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sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <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">Type of magnetic state</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Altermagnetism1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Altermagnetism1.jpg/220px-Altermagnetism1.jpg" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Altermagnetism1.jpg/330px-Altermagnetism1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Altermagnetism1.jpg/440px-Altermagnetism1.jpg 2x" data-file-width="922" data-file-height="739" /></a><figcaption>An example of an altermagnetic ordering, with the direction of the spins and the spatial orientation of the atoms alternating on the neighbouring sites in the crystal.</figcaption></figure> <p>In <a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">condensed matter physics</a>, <b>altermagnetism</b> is a type of persistent <a href="/wiki/Magnetism" title="Magnetism">magnetic state</a> in <a href="/wiki/Crystal#Defects,_impurities,_and_twinning" title="Crystal">ideal crystals</a>.<sup id="cite_ref-punchline_1-0" class="reference"><a href="#cite_note-punchline-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-mazin_2-0" class="reference"><a href="#cite_note-mazin-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-mazin_smejkal_3-0" class="reference"><a href="#cite_note-mazin_smejkal-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-savitsky_science_5-0" class="reference"><a href="#cite_note-savitsky_science-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Altermagnetic structures are collinear and crystal-symmetry compensated, resulting in zero net magnetisation.<sup id="cite_ref-punchline_1-1" class="reference"><a href="#cite_note-punchline-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-savitsky_science_5-1" class="reference"><a href="#cite_note-savitsky_science-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_landscape_6-0" class="reference"><a href="#cite_note-smejkal_landscape-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_symm_7-0" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Unlike in an ordinary collinear <a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">antiferromagnet</a>, another magnetic state with zero net magnetization, the <a href="/wiki/Electronic_band_structure" title="Electronic band structure">electronic bands</a> in an altermagnet are not <a href="/wiki/Kramers_theorem" class="mw-redirect" title="Kramers theorem">Kramers degenerate</a>, but instead depend on the wavevector in a spin-dependent way.<sup id="cite_ref-punchline_1-2" class="reference"><a href="#cite_note-punchline-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Related to this feature, key experimental observations were published in 2024.<sup id="cite_ref-krempasky2024_8-0" class="reference"><a href="#cite_note-krempasky2024-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-fedchenko_9-0" class="reference"><a href="#cite_note-fedchenko-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> It has been speculated that altermagnetism may have applications in the field of <a href="/wiki/Spintronics" title="Spintronics">spintronics</a>.<sup id="cite_ref-smejkal_landscape_6-1" class="reference"><a href="#cite_note-smejkal_landscape-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-scidaily_10-0" class="reference"><a href="#cite_note-scidaily-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Crystal_structure_and_symmetry">Crystal structure and symmetry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Altermagnetism&action=edit&section=1" title="Edit section: Crystal structure and symmetry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In altermagnetic materials, atoms form a regular pattern with alternating spin and spatial orientation at adjacent magnetic sites in the crystal.<sup id="cite_ref-savitsky_science_5-2" class="reference"><a href="#cite_note-savitsky_science-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_symm_7-1" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Atoms with opposite <a href="/wiki/Magnetic_moment" title="Magnetic moment">magnetic moment</a> are in altermagnets coupled by crystal rotation or mirror symmetry.<sup id="cite_ref-punchline_1-3" class="reference"><a href="#cite_note-punchline-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-savitsky_science_5-3" class="reference"><a href="#cite_note-savitsky_science-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_landscape_6-2" class="reference"><a href="#cite_note-smejkal_landscape-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_symm_7-2" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-krempasky2024_8-1" class="reference"><a href="#cite_note-krempasky2024-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-fedchenko_9-1" class="reference"><a href="#cite_note-fedchenko-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The spatial orientation of magnetic atoms may originate from the surrounding cages of non-magnetic atoms.