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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <base href="https://journals.iucr.org/a/issues/2019/03/00/lk5043/" /> <title>(IUCr) Automatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server</title> <script type="text/javascript" src="https://journals.iucr.org/javascript/analytics.js"></script> <link rel="schema.DC" href="https://purl.org/dc/elements/1.1/" /> <link rel="schema.DCTERMS" href="https://purl.org/dc/terms/" /> <link rel="schema.prism" href="https://prismstandard.org/namespaces/1.2/basic/" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:description" content="Two new tools hosted on the Bilbao Crystallographic Server are presented. The programs permit the automatic calculation of symmetry-adapted forms of tensor properties for magnetic and non-magnetic groups. The cases of equilibrium, transport, optical and nonlinear optical susceptibility tensors are studied separately." /> <meta name="twitter:image" content="https://journals.iucr.org/a/issues/2019/03/00/lk5043/lk5043largethumb.jpg" /> <meta name="twitter:site" content="@ActaCrystA" /> <meta name="twitter:title" content="Automatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server" /> <meta property="og:description" content="Two new tools hosted on the Bilbao Crystallographic Server are presented. The programs permit the automatic calculation of symmetry-adapted forms of tensor properties for magnetic and non-magnetic groups. The cases of equilibrium, transport, optical and nonlinear optical susceptibility tensors are studied separately." /> <meta property="og:image" content="https://journals.iucr.org/a/issues/2019/03/00/lk5043/lk5043largethumb.jpg" /> <meta property="og:image:alt" content="Image from Automatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server" /> <meta property="og:image:height" content="300" /> <meta property="og:image:secureurl" content="https://journals.iucr.org/a/issues/2019/03/00/lk5043/lk5043largethumb.jpg" /> <meta property="og:image:type" content="image/jpeg" /> <meta property="og:image:width" content="300" /> <meta property="og:locale" content="en_US" /> <meta property="og:site_name" content="Acta Crystallographica Section A" /> <meta property="og:title" content="Automatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server" /> <meta property="og:type" content="article" /> <meta property="og:updated_time" content="2024-05-21T09:10:08Z" /> <meta property="og:url" content="https://journals.iucr.org/a/issues/2019/03/00/lk5043/" /> <meta name="DC.copyright" content="Copyright (c) 2019 International Union of Crystallography" /> <meta name="DC.coverage" content="" /> <meta name="DC.creator" content="Gallego, S.V." /> <meta name="DC.creator" content="Etxebarria, J." /> <meta name="DC.creator" content="Elcoro, L." /> <meta name="DC.creator" content="Tasci, E.S." /> <meta name="DC.creator" content="Perez-Mato, J.M." /> <meta name="authors" content="Gallego, S.V.|Etxebarria, J.|Elcoro, L.|Tasci, E.S.|Perez-Mato, J.M." /> <meta name="DC.date" content="2019-04-30" /> <meta name="DC.description" content="Two new programs, MTENSOR and TENSOR, hosted on the open-access website known as the Bilbao Crystallographic Server, are presented. The programs provide automatically the symmetry-adapted form of tensor properties for any magnetic or non-magnetic point group or space group. The tensor is chosen from a list of 144 known tensor properties gathered from the scientific literature or, alternatively, the user can also build a tensor that possesses an arbitrary intrinsic symmetry. Four different tensor types are considered: equilibrium, transport, optical and nonlinear optical susceptibility tensors. For magnetically ordered structures, special attention is devoted to a detailed discussion of the transformation rules of the tensors under the time-reversal operation 1′. It is emphasized that for non-equilibrium properties it is the Onsager theorem, and not the constitutive relationships, that indicates how these tensors transform