px-Paraelectric_polarisation.svg.png 2x" data-file-width="160" data-file-height="161" /></a></span></div><div class="thumbcaption"><b>Figure 5.</b> (Above <span class="texhtml"><i>T</i><sub>0</sub></span>) Dielectric polarisation <span class="texhtml"><b>P</b></span> in an applied electric field <span class="texhtml"><b>E</b></span></div></div></div></div></div> <table> <tbody><tr> <th>Below <span class="texhtml"><i>T</i><sub>C</sub></span></th> <th>Above <span class="texhtml"><i>T</i><sub>C</sub></span><sup id="cite_ref-Kovetz_50-0" class="reference"><a href="#cite_note-Kovetz-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </th></tr> <tr> <td>Ferroelectric</td> <td>↔ Dielectric (paraelectric) </td></tr> <tr> <td>Antiferroelectric</td> <td>↔ Dielectric (paraelectric) </td></tr> <tr> <td>Ferrielectric</td> <td>↔ Dielectric (paraelectric) </td></tr> <tr> <td>Helielectric</td> <td>↔ Dielectric (paraelectric) </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Ferroelectric_and_dielectric">Ferroelectric and dielectric</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=22" title="Edit section: Ferroelectric and dielectric"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Materials are only ferroelectric below their corresponding transition temperature <span class="texhtml"><i>T</i><sub>0</sub></span>.<sup id="cite_ref-Myers404_51-0" class="reference"><a href="#cite_note-Myers404-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> Ferroelectric materials are all <a href="/wiki/Pyroelectricity" title="Pyroelectricity">pyroelectric</a> and therefore have a spontaneous electric polarisation as the structures are unsymmetrical. </p><p>Ferroelectric materials' polarization is subject to <a href="/wiki/Hysteresis" title="Hysteresis">hysteresis</a> (Figure 4); that is they are dependent on their past state as well as their current state. As an electric field is applied the dipoles are forced to align and polarisation is created, when the electric field is removed polarisation remains. The hysteresis loop depends on temperature and as a result as the temperature is increased and reaches <span class="texhtml"><i>T</i><sub>0</sub></span> the two curves become one curve as shown in the dielectric polarisation (Figure 5).<sup id="cite_ref-Pascoe1_52-0" class="reference"><a href="#cite_note-Pascoe1-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Relative_permittivity">Relative permittivity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=23" title="Edit section: Relative permittivity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A modified version of the Curie–Weiss law applies to the dielectric constant, also known as the <a href="/wiki/Relative_permittivity" title="Relative permittivity">relative permittivity</a>:<sup id="cite_ref-Webster_49-1" class="reference"><a href="#cite_note-Webster-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon =\epsilon _{0}+{\frac {C}{T-T_{\mathrm {0} }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϵ</mi> <mo>=</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>C</mi> <mrow> <mi>T</mi> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon =\epsilon _{0}+{\frac {C}{T-T_{\mathrm {0} }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5a6698f186dab9aeb3f8b347e94b700dd264198" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.253ex; height:5.843ex;" alt="{\displaystyle \epsilon =\epsilon _{0}+{\frac {C}{T-T_{\mathrm {0} }}}.}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=24" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A heat-induced ferromagnetic-paramagnetic transition is used in <a href="/wiki/Magneto-optical_drive" title="Magneto-optical drive">magneto-optical</a> storage media for erasing and writing of new data. Famous examples include the <a href="/wiki/MiniDisc" title="MiniDisc">Sony Minidisc</a> format as well as the now-obsolete <a href="/wiki/CD-RW#CD-MO" title="CD-RW">CD-MO</a> format. Curie point electro-magnets have been proposed and tested for actuation mechanisms in passive safety systems of <a href="/wiki/Breeder_reactor" title="Breeder reactor">fast breeder reactors</a>, where <a href="/wiki/Control_rod" title="Control rod">control rods</a> are dropped into the reactor core if the actuation mechanism heats up beyond the material's Curie point.<sup id="cite_ref-Takamatsu_54-0" class="reference"><a href="#cite_note-Takamatsu-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> Other uses include temperature control in <a href="/wiki/Soldering_iron" title="Soldering iron">soldering irons</a><sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> and stabilizing the magnetic field of <a href="/wiki/Tachometer" title="Tachometer">tachometer</a> generators against temperature variation.