<sup id="cite_ref-smejkal_symm_7-3" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_sciadv_11-0" class="reference"><a href="#cite_note-smejkal_sciadv-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The opposite spin sublattices in altermagnetic <a href="/wiki/Manganese(II)_telluride" title="Manganese(II) telluride">manganese telluride</a> (MnTe) are related by spin rotation combined with six-fold crystal rotation and half-unit cell translation.<sup id="cite_ref-smejkal_symm_7-4" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-krempasky2024_8-2" class="reference"><a href="#cite_note-krempasky2024-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> In altermagnetic <a href="/wiki/Ruthenium(IV)_oxide" title="Ruthenium(IV) oxide">ruthenium dioxide</a> (RuO<sub>2</sub>), the opposite spin sublattices are related by four-fold crystal rotation.<sup id="cite_ref-smejkal_symm_7-5" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-fedchenko_9-2" class="reference"><a href="#cite_note-fedchenko-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Altermagnetism2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Altermagnetism2.jpg/500px-Altermagnetism2.jpg" decoding="async" width="500" height="254" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Altermagnetism2.jpg/750px-Altermagnetism2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Altermagnetism2.jpg/1000px-Altermagnetism2.jpg 2x" data-file-width="1060" data-file-height="539" /></a><figcaption>Alternating magnetic and crystal pattern in altermagnetic manganese telluride (MnTe, left) and ruthenium dioxide (RuO<sub>2</sub>, right).</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Electronic_structure">Electronic structure</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Altermagnetism&action=edit&section=2" title="Edit section: Electronic structure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>One of the distinctive features of altermagnets is a specifically spin-split <a href="/wiki/Electronic_band_structure" title="Electronic band structure">band structure</a><sup id="cite_ref-smejkal_symm_7-6" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> which was first experimentally observed in work that was published in 2024.<sup id="cite_ref-krempasky2024_8-3" class="reference"><a href="#cite_note-krempasky2024-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Altermagnetic band structure breaks time-reversal symmetry,<sup id="cite_ref-smejkal_symm_7-7" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_sciadv_11-1" class="reference"><a href="#cite_note-smejkal_sciadv-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <i>E<sub>ks</sub></i>=<i>E<sub>-ks</sub></i> (<i>E</i> is energy, <i>k</i> wavevector and <i>s</i> spin) as in ferromagnets, however unlike in ferromagnets, it does not generate net magnetization. The altermagnetic spin polarisation alternates in wavevector space and forms characteristic 2, 4, or 6 spin-degenerate nodes, respectively, which correspond to d-, g, or i-wave order parameters.<sup id="cite_ref-smejkal_symm_7-8" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> A <i>d</i>-wave altermagnet can be regarded as the magnetic counterpart of a <i>d</i>-wave <a href="/wiki/Superconductivity" title="Superconductivity">superconductor</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1248256098">@media all and (max-width:720px){.mw-parser-output .mod-gallery{width:100%!important}}.mw-parser-output .mod-gallery{display:table}.mw-parser-output .mod-gallery-default{background:transparent;margin-top:4px}.mw-parser-output .mod-gallery-center{margin-left:auto;margin-right:auto}.mw-parser-output .mod-gallery-left{float:left}.mw-parser-output .mod-gallery-right{float:right}.mw-parser-output .mod-gallery-none{float:none}.mw-parser-output .mod-gallery-collapsible{width:100%}.mw-parser-output .mod-gallery .title,.mw-parser-output .mod-gallery .main,.mw-parser-output .mod-gallery .footer{display:table-row}.mw-parser-output .mod-gallery .title>div{display:table-cell;padding:0 4px 4px;text-align:center;font-weight:bold}.mw-parser-output .mod-gallery .main>div{display:table-cell}.mw-parser-output .mod-gallery .gallery{line-height:1.35em}.mw-parser-output .mod-gallery .footer>div{display:table-cell;padding:4px;text-align:right;font-size:85%;line-height:1em}.mw-parser-output .mod-gallery .title>div *,.mw-parser-output .mod-gallery .footer>div *{overflow:visible}.mw-parser-output .mod-gallery .gallerybox img{background:none!important}.mw-parser-output .mod-gallery .bordered-images .thumb img{border:solid var(--background-color-neutral,#eaecf0)1px}.mw-parser-output .mod-gallery .whitebg .thumb{background:var(--background-color-base,#fff)!important}</style><div class="mod-gallery mod-gallery-default mod-gallery-center"><div class="main"><div><ul class="gallery mw-gallery-traditional nochecker bordered-images whitebg"> <li class="gallerybox" style="width: 285px"> <div class="thumb" style="width: 280px; height: 210px;"><span typeof="mw:File"><a href="/wiki/File:Altermagnetism3.png" class="mw-file-description" title="Fermi surface of an altermagnetic metal. The blue and red colors correspond to the up and down polarization of the spin."