under 1′. In this way it is not necessary to restrict the validity of Neumann's principle. New Jahn symbols describing the intrinsic symmetry of the tensors are introduced for several transport and optical properties. In the case of some nonlinear optical susceptibilities of practical interest, an intuitive method is proposed based on simple diagrams, which allows easy deduction of the action of 1′ on the susceptibilities. This topic has not received sufficient attention in the literature and, in fact, it is usual to find published results where the symmetry restrictions for such tensors are incomplete." /> <meta name="DC.format" content="unicode" /> <meta name="DC.identifier" content="doi:10.1107/S2053273319001748" /> <meta name="DC.language" content="en" /> <meta name="DC.link" content="https://journals.iucr.org/paper?lk5043" /> <meta name="DC.publisher" content="International Union of Crystallography" /> <meta name="DC.relation" content="" /> <meta name="DC.rights" content="Copyright (c) 2019 International Union of Crystallography" /> <meta name="DC.source" content="urn:issn:2053-2733" /> <meta name="DC.subject" content="EQUILIBRIUM TENSORS" /> <meta name="DC.subject" content="TRANSPORT TENSORS" /> <meta name="DC.subject" content="OPTICAL TENSORS" /> <meta name="DC.subject" content="NONLINEAR OPTICAL SUSCEPTIBILITY TENSORS" /> <meta name="DC.subject" content="MAGNETIC GROUPS" /> <meta name="DC.subject" content="TIME-REVERSAL SYMMETRY" /> <meta name="DC.subject" content="ONSAGER RELATIONSHIPS" /> <meta name="DC.teaser" content="Two new tools hosted on the Bilbao Crystallographic Server are presented. The programs permit the automatic calculation of symmetry-adapted forms of tensor properties for magnetic and non-magnetic groups. The cases of equilibrium, transport, optical and nonlinear optical susceptibility tensors are studied separately." /> <meta name="description" content="Automatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server" /> <meta name="title" content="Automatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server" /> <meta name="DC.title" content="Automatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server" /> <meta name="DC.type" content="text" /> <meta name="DCTERMS.abstract" content="Two new programs, MTENSOR and TENSOR, hosted on the open-access website known as the Bilbao Crystallographic Server, are presented. The programs provide automatically the symmetry-adapted form of tensor properties for any magnetic or non-magnetic point group or space group. The tensor is chosen from a list of 144 known tensor properties gathered from the scientific literature or, alternatively, the user can also build a tensor that possesses an arbitrary intrinsic symmetry. Four different tensor types are considered: equilibrium, transport, optical and nonlinear optical susceptibility tensors. For magnetically ordered structures, special attention is devoted to a detailed discussion of the transformation rules of the tensors under the time-reversal operation 1′. It is emphasized that for non-equilibrium properties it is the Onsager theorem, and not the constitutive relationships, that indicates how these tensors transform under 1′. In this way it is not necessary to restrict the validity of Neumann's principle. New Jahn symbols describing the intrinsic symmetry of the tensors are introduced for several transport and optical properties. In the case of some nonlinear optical susceptibilities of practical interest, an intuitive method is proposed based on simple diagrams, which allows easy deduction of the action of 1′ on the susceptibilities. This topic has not received sufficient attention in the literature and, in fact, it is usual to find published results where the symmetry restrictions for such tensors are incomplete." /> <meta name="prism.copyright" content="Copyright (c) 2019 International Union of Crystallography" /> <meta name="prism.doi" content="https://doi.org/10.1107/S2053273319001748" /> <meta name="prism.eissn" content="2053-2733" /> <meta