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=25" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Ferroelectricity" title="Ferroelectricity">Ferroelectricity</a> – Property of materials which both possess and are affected by electric fields</li> <li><a href="/wiki/Curie%27s_law" title="Curie's law">Curie's law</a> – Relation of magnetization to applied magnetic field and temperature</li> <li><a href="/wiki/Hopkinson_effect" title="Hopkinson effect">Hopkinson effect</a> – Feature of ferromagnetic or ferrimagnetic materials</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=26" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 20em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a href="#CITEREFPierre_Curie_–_Biography">Pierre Curie – Biography</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a href="#CITEREFBuschow2001">Buschow 2001</a>, p5021, table 1</span> </li> <li id="cite_note-table_3.1-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-table_3.1_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFJullienGuinier1989">Jullien & Guinier 1989</a>, p. 155</span> </li> <li id="cite_note-Kitteltable-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kitteltable_4-0">^</a></b></span> <span class="reference-text"> <a href="#CITEREFKittel1986">Kittel 1986</a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFNighLegvoldSpedding1963" class="citation journal cs1">Nigh, H. E.; Legvold, S.; Spedding, F. H. (1 November 1963). <a rel="nofollow" class="external text" href="https://link.aps.org/doi/10.1103/PhysRev.132.1092">"Magnetization and Electrical Resistivity of Gadolinium Single Crystals"</a>. <i>Physical Review</i>. <b>132</b> (3): <span class="nowrap">1092–</span>1097. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.132.1092">10.1103/PhysRev.132.1092</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-899X">0031-899X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Magnetization+and+Electrical+Resistivity+of+Gadolinium+Single+Crystals&rft.volume=132&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1092-%3C%2Fspan%3E1097&rft.date=1963-11-01&rft_id=info%3Adoi%2F10.1103%2FPhysRev.132.1092&rft.issn=0031-899X&rft.aulast=Nigh&rft.aufirst=H.+E.&rft.au=Legvold%2C+S.&rft.au=Spedding%2C+F.+H.&rft_id=https%3A%2F%2Flink.aps.org%2Fdoi%2F10.1103%2FPhysRev.132.1092&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></span> </li> <li id="cite_note-Hall-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hall_6-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHallHook1994">Hall & Hook 1994</a>, p. 200</span> </li> <li id="cite_note-Jullien136-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Jullien136_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFJullienGuinier1989">Jullien & Guinier 1989</a>, pp. 136–38</span> </li> <li id="cite_note-Ibach-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Ibach_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Ibach_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFIbachLüth2009">Ibach & Lüth 2009</a></span> </li> <li id="cite_note-Levy-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-Levy_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Levy_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFLevy1968">Levy 1968</a>, pp. 236–39</span> </li> <li id="cite_note-Dekker1-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Dekker1_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDekker1958">Dekker 1958</a>, pp. 217–20</span> </li> <li id="cite_note-Levy4-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Levy4_11-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFLevy1968">Levy 1968</a></span> </li> <li id="cite_note-Fan-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-Fan_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Fan_12-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Fan_12-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFFan1987">Fan 1987</a>, pp. 164–65</span> </li> <li id="cite_note-Dekker-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Dekker_13-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDekker1958">Dekker 1958</a>, pp. 454–55</span> </li> <li id="cite_note-Mendelssohn3-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Mendelssohn3_14-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMendelssohn1977">Mendelssohn 1977</a>, p. 162</span> </li> <li id="cite_note-Levy1-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Levy1_15-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFLevy1968">Levy 1968</a>, pp. 198–202</span> </li> <li id="cite_note-Cusack-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-Cusack_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Cusack_16-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Cusack_16-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFCusack1958">Cusack 1958</a>, p. 269</span> </li> <li id="cite_note-Hall1-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hall1_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hall1_17-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Hall1_17-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Hall1_17-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFHallHook1994">Hall & Hook 1994</a>, pp. 220–21</span> </li> <li id="cite_note-Palmer-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Palmer_18-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFPalmer2007">Palmer 2007</a></span> </li> <li id="cite_note-Hall3-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hall3_19-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHallHook1994">Hall & Hook 1994</a>, p. 220</span> </li> <li id="cite_note-Jullien158-20"><span class="mw-cite-backlink">^ <a href="#cite_ref-Jullien158_20-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Jullien158_20-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Jullien158_20-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Jullien158_20-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFJullienGuinier1989">Jullien & Guinier 1989</a>, pp. 158–59</span> </li> <li id="cite_note-spaldin-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-spaldin_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSpaldin2006" class="citation 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href="https://doi.org/10.1246%2Fbcsj.46.79">"Mössbauer Study of the Thermal Decomposition Products of K2FeO4"</a>. <i>Bulletin of the Chemical Society of Japan</i>. <b>46</b> (1): <span class="nowrap">79–</span>82. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1246%2Fbcsj.46.79">10.1246/bcsj.46.79</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+Chemical+Society+of+Japan&rft.atitle=M%C3%B6ssbauer+Study+of+the+Thermal+Decomposition+Products+of+K2FeO4&rft.volume=46&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E79-%3C%2Fspan%3E82&rft.date=1973&rft_id=info%3Adoi%2F10.1246%2Fbcsj.46.79&rft.aulast=Ichida&rft.aufirst=Toshio&rft_id=https%3A%2F%2Fdoi.org%2F10.1246%252Fbcsj.46.79&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" 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title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Nuclear+Science+and+Technology&rft.atitle=Demonstration+of+Control+Rod+Holding+Stability+of+the+Self+Actuated+Shutdown+System+in+Joyo+for+Enhancement+of+Fast+Reactor+Inherent+Safety&rft.volume=44&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E511-%3C%2Fspan%3E517&rft.date=2007&rft_id=info%3Adoi%2F10.1080%2F18811248.2007.9711316&rft_id=info%3Abibcode%2F2007JNST...44..511T&rft.au=Takamatsu&rft_id=https%3A%2F%2Fdoi.org%2F10.1080%252F18811248.2007.9711316&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text"><a href="#CITEREFTMT-9000S">TMT-9000S</a></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><a href="#CITEREFPallàs-ArenyWebster2001">Pallàs-Areny & Webster 2001</a>, pp. 262–63</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=27" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBuschow2001" class="citation book cs1">Buschow, K. 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Cambridge: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521886697" title="Special:BookSources/9780521886697"><bdi>9780521886697</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Magnetic+Materials%3A+Fundamentals+and+Applications&rft.place=Cambridge&rft.edition=2nd&rft.pub=Cambridge+University+Press&rft.date=2010&rft.isbn=9780521886697&rft.aulast=Spaldin&rft.aufirst=Nicola+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIbachLüth2009" class="citation book cs1">Ibach, Harald; Lüth, Hans (2009). <i>Solid-State Physics: An Introduction to Principles of Materials Science</i> (4th ed.). Berlin: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783540938033" title="Special:BookSources/9783540938033"><bdi>9783540938033</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Solid-State+Physics%3A+An+Introduction+to+Principles+of+Materials+Science&rft.place=Berlin&rft.edition=4th&rft.pub=Springer&rft.date=2009&rft.isbn=9783540938033&rft.aulast=Ibach&rft.aufirst=Harald&rft.au=L%C3%BCth%2C+Hans&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLevy1968" class="citation book cs1">Levy, Robert A. 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Academic Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0124457508" title="Special:BookSources/978-0124457508"><bdi>978-0124457508</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+Solid+State+Physics&rft.pub=Academic+Press&rft.date=1968&rft.isbn=978-0124457508&rft.aulast=Levy&rft.aufirst=Robert+A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fprinciplesofsoli00levy&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFan1987" class="citation book cs1">Fan, H. Y. (1987). <i>Elements of Solid State Physics</i>. Wiley-Interscience. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780471859871" title="Special:BookSources/9780471859871"><bdi>9780471859871</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elements+of+Solid+State+Physics&rft.pub=Wiley-Interscience&rft.date=1987&rft.isbn=9780471859871&rft.aulast=Fan&rft.aufirst=H.+Y.