><img alt="Fermi surface of an altermagnetic metal. The blue and red colors correspond to the up and down polarization of the spin." src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Altermagnetism3.png/188px-Altermagnetism3.png" decoding="async" width="188" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Altermagnetism3.png/282px-Altermagnetism3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Altermagnetism3.png/376px-Altermagnetism3.png 2x" data-file-width="605" data-file-height="580" /></a></span></div> <div class="gallerytext">Fermi surface of an altermagnetic metal. The blue and red colors correspond to the up and down polarization of the spin.</div> </li> <li class="gallerybox" style="width: 285px"> <div class="thumb" style="width: 280px; height: 210px;"><span typeof="mw:File"><a href="/wiki/File:Altermagnetism4.jpg" class="mw-file-description" title="The band structure of an altermagnet."><img alt="The band structure of an altermagnet." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Altermagnetism4.jpg/180px-Altermagnetism4.jpg" decoding="async" width="180" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Altermagnetism4.jpg/270px-Altermagnetism4.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Altermagnetism4.jpg/360px-Altermagnetism4.jpg 2x" data-file-width="647" data-file-height="647" /></a></span></div> <div class="gallerytext">The band structure of an altermagnet.</div> </li> </ul></div></div></div> <p>The altermagnetic spin polarization in band structure (energy–wavevector diagram) is collinear and does not break inversion symmetry.<sup id="cite_ref-smejkal_symm_7-9" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The altermagnetic spin splitting is even in wavector, i.e. <i>(k<sub>x</sub><sup>2</sup>-k<sub>y</sub><sup>2</sup>)s<sub>z</sub></i>.<sup id="cite_ref-smejkal_symm_7-10" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-krempasky2024_8-4" class="reference"><a href="#cite_note-krempasky2024-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> It is thus also distinct from noncollinear Rasba or Dresselhaus spin texture which break inversion symmetry in noncentrosymmetric nonmagnetic or antiferromagnetic materials due to the spin-orbit coupling. Unconventional time-reversal symmetry breaking, giant ~1eV spin splitting and anomalous <a href="/wiki/Hall_effect" title="Hall effect">Hall effect</a> was first theoretically predicted<sup id="cite_ref-smejkal_sciadv_11-2" class="reference"><a href="#cite_note-smejkal_sciadv-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and experimentally confirmed<sup id="cite_ref-feng_13-0" class="reference"><a href="#cite_note-feng-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> in RuO<sub>2</sub>. </p> <div class="mw-heading mw-heading2"><h2 id="Materials">Materials</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Altermagnetism&action=edit&section=3" title="Edit section: Materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Direct experimental evidence of altermagnetic band structure in semiconducting <a href="/wiki/Manganese(II)_telluride" title="Manganese(II) telluride">MnTe</a> and metallic <a href="/wiki/Ruthenium(IV)_oxide" title="Ruthenium(IV) oxide">RuO<sub>2</sub></a> was first published in 2024.<sup id="cite_ref-krempasky2024_8-5" class="reference"><a href="#cite_note-krempasky2024-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-fedchenko_9-3" class="reference"><a href="#cite_note-fedchenko-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Many more materials are predicted to be altermagnets – ranging from insulators, semiconductors, and metals to superconductors.<sup id="cite_ref-smejkal_landscape_6-3" class="reference"><a href="#cite_note-smejkal_landscape-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_symm_7-11" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Altermagnetism was predicted in 3D and 2D materials<sup id="cite_ref-mazin_smejkal_3-1" class="reference"><a href="#cite_note-mazin_smejkal-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_landscape_6-4" class="reference"><a href="#cite_note-smejkal_landscape-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> with both light as well as heavy elements and can be found in nonrelativistic as well as relativistic band structures.<sup id="cite_ref-smejkal_symm_7-12" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-krempasky2024_8-6" class="reference"><a href="#cite_note-krempasky2024-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_sciadv_11-3" class="reference"><a href="#cite_note-smejkal_sciadv-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Altermagnetism&action=edit&section=4" title="Edit section: Properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Altermagnets exhibit an unusual combination of ferromagnetic and antiferromagnetic properties, which remarkably more closely resemble those of ferromagnets.