name="prism.endingPage" content="447" /> <meta name="prism.issn" content="2053-2733" /> <meta name="prism.number" content="3" /> <meta name="prism.publicationDate" content="2019-04-30" /> <meta name="prism.publicationName" content="Acta Crystallographica Section A: Foundations and Advances" /> <meta name="prism.rightsAgent" content="med@iucr.org" /> <meta name="prism.section" content="research papers" /> <meta name="prism.startingPage" content="438" /> <meta name="prism.volume" content="75" /> <meta name="keywords" content="EQUILIBRIUM TENSORS; TRANSPORT TENSORS; OPTICAL TENSORS; NONLINEAR OPTICAL SUSCEPTIBILITY TENSORS; MAGNETIC GROUPS; TIME-REVERSAL SYMMETRY; ONSAGER RELATIONSHIPS" /> <meta name="copyright" content="Copyright (c) 2019 International Union of Crystallography" /> <meta name="ROBOTS" content="NOARCHIVE" /> <meta name="citation_abstract" content="Two new programs, MTENSOR and TENSOR, hosted on the open-access website known as the Bilbao Crystallographic Server, are presented. The programs provide automatically the symmetry-adapted form of tensor properties for any magnetic or non-magnetic point group or space group. The tensor is chosen from a list of 144 known tensor properties gathered from the scientific literature or, alternatively, the user can also build a tensor that possesses an arbitrary intrinsic symmetry. Four different tensor types are considered: equilibrium, transport, optical and nonlinear optical susceptibility tensors. For magnetically ordered structures, special attention is devoted to a detailed discussion of the transformation rules of the tensors under the time-reversal operation 1′. It is emphasized that for non-equilibrium properties it is the Onsager theorem, and not the constitutive relationships, that indicates how these tensors transform under 1′. In this way it is not necessary to restrict the validity of Neumann's principle. New Jahn symbols describing the intrinsic symmetry of the tensors are introduced for several transport and optical properties. In the case of some nonlinear optical susceptibilities of practical interest, an intuitive method is proposed based on simple diagrams, which allows easy deduction of the action of 1′ on the susceptibilities. This topic has not received sufficient attention in the literature and, in fact, it is usual to find published results where the symmetry restrictions for such tensors are incomplete." /> <meta name="citation_abstract_html_url" content="https://journals.iucr.org/paper?lk5043" /> <meta name="citation_author" content="Gallego, S.V." /> <meta name="citation_author_institution" content="Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain" /> <meta name="citation_author_email" content="twmpatd@gmail.com" /> <meta name="citation_author" content="Etxebarria, J." /> <meta name="citation_author_institution" content="Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain" /> <meta name="citation_author_email" content="j.etxeba@ehu.es" /> <meta name="citation_author" content="Elcoro, L." /> <meta name="citation_author_institution" content="Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain" /> <meta name="citation_author_email" content="luis.elcoro@ehu.eus" /> <meta name="citation_author" content="Tasci, E.S." /> <meta name="citation_author_institution" content="Department of Physics Engineering, Hacettepe University, Ankara 06800, Turkey" /> <meta name="citation_author_email" content="emre.tasci@hacettepe.edu.tr" /> <meta name="citation_author" content="Perez-Mato, J.M." /> <meta name="citation_author_institution" content="Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain" /> <meta name="citation_author_email" content="jm.perez-mato@ehu.eus" /> <meta name="citation_date" content="2019-05-01" /> <meta name="citation_doi" content="10.1107/S2053273319001748" /> <meta name="citation_firstpage" content="438" /> <meta name="citation_fulltext_url" content="https://journals.iucr.org/a/issues/2019/03/00/lk5043/" /> <meta name="citation_issn" content="2053-2733" /> <meta name="citation_issue" content="3" /> <meta