{"id":331,"date":"2018-05-30T10:20:28","date_gmt":"2018-05-30T01:20:28","guid":{"rendered":"https:\/\/www2.tagen.tohoku.ac.jp\/lab\/sato_tj\/?page_id=331"},"modified":"2018-06-01T09:27:18","modified_gmt":"2018-06-01T00:27:18","slug":"magnetic-representations-and-magnetic-space-groups","status":"publish","type":"page","link":"https:\/\/www2.tagen.tohoku.ac.jp\/lab\/sato_tj\/magnetic-representations-and-magnetic-space-groups\/","title":{"rendered":"Magnetic representations and magnetic space groups"},"content":{"rendered":"

Magnetic representations and magnetic space groups<\/strong><\/p>\n

As is well known nowadays, there are two streams for describing magnetic structures.\u00a0 (In fact, there are more, but widely used ones are the following two.)\u00a0 One way is to use the “magnetic representations”.\u00a0 Any axial vector configurations in periodic crystals should be classified by the symmetry of the underlying crystal lattice, so that they should be described as a certain linear combination of basis vectors of irreducible (axial) representations of the crystal’s space group.\u00a0 Indeed, in many real magnets, one (or a few) irreducible representations are enough for describing their magnetic structure, and hence, using “magnetic representation” sounds quite reasonable for practical magnetic structure description.\u00a0 One advantage of this method is that it can deal with incommensurate magnetic structures; simply, the irreducible representations for the (incommensurate) k-group can be used for the incommensurate structures, and hence there is no essential difference in formulation between commensurate and incommensurate structures.<\/p>\n

The other way to go is to use the “magnetic space group”.\u00a0\u00a0 The ordinary crystal space group contains symmetry operations such as translations, rotations, inversions etc…\u00a0 The “magnetic space group” further include time-reversal symmetry operation which just simply flips the magnetic moment direction (classical axial vectors).\u00a0 Inclusion of the time reversal symmetry enlarges the number of the groups from 230 to 1651.\u00a0 An advantage of using this approach is that we can see the symmetry operations (either globally or around a specific site) rather clearly.\u00a0 Quite often, the symmetry determines physical properties, either globally or locally, so this apparent visibility of (either global or local) magnetic symmetry in crystalline magnets is of great help for understanding and classifying their physical properties.<\/p>\n

There are quite a few existing tools for exploring magnetic representations and magnetic space groups, which you can quickly find by google them.\u00a0 That said, I would like to list two of mine in the following.<\/p>\n

One is to calculate magnetic representation basis vectors for any given k-vectors and for any given 230 space groups.\u00a0 The good point of this code is that by selecting basis vectors (and giving their coefficients), it will draw the magnetic structure!\u00a0 The drawing is done with Web3D technology, so you can just save html file to see it at hand later.\u00a0 The code behind it indeed calculates the irreducible representations from scratch (not using any database), so it takes a little long time; please be patient if you calculate high-symmetry crystal such as Fd-3m.<\/p>\n

Magnetic representation analysis <\/a><\/p>\n

The other is to visualize a magnetic structure of a given magnetic space group.\u00a0 Sometimes, people like me with lack of imagination cannot imagine magnetic structures solely from the magnetic space group symbols.\u00a0 For such a case, this software may be of help for understanding them visually.\u00a0 The code behind this uses the “magnetic space group table”<\/a> compiled by Harold T. Stokes and Branton J. Campbell.\u00a0 Without this table I am sure my life gets much complicated.\u00a0\u00a0 (Please note that the code below uses “OG” setting only.)<\/p>\n

Magnetic structure visualization using magnetic space group<\/a><\/p>\n

Note: Please regard the above two codes as experimental.\u00a0 I can not ensure the results provided by the codes, not by any means.\u00a0 It is always a good practice to double check the results using other (much established) software.\u00a0 I am very happy, however, if you could let me know erroneous behavior you may encounter.<\/p>\n","protected":false},"excerpt":{"rendered":"

Magnetic representations and magnetic space groups As is well …<\/p>\n","protected":false},"author":40,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-331","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www2.tagen.tohoku.ac.jp\/lab\/sato_tj\/wp-json\/wp\/v2\/pages\/331","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www2.tagen.tohoku.ac.jp\/lab\/sato_tj\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www2.tagen.tohoku.ac.jp\/lab\/sato_tj\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www2.tagen.tohoku.ac.jp\/lab\/sato_tj\/wp-json\/wp\/v2\/users\/40"}],"replies":[{"embeddable":true,"href":"https:\/\/www2.tagen.tohoku.ac.jp\/lab\/sato_tj\/wp-json\/wp\/v2\/comments?post=331"}],"version-history":[{"count":7,"href":"https:\/\/www2.tagen.tohoku.ac.jp\/lab\/sato_tj\/wp-json\/wp\/v2\/pages\/331\/revisions"}],"predecessor-version":[{"id":342,"href":"https:\/\/www2.tagen.tohoku.ac.jp\/lab\/sato_tj\/wp-json\/wp\/v2\/pages\/331\/revisions\/342"}],"wp:attachment":[{"href":"https:\/\/www2.tagen.tohoku.ac.jp\/lab\/sato_tj\/wp-json\/wp\/v2\/media?parent=331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}