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDekker1958" class="citation book cs1">Dekker, Adrianus J. (1958). <i>Solid State Physics</i>. Macmillan. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780333106235" title="Special:BookSources/9780333106235"><bdi>9780333106235</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Solid+State+Physics&rft.pub=Macmillan&rft.date=1958&rft.isbn=9780333106235&rft.aulast=Dekker&rft.aufirst=Adrianus+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCusack1958" class="citation book cs1">Cusack, N. (1958). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/electricalmagnet0096cusa"><i>The Electrical and Magnetic Properties of Solids</i></a></span>. Longmans, Green.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Electrical+and+Magnetic+Properties+of+Solids&rft.pub=Longmans%2C+Green&rft.date=1958&rft.aulast=Cusack&rft.aufirst=N.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felectricalmagnet0096cusa&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHallHook1994" class="citation book cs1">Hall, J. R.; Hook, H. E. (1994). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/candidevo00volt"><i>Solid State Physics</i></a></span> (2nd ed.). Chichester: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0471928054" title="Special:BookSources/0471928054"><bdi>0471928054</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Solid+State+Physics&rft.place=Chichester&rft.edition=2nd&rft.pub=Wiley&rft.date=1994&rft.isbn=0471928054&rft.aulast=Hall&rft.aufirst=J.+R.&rft.au=Hook%2C+H.+E.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcandidevo00volt&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJullienGuinier1989" class="citation book cs1">Jullien, André; Guinier, Rémi (1989). <i>The Solid State from Superconductors to Superalloys</i>. Oxford: Oxford Univ. 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London: Taylor and Francis. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0850661196" title="Special:BookSources/0850661196"><bdi>0850661196</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Quest+for+Absolute+Zero%3A+The+Meaning+of+Low+Temperature+Physics&rft.place=London&rft.edition=2nd&rft.pub=Taylor+and+Francis&rft.date=1977&rft.isbn=0850661196&rft.aulast=Mendelssohn&rft.aufirst=K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMyers1997" class="citation book cs1">Myers, H. P. (1997). <i>Introductory Solid State Physics</i> (2nd ed.). London: Taylor & Francis. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0748406603" title="Special:BookSources/0748406603"><bdi>0748406603</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introductory+Solid+State+Physics&rft.place=London&rft.edition=2nd&rft.pub=Taylor+%26+Francis&rft.date=1997&rft.isbn=0748406603&rft.aulast=Myers&rft.aufirst=H.+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKittel1996" class="citation book cs1">Kittel, Charles (1996). <i>Introduction to Solid State Physics</i> (7th ed.). 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Nobel Media AB. 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">14 March</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Nobelprize.org&rft.atitle=Pierre+Curie+%E2%80%93+Biography&rft.date=2014&rft_id=https%3A%2F%2Fwww.nobelprize.org%2Fnobel_prizes%2Fphysics%2Flaureates%2F1903%2Fpierre-curie-bio.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTMT-9000S" class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.thermaltronics.com/tmt-9000s.php">"TMT-9000S Soldering and Rework Station"</a>. <i>thermaltronics.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">13 January</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=thermaltronics.com&rft.atitle=TMT-9000S+Soldering+and+Rework+Station&rft_id=http%3A%2F%2Fwww.thermaltronics.com%2Ftmt-9000s.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACurie+temperature" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curie_temperature&action=edit&section=28" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=X8ZHQQUusGo"><i>Ferromagnetic Curie Point</i></a>. Video by <a href="/wiki/Walter_Lewin" title="Walter Lewin">Walter Lewin</a>, <a href="/wiki/M.I.T." class="mw-redirect" title="M.I.T.">M.I.T.</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output 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class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 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title="Marie Curie"> Marie</a> and <a href="/wiki/Pierre_Curie" title="Pierre Curie"> Pierre</a> Curie</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Discoveries</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Curie%27s_law" title="Curie's law">Curie's law</a></li> <li><a href="/wiki/Curie%E2%80%93Weiss_law" title="Curie–Weiss law">Curie–Weiss law</a></li> <li><a class="mw-selflink selflink">Curie temperature</a></li> <li><a href="/wiki/Mean-field_theory" title="Mean-field theory">Mean-field