name="citation_journal_abbrev" content="Acta Cryst A" /> <meta name="citation_journal_abbrev" content="Acta Cryst Sect A" /> <meta name="citation_journal_abbrev" content="Acta Crystallogr A" /> <meta name="citation_journal_abbrev" content="Acta Crystallogr Sect A" /> <meta name="citation_journal_abbrev" content="Acta Crystallogr A Cryst Phys Diffr Theor Gen Crystallogr" /> <meta name="citation_journal_abbrev" content="Acta Crystallogr Sect A Cryst Phys Diffr Theor Gen Crystallogr" /> <meta name="citation_journal_title" content="Acta Crystallographica Section A: Foundations and Advances" /> <meta name="citation_keywords" content="EQUILIBRIUM TENSORS; TRANSPORT TENSORS; OPTICAL TENSORS; NONLINEAR OPTICAL SUSCEPTIBILITY TENSORS; MAGNETIC GROUPS; TIME-REVERSAL SYMMETRY; ONSAGER RELATIONSHIPS" /> <meta name="citation_language" content="en" /> <meta name="citation_lastpage" content="447" /> <meta name="citation_online_date" content="2019-04-30" /> <meta name="citation_pdf_url" content="https://journals.iucr.org/a/issues/2019/03/00/lk5043/lk5043.pdf" /> <meta name="citation_publisher" content="International Union of Crystallography" /> <meta name="citation_reference" content="citation_author=Birss R. 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The programs permit the automatic calculation of symmetry-adapted forms of tensor properties for magnetic and non-magnetic groups. The cases of equilibrium, transport, optical and nonlinear optical susceptibility tensors are studied separately. 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The programs permit the automatic calculation of symmetry-adapted forms of tensor properties for magnetic and non-magnetic groups. The cases of equilibrium, transport, optical and nonlinear optical susceptibility tensors are studied separately. " href="#" class="addthis_button_compact"><img onclick="$('#lk5043pl').css('display','none')" class="art_icon" src="https://journals.iucr.org/logos/buttonlogos/addthis.png" alt="share" style="top: 0px; left: 92px; width: 20px;"/></a></div><div id="lk5043pl" style="opacity: 0;" class="popup"><span class="popuphd" onclick="$(this).parent().css('display','none');$('#lk5043cl').trigger('click');return false;"><a href="" onclick="return false;">Share</a></span><img class="but_close" src="/logos/buttonlogos/cross.png" alt="close" /></div></div></div> </div><div class="jh_openaccesslogo"><div class="openaccesslogo"><div class="oalogotext" title="To purchase a pay per view version of this article click here"><a class="scrpt_buylogotext" href="https://journals.iucr.org/paper?cnor=lk5043&buy=yes#buy">Access<img alt="pay per view" class="scriptaccesslogo" src="/logos/buttonlogos/buy.gif" /></a> <a title="IUCr Associates, click here to download this article" class="scrpt_buylogotext" href="https://scripts.iucr.org/cgi-bin/adla.pl?cnor=lk5043"><img style="height:18px;" alt="Associates download" class="scriptaccesslogo" src="/logos/buttonlogos/associates_download.gif" /></a></div></div></div></div><div class="clear"></div></div><div class="ica_body"> <div class="ica_bodyleft"><div class="thumbinmain"><a href="//journals.iucr.org/a/issues/2019/03/00/lk5043/index.html" target="_parent"><img id="lk5043issthumbinmain" src="https://scripts.iucr.org/cgi-bin/sendimage?image=/a/issues/2019/03/00/lk5043/lk5043thumbnail.gif" alt="link to html" /></a></div></div><div class="ica_bodyright"><div class="ica_title"><h1 class="atl"><a href="//journals.iucr.org/a/issues/2019/03/00/lk5043/index.html"> Automatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server</a></h1></div> <div style="float: right; text-align: right; width: 100px;"> <script type="text/javascript" src="https://crossmark-cdn.crossref.org/widget/v2.0/widget.js"></script> <a data-target="crossmark"><img src="https://crossmark-cdn.crossref.org/widget/v2.0/logos/CROSSMARK_Color_square_no_text.svg" width="60" /></a> </div>  <div class="ica_authors"><a href="https://scripts.iucr.org/cgi-bin/citedin?search_on=name&author_name=Gallego, S.V."