In recent years, two important advances have opened new doors for the characterization and determination of magnetic structures. Firstly, researchers have produced computer-readable listings of the magnetic or Shubnikov space groups. Secondly, they have extended and applied the superspace formalism, which is presently the standard approach for the description of nonmagnetic incommensurate structures and their symmetry, to magnetic structures. These breakthroughs have been the basis for the subsequent development of a series of computer tools that allow a more efficient and comprehensive application of magnetic symmetry, both commensurate and incommensurate. Here we briefly review the capabilities of these computation instruments and present the fundamental concepts on which they are based, providing various examples. We show how these tools facilitate the use of symmetry arguments expressed as either a magnetic space group or a magnetic superspace group and allow the exploration of the possible magnetic orderings associated with one or more propagation vectors in a form that complements and goes beyond the traditional representation method. Special focus is placed on the programs available online at the Bilbao Crystallographic Server ().


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Literature Cited

  1. Koptsik VA. 1.  1966. Shubnikov Groups. Handbook on the Symmetry and Physical Properties of Crystal Structures. Moscow: Moscow Univ. Press. In Russian [Google Scholar]
  2. Bradley CJ, Cracknell AP. 2.  1972. The Mathematical Theory of Symmetry in Solids Oxford, UK: Clarendon [Google Scholar]
  3. Perez-Mato JM, Ribeiro JL, Petricek V, Aroyo MI. 3.  2012. Magnetic superspace groups and symmetry constraints in incommensurate magnetic phases. J. Phys. Condens. Matter. 24:163201 [Google Scholar]
  4. Petříček V, Fuksa J, Dušek M. 4.  2010. Magnetic space and superspace groups, representation analysis: competing or friendly concepts?. Acta Crystallogr. Sect. A 66:649–55 [Google Scholar]
  5. Janner A, Janssen T. 5.  1980. Symmetry of incommensurate crystal phases. I. Commensurate basic structures. Acta Crystallogr. Sect. A 36:399–408 [Google Scholar]
  6. Bertaut EF. 6.  1968. Representation analysis of magnetic structures. Acta Crystallogr. Sect. A 24:217–31 [Google Scholar]
  7. Bertaut EF. 7.  1971. Magnetic structure analysis and group theory. J. Phys. Colloques 32:C1–46270 [Google Scholar]
  8. Izyumov YA, Naish VE. 8.  1979. Symmetry analysis in neutron diffraction studies of magnetic structures: 1. A phase transition concept to describe magnetic structures in crystals. J. Magn. Magn. Mater. 12:239–48 [Google Scholar]
  9. Izyumov YA, Naish VE, Ozerov RP. 9.  1991. Neutron Diffraction of Magnetic Materials Dordrecht, Neth: Kluwer Acad. [Google Scholar]
  10. Izyumov YA, Naish VE, Syromiatnikov VN. 10.  1979. Symmetry analysis in neutron diffraction studies of magnetic structures: 2. Changes in periodicity at magnetic phase transitions. J. Magn. Magn. Mater. 12:249–61 [Google Scholar]
  11. Izyumov YA, Naish VE, Petrov SB. 11.  1979. Symmetry analysis in neutron diffraction studies of magnetic structures: 3. An example: the magnetic structure of spinels. J. Magn. Magn. Mater. 13:267–74 [Google Scholar]
  12. Rodríguez-Carvajal J. 12.  1993. Recent advances in magnetic structure determination by neutron powder diffraction. Physica B 192:55–69 [Google Scholar]
  13. Wills AS. 13.  2000. A new protocol for the determination of magnetic structures using simulated annealing and representational analysis (SARAh). Physica B 276–78:680–81 [Google Scholar]
  14. Sikora W, Białas F, Pytlik L. 14.  2004. MODY: a program for calculation of symmetry-adapted functions for ordered structures in crystals. J. Appl. Crystallogr. 37:1015–19 [Google Scholar]
  15. Dul M, Lesniewska B, Oles A, Pytlik L, Sikora W. 15.  1997. Computer database of magnetic structures determined by neutron diffraction. Physica B 234–36:790–91 [Google Scholar]