<sup id="cite_ref-punchline_1-4" class="reference"><a href="#cite_note-punchline-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-savitsky_science_5-4" class="reference"><a href="#cite_note-savitsky_science-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_landscape_6-5" class="reference"><a href="#cite_note-smejkal_landscape-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smejkal_symm_7-13" class="reference"><a href="#cite_note-smejkal_symm-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Hallmarks of altermagnetic materials such as the anomalous <a href="/wiki/Hall_effect" title="Hall effect">Hall effect</a><sup id="cite_ref-smejkal_sciadv_11-4" class="reference"><a href="#cite_note-smejkal_sciadv-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> have been observed before<sup id="cite_ref-feng_13-1" class="reference"><a href="#cite_note-feng-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-gonzalez_14-0" class="reference"><a href="#cite_note-gonzalez-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> (but this effect occurs also in other magnetically compensated systems such as non-collinear antiferromagnets<sup id="cite_ref-nakatsuji_15-0" class="reference"><a href="#cite_note-nakatsuji-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>). Altermagnets also exhibit unique properties such as anomalous and spin currents that can change sign as the crystal rotates.<sup id="cite_ref-RGH_16-0" class="reference"><a href="#cite_note-RGH-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <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=Altermagnetism&action=edit&section=5" title="Edit section: References"><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"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-punchline-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-punchline_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-punchline_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-punchline_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-punchline_1-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-punchline_1-4"><sup><i><b>e</b></i></sup></a></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="CITEREFMazin2022" class="citation journal cs1">Mazin, Igor (2022-12-08). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysrevx.12.040002">"Altermagnetism—A New Punch Line of Fundamental Magnetism"</a>. <i>Physical Review X</i>. <b>12</b> (4): 040002. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2022PhRvX..12d0002M">2022PhRvX..12d0002M</a>. <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/10.1103%2Fphysrevx.12.040002">10.1103/physrevx.12.040002</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+X&rft.atitle=Altermagnetism%E2%80%94A+New+Punch+Line+of+Fundamental+Magnetism&rft.volume=12&rft.issue=4&rft.pages=040002&rft.date=2022-12-08&rft_id=info%3Adoi%2F10.1103%2Fphysrevx.12.040002&rft_id=info%3Abibcode%2F2022PhRvX..12d0002M&rft.aulast=Mazin&rft.aufirst=Igor&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252Fphysrevx.12.040002&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAltermagnetism" class="Z3988"></span></span> </li> <li id="cite_note-mazin-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-mazin_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMazin2024" class="citation journal cs1">Mazin, Igor (2024-01-08). <a rel="nofollow" class="external text" href="https://physics.aps.org/articles/v17/4">"Altermagnetism Then and Now"</a>. <i><a href="/wiki/Physical_Review_X" title="Physical Review X">Physical Review X</a></i>. <b>17</b>: 4. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2105.05820">2105.05820</a></span>. <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%2FPhysRevX.12.031042">10.1103/PhysRevX.12.031042</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+X&rft.atitle=Altermagnetism+Then+and+Now&rft.volume=17&rft.pages=4&rft.date=2024-01-08&rft_id=info%3Aarxiv%2F2105.05820&rft_id=info%3Adoi%2F10.1103%2FPhysRevX.12.031042&rft.aulast=Mazin&rft.aufirst=Igor&rft_id=https%3A%2F%2Fphysics.aps.org%2Farticles%2Fv17%2F4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAltermagnetism" class="Z3988"></span></span> </li> <li id="cite_note-mazin_smejkal-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-mazin_smejkal_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-mazin_smejkal_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMazinGonzález-HernándezŠmejkal2023" class="citation cs2">Mazin, Igor; González-Hernández, Rafael; Šmejkal, Libor (2023-09-05), <i>Induced Monolayer Altermagnetism in MnP(S,Se)$_3$ and 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