><span class="au">S. V. Gallego</span></a>, <a href="https://scripts.iucr.org/cgi-bin/citedin?search_on=name&author_name=Etxebarria, J."><span class="au">J. Etxebarria</span></a>, <a href="https://scripts.iucr.org/cgi-bin/citedin?search_on=name&author_name=Elcoro, L."><span class="au">L. Elcoro</span></a>, <a href="https://scripts.iucr.org/cgi-bin/citedin?search_on=name&author_name=Tasci, E.S."><span class="au">E. S. Tasci</span></a> and <a href="https://scripts.iucr.org/cgi-bin/citedin?search_on=name&author_name=Perez-Mato, J.M."><span class="au">J. M. Perez-Mato</span></a></div><div class="ica_abstract">Two new programs, <span class="it"><i>MTENSOR</i></span> and <span class="it"><i>TENSOR</i></span>, hosted on the open-access website known as the Bilbao Crystallographic Server, are presented. The programs provide automatically the symmetry-adapted form of tensor properties for any magnetic or non-magnetic point group or space group. The tensor is chosen from a list of 144 known tensor properties gathered from the scientific literature or, alternatively, the user can also build a tensor that possesses an arbitrary intrinsic symmetry. Four different tensor types are considered: equilibrium, transport, optical and nonlinear optical susceptibility tensors. For magnetically ordered structures, special attention is devoted to a detailed discussion of the transformation rules of the tensors under the time-reversal operation 1′. It is emphasized that for non-equilibrium properties it is the Onsager theorem, and not the constitutive relationships, that indicates how these tensors transform under 1′. In this way it is not necessary to restrict the validity of Neumann's principle. New Jahn symbols describing the intrinsic symmetry of the tensors are introduced for several transport and optical properties. In the case of some nonlinear optical susceptibilities of practical interest, an intuitive method is proposed based on simple diagrams, which allows easy deduction of the action of 1′ on the susceptibilities. This topic has not received sufficient attention in the literature and, in fact, it is usual to find published results where the symmetry restrictions for such tensors are incomplete.</div><div class="kwdg"><span class="kwdg_head">Keywords: </span><a href="https://scripts.iucr.org/cgi-bin/full_search?words=equilibrium%20tensors&Action=Search">equilibrium tensors</a>; <a href="https://scripts.iucr.org/cgi-bin/full_search?words=transport%20tensors&Action=Search">transport tensors</a>; <a href="https://scripts.iucr.org/cgi-bin/full_search?words=optical%20tensors&Action=Search">optical tensors</a>; <a href="https://scripts.iucr.org/cgi-bin/full_search?words=nonlinear%20optical%20susceptibility%20tensors&Action=Search">nonlinear optical susceptibility tensors</a>; <a href="https://scripts.iucr.org/cgi-bin/full_search?words=magnetic%20groups&Action=Search">magnetic groups</a>; <a href="https://scripts.iucr.org/cgi-bin/full_search?words=time-reversal%20symmetry&Action=Search">time-reversal symmetry</a>; <a href="https://scripts.iucr.org/cgi-bin/full_search?words=Onsager%20relationships&Action=Search">Onsager relationships</a>.</div><div class="ica_readmore"><a href="//journals.iucr.org/a/issues/2019/03/00/lk5043/index.html">Read article</a><a href="https://scripts.iucr.org/cgi-bin/similar?wordList=%22equilibrium%20tensors%22%20or%20%22transport%20tensors%22%20or%20%22optical%20tensors%22%20or%20%22nonlinear%20optical%20susceptibility%20tensors%22%20or%20%22magnetic%20groups%22%20or%20%22time-reversal%20symmetry%22%20or%20%22onsager%20relationships%22&from=lk5043">Similar articles</a></div></div>  </div>  <div class="clear"></div> <script src="//api.growkudos.com/widgets/article/10.1107/S2053273319001748"></script> <script src="//api.growkudos.com/widgets/resources/10.1107/S2053273319001748"></script><br/></div> <div class="clear"></div></div> </div> <div class="clear"></div> <div id="journalsocialmedia"><table summary="social media" class="sociala"><tbody><tr><td 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