  16. Schmid H. 16.  2008. Some symmetry aspects of ferroics and single phase multiferroics. J. Phys. Condens. Matter 20:434201 [Google Scholar]
  17. Fiebig M. 17.  2005. Revival of the magnetoelectric effect. J. Phys. D 38:R123–52 [Google Scholar]
  18. Johnson RD, Radaelli PG. 18.  2014. Diffraction studies of multiferroics. Annu. Rev. Mater. Res. 44:269–98 [Google Scholar]
  19. Kimura T. 19.  2007. Spiral magnets as magnetoelectrics. Annu. Rev. Mater. Res. 37:387–413 [Google Scholar]
  20. Hall SR, Allen FH, Brown ID. 20.  1991. The Crystallographic Information File (CIF): a new standard archive file for crystallography. Acta Crystallogr. Sect. A 47:655–85 [Google Scholar]
  21. 21. Int. Union Crystallogr 2015. Commission on Magnetic Structures. http://www.iucr.org/iucr/commissions/magnetic-structures [Google Scholar]
  22. 22. Bilbao Crystallogr. Serv 2014. MAGNDATA: a collection of magnetic structures with portable cif-type files. Bilbao Crystallographic Server. http://www.cryst.ehu.es/magndata/ [Google Scholar]
  23. Aroyo MI, Perez-Mato JM, Capillas C, Kroumova E, Ivantchev S. 23.  et al. 2006. Bilbao Crystallographic Server: I. Databases and crystallographic computing programs. Z. Krist. 221 1:15–27 [Google Scholar]
  24. Aroyo MI, Kirov A, Capillas C, Perez-Mato JM, Wondratschek H. 24.  2006. Bilbao Crystallographic Server: II. Representations of crystallographic point groups and space groups. Acta Crystallogr. Sect. A 62:115–28 [Google Scholar]
  25. Glazer AM, Aroyo MI, Authier A. 25.  2014. Seitz symbols for crystallographic symmetry operations. Acta Crystallogr. Sect. A 70:300–2 [Google Scholar]
  26. Wondratschek H, Müller U. 26.  2011. International Tables for Crystallography A1 Symmetry Relations Between Space Groups Dordrecht, Neth: Kluwer Acad http://it.iucr.org/A1/ [Google Scholar]
  27. Momma K, Izumi F. 27.  2011. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44:1272–76 [Google Scholar]
  28. Hanson R. 28.  2013. Jmol: an open-source Java viewer for chemical structures in 3D http://www.jmol.org/ [Google Scholar]
  29. Litvin DB. 29.  2013. Magnetic Group Tables: 1-, 2- and 3-Dimensional Magnetic Subperiodic Groups and Magnetic Space Groups Chester, UK: Int. Union Crystallogr http://www.iucr.org/publ/978-0-9553602-2-0 [Google Scholar]
  30. Hahn T. 30.  2002. International Tables for Crystallography A Space-Group Symmetry Dordrecht, Neth: Kluwer Acad, 5th ed.. [Google Scholar]
  31. Opechowski W, Guccione R. 31.  1965. Magnetic symmetry. Magnetism II, Part A GT Rado, H Suhl 105–65 New York: Academic [Google Scholar]
  32. Belov NV, Neronova NN, Smirnova TS. 32.  1957. Shubnikov groups. Sov. Phys. Crystallogr. 2:311–22 [Google Scholar]
  33. Stokes HT, Campbell BJ. 33.  2011. ISO-MAG: table of magnetic space groups. ISOTROPY Software Suite. http://iso.byu.edu [Google Scholar]
  34. Gallego SV, Tasci ES, de la Flor G, Perez-Mato JM, Aroyo MI. 34.  2012. Magnetic symmetry in the Bilbao Crystallographic Server: a computer program to provide systematic absences of magnetic neutron diffraction. J. Appl. Crystallogr. 45:1236–47 [Google Scholar]
  35. Lee N, Vecchini C, Choi YJ, Chapon LC, Bombardi A. 35.  et al. 2013. Giant tunability of ferroelectric polarization in GdMn2O5. Phys. Rev. Lett. 110:137203 [Google Scholar]
  36. FIZ Karlsruhe. 36.  2014. ICSD: Inorganic Crystal Structure Database Eggenstein-Leopoldshafen, Ger. http://icsd.fiz-karlsruhe.de [Google Scholar]
  37. Kagomiya I, Kohn K, Uchiyama T. 37.  2002. Structure and ferroelectricity of RMn2O5. Ferroelectrics 280:131–43 [Google Scholar]
  38. 38. Bilbao Crystallogr. Serv 2014. IDENTIFY GROUP: identification of a space group from a set of generators in an arbitrary setting. Bilbao Crystallographic Server. http://www.cryst.ehu.es/cryst/identify_group [Google Scholar]
  39. 39. Bilbao Crystallogr. Serv 2014. IDENTIFY MAGNETIC GROUP: identification of a magnetic space group from a set of generators in an arbitrary setting. Bilbao Crystallographic Server. http://www.cryst.ehu.es/cryst/identify_mgroup [Google Scholar]