theory</a></li> <li><a href="/wiki/Piezoelectricity" title="Piezoelectricity">Piezoelectricity</a></li> <li><a href="/wiki/Polonium" title="Polonium">Polonium</a></li> <li><a href="/wiki/Radioactive_decay" title="Radioactive decay">Radioactivity</a></li> <li><a href="/wiki/Radium" title="Radium">Radium</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Publications</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Curie%27s_principle" title="Curie's principle">Curie's principle</a></li> <li><i><a href="/wiki/Treatise_on_Radioactivity" title="Treatise on Radioactivity">Treatise on Radioactivity</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Museums</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Maria_Sk%C5%82odowska-Curie_Museum" title="Maria Skłodowska-Curie Museum">Maria Skłodowska-Curie Museum</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Curie_family" title="Curie family">Family</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ir%C3%A8ne_Joliot-Curie" title="Irène Joliot-Curie">Irène Joliot-Curie</a> (daughter)</li> <li><a href="/wiki/%C3%88ve_Curie" title="Ève Curie">Ève Curie</a> (daughter)</li> <li><a href="/wiki/H%C3%A9l%C3%A8ne_Langevin-Joliot" title="Hélène Langevin-Joliot">Hélène Langevin-Joliot</a> (granddaughter)</li> <li><a href="/wiki/Pierre_Joliot" title="Pierre Joliot">Pierre Joliot</a> (grandson)</li> <li><a href="/wiki/Paul-Jacques_Curie" title="Paul-Jacques Curie">Paul-Jacques Curie</a> (Pierre's brother)</li> <li><a href="/wiki/Fr%C3%A9d%C3%A9ric_Joliot-Curie" title="Frédéric Joliot-Curie">Frédéric Joliot-Curie</a> (son-in-law)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Namesakes</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Curie_Institute_(Paris)" title="Curie Institute (Paris)">Curie Institute</a></li> <li><a href="/wiki/Curie_(unit)" title="Curie (unit)">Curie</a></li> <li><a href="/wiki/Curium" title="Curium">Curium</a></li> <li><a href="/wiki/IEEE_Marie_Sklodowska-Curie_Award" title="IEEE Marie Sklodowska-Curie Award">IEEE Marie Sklodowska-Curie Award</a></li> <li><a href="/wiki/Marie_Curie_Medal" title="Marie Curie Medal">Marie Curie Medal</a></li> <li><a href="/wiki/Maria_Sk%C5%82odowska-Curie_Bridge,_Warsaw" title="Maria Skłodowska-Curie Bridge, Warsaw">Maria Skłodowska-Curie Bridge</a></li> <li><a href="/wiki/Maria_Sk%C5%82odowska-Curie_Park" title="Maria Skłodowska-Curie Park">Maria Skłodowska-Curie Park</a></li> <li><a href="/wiki/Maria_Curie-Sk%C5%82odowska_University" title="Maria Curie-Skłodowska University">Maria Curie-Skłodowska University</a></li> <li><a href="/wiki/Pierre_and_Marie_Curie_University" title="Pierre and Marie Curie University">Pierre and Marie Curie University</a></li> <li><a href="/wiki/Maria_Sk%C5%82odowska-Curie_National_Research_Institute_of_Oncology" title="Maria Skłodowska-Curie National Research Institute of Oncology">Maria Skłodowska-Curie National Research Institute of Oncology</a></li> <li><a href="/wiki/Curie_Island" title="Curie Island">Curie Island</a></li> <li><a href="/wiki/7000_Curie" class="mw-redirect" title="7000 Curie">7000 Curie</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Depictions</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Maria_Sk%C5%82odowska-Curie_Monument_(Lublin)" title="Maria Skłodowska-Curie Monument (Lublin)">Maria Skłodowska-Curie Monument in Lublin</a></li> <li><a href="/wiki/Maria_Sk%C5%82odowska-Curie_Monument_(Downtown,_Warsaw)" title="Maria Skłodowska-Curie Monument (Downtown, Warsaw)">Maria Skłodowska-Curie Monument in Warsaw (Downtown)</a></li> <li><a href="/wiki/Maria_Sk%C5%82odowska-Curie_Monument_(Ochota)" title="Maria Skłodowska-Curie Monument (Ochota)">Maria Skłodowska-Curie Monument in Warsaw (Ochota)</a></li> <li><i><a href="/wiki/Marie_Curie_Gargoyle" title="Marie Curie Gargoyle">Marie Curie Gargoyle</a></i></li> <li><i><a href="/wiki/Maria_Sk%C5%82odowska-Curie_Medallion" title="Maria Skłodowska-Curie Medallion">Maria Skłodowska-Curie Medallion</a></i></li> <li><i><a href="/wiki/Madame_Curie_(film)" title="Madame Curie (film)">Madame Curie</a></i> (1943 film)</li> <li><i><a href="/wiki/Les_Palmes_de_M._Schutz" title="Les Palmes de M. Schutz">Les Palmes de M. Schutz</a></i> (1997 film)</li> <li><i><a href="/wiki/Marie_Curie,_une_femme_sur_le_front" title="Marie Curie, une femme sur le front">Marie Curie, une femme sur le front</a></i> (2014 film)</li> <li><i><a href="/wiki/Marie_Curie:_The_Courage_of_Knowledge" title="Marie Curie: The Courage of Knowledge">Marie Curie: The Courage of Knowledge</a></i> (2016 film)</li> <li><i><a href="/wiki/Radioactive_(film)" title="Radioactive (film)">Radioactive</a></i> (2019 film)</li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox390" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q191073#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4148403-4">Germany</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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