  40. Doubrovsky C, André G, Gukasov A, Auban-Senzier P, Pasquier CR. 40.  et al. 2012. Magnetic phase transitions in PrMn2O5: Importance of ion-size threshold size effects in RMn2O5 compounds (R = rare earth). Phys. Rev. B 86:174417 [Google Scholar]
  41. Stokes HT, Campbell BJ. 41.  2014. ISOCIF: create or modify CIF files. ISOTROPY Software Suite. http://iso.byu.edu [Google Scholar]
  42. 42. Bilbao Crystallogr. Serv 2014. STRCONVERT: structure data converter & editor. Bilbao Crystallographic Server. http://www.cryst.ehu.es/cryst/strconvert [Google Scholar]
  43. Stokes HT, Campbell BJ. 43.  1998. FINDSYM: identify the space group of a crystal, given the positions of the atoms in a unit cell. ISOTROPY Software Suite http://iso.byu.edu [Google Scholar]
  44. Kresse G, Furthmüller J. 44.  1996. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54:11169–86 [Google Scholar]
  45. 45. Bilbao Crystallogr. Serv 2014. MVISUALIZE: 3D visualization of magnetic structures with Jmol. Bilbao Crystallographic Server. http://www.cryst.ehu.es/cryst/mvisualize [Google Scholar]
  46. 46. Bilbao Crystallogr. Serv 2013. MAXMAGN: maximal magnetic space groups for a given a propagation vector and resulting magnetic structural models. Bilbao Crystallographic Server. http://www.cryst.ehu.es/cryst/maxmagn [Google Scholar]
  47. Petricek V, Dusek M, Palatinus L. 47.  2006. Jana2006: The Crystallographic Computing System http://jana.fzu.cz/ [Google Scholar]
  48. Petříček V, Dušek M, Palatinus L. 48.  2014. Crystallographic computing system JANA2006: general features. Z. Krist. 229:5345–52 [Google Scholar]
  49. Muñoz A, Casais MT, Alonso JA, Martinez-Lope MJ, Martinez JL. 49.  et al. 2001. Complex magnetism and magnetic structures of the metastable HoMnO3 perovskite. Inorg. Chem. 40:1020–28 [Google Scholar]
  50. Lee N, Choi YJ, Ramazanoglu M, Ratcliff W, Kiryukhin V, Cheong SW. 50.  2011. Mechanism of exchange striction of ferroelectricity in multiferroic orthorhombic HoMnO3 single crystals. Phys. Rev. B 84:020101 [Google Scholar]
  51. Fu Z, Zheng Y, Xiao Y, Bedanta S, Senyshyn A. 51.  et al. 2013. Coexistence of magnetic order and spin-glass-like phase in the pyrochlore antiferromagnet Na3Co(CO3)2Cl. Phys. Rev. 87:214406 [Google Scholar]
  52. 52. Bilbao Crystallogr. Serv 2014. k-SUBGROUPSMAG: magnetic subgroups consistent with some given propagation vector(s) or a supercell. Bilbao Crystallographic Server. http://www.cryst.ehu.es/cryst/k_subgroupsmag [Google Scholar]
  53. Ressouche E, Kernavanois N, Regnault LP, Henry JY. 53.  2006. Magnetic structures of the metal monoxides NiO and CoO re-investigated by spherical neutron polarimetry. Physica B385–86394–97 [Google Scholar]
  54. Herrmann-Ronzaud D, Burlet P, Rossat-Mignod J. 54.  1978. Equivalent type-II magnetic structures: CoO, a collinear antiferromagnet. J. Phys. C: Solid State Phys. 11:2123–37 [Google Scholar]
  55. Jauch W, Reehuis M, Bleif HJ, Kubanek F, Pattison P. 55.  2001. Crystallographic symmetry and magnetic structure of CoO. Phys. Rev. B 64:052102 [Google Scholar]
  56. 56. Bilbao Crystallogr. Serv 2014. MAGMODELIZE: magnetic structure models for any given magnetic symmetry. Bilbao Crystallographic Server. http://www.cryst.ehu.es/cryst/magmodelize [Google Scholar]
  57. Zhao LL, Wu S, Wang JK, Hodges JP, Broholm C, Morosan E. 57.  2013. Quasi-two-dimensional noncollinear magnetism in the Mott insulator Sr2F2Fe2OS2. Phys. Rev. B 87:020406 [Google Scholar]
  58. Aroyo MI, Orobengoa D, de la Flor G, Perez-Mato JM, Wondratschek H. 58.  2014. Brillouin-zone databases on the Bilbao Crystallographic Server. Acta Crystallogr. Sect. A 70:126–37 [Google Scholar]
  59. Chattopadhyay T, Brown PJ, Roessli B, Stepanov AA, Barilo SN, Zhigunov DI. 59.  1992. Magnetic ordering of Cu in Gd2CuO4. Phys. Rev. B 46:5731–34 [Google Scholar]
  60. Perez-Mato JM, Aroyo MI, García A, Blaha P, Schwarz K. 60.  et al. 2004. Competing structural instabilities in the ferroelectric Aurivillius compound SrBi2Ta2O9. Phys. Rev. B 70:214111 [Google Scholar]
  61. Etxebarria I, Perez-Mato JM, Boullay P. 61.  2010. The role of trilinear couplings in the phase transitions of Aurivillius compounds. Ferroelectrics 401:17–23 [Google Scholar]
  62. Ghosez P, Triscone JM. 62.  2011. Multiferroics: coupling of three lattice instabilities. Nat. Mater. 10:269–70 [Google Scholar]
  63. Quintero M, Morocoima M, Guerrero E, Ruiz J. 63.  1994. Temperature variation of lattice parameters and thermal expansion coefficients of the compound MnGa2Se4. Phys. Status Solidi A 146:587–93 [Google Scholar]
  64. Opechowski W, Dreyfus T. 64.  1971. Classifications of magnetic structures. Acta Crystallogr. Sect. A 27:470–84 [Google Scholar]
  65. Opechowski W. 65.  1971. Analyse des structures magnétiques et théorie des groupes: on two classifications of magnetic structures. J. Phys. Colloques 32:C1–45761 [Google Scholar]
  66. Opechowski W, Litvin DB. 66.  1977. Error corrections corrected, remarks on Bertaut's article “Simple derivation of magnetic space groups”. Ann. Phys. 2:121–25 [Google Scholar]
  67. Campbell BJ, Stokes HT, Tanner DE, Hatch DM. 67.  2006. ISODISPLACE: a web-based tool for exploring structural distortions. J. Appl. Crystallogr. 39:607–14 http://stokes.byu.edu/isodistort.html [Google Scholar]
  68. Ascher E. 68.  1977. Permutation representations, epikernels and phase transitions. J. Phys. C Solid State Phys. 10:1365–77 [Google Scholar]
  69. de Wolff PM. 69.  1974. The pseudo-symmetry of modulated crystal structures. Acta Crystallogr. Sect. A 30:777–85 [Google Scholar]
  70. Janner A, Janssen T. 70.  1980. Symmetry of incommensurate crystal phases. II. Incommensurate basic structure. Acta Crystallogr. Sect. A 36:408–15 [Google Scholar]
  71. Janssen T, Janner A. 71.  2014. Aperiodic crystals and superspace concepts. Acta Crystallogr. Sect. B 70:617–51 [Google Scholar]
  72. Janssen T, Janner A, Looijenga-Vos A, de Wolff PM. 72.  2006. Incommensurate and commensurate modulated structures. International Tables for Crystallography C Mathematical, Physical and Chemical Tables E. Prince 907–55 Dordrecht, Neth: Kluwer Acad. [Google Scholar]
  73. Janssen T, Chapuis G, de Boissieu M. 73.  2007. Aperiodic Crystals: From Modulated Phases to Quasicrystals IUCr Monogr. Crystallogr. No. 20 Oxford, UK: Oxford Univ. Press [Google Scholar]
  74. Van Smaalen S. 74.  2007. Incommensurate Crystallography. IUCr Monogr. Crystallogr. No. 21 Oxford, UK: Oxford Univ. Press [Google Scholar]
  75. Schobinger-Papamantellos P, Janssen T. 75.  2006. The symmetry of the incommensurate magnetic phase of ErFe4Ge2. Z. Krist. 221:732–34 [Google Scholar]
  76. Schönleber A, van Smaalen S, Palatinus L. 76.  2006. Structure of the incommensurate phase of the quantum magnet TiOC. Phys. Rev. B 73:214410 [Google Scholar]
  77. Slawinski W, Przenioslo R, Sosnowska I, Bieringer M, Margiolaki I, Suard E. 77.  2009. Modulation of atomic positions in CaCuxMn7−xO12 (x < 0.1). Acta Crystallogr. Sect. B 65:535–42 [Google Scholar]
  78. Meddar L, Josse M, Deniard P, La C, Andre G. 78.  et al. 2009. Effect of nonmagnetic substituents Mg and Zn on the phase competition in the multiferroic antiferromagnet MnWO4. Chem. Mater. 21:5203–14 [Google Scholar]
  79. Ribeiro JL, Vieira LG. 79.  2010. Landau model for the phase diagrams of the orthorhombic rare-earth manganites RMnO3 (R = Eu, Gd, Tb, Dy, Ho). Phys. Rev. B 82:064410 [Google Scholar]
  80. Ribeiro JL. 80.  2010. Symmetry, incommensurate magnetism and ferroelectricity: the case of the rare-earth manganites RMnO3. J. Phys. Conf. Ser. 226:012013 [Google Scholar]
  81. Janoschek M, Fischer P, Schefer J, Roessli B, Pomjakushin V. 81.  et al. 2010. Single magnetic chirality in the magnetoelectric NdFe3(11BO3)4. Phys. Rev. B 81:094429 [Google Scholar]
  82. Ribeiro JL, Perez-Mato JM. 82.  2011. Symmetry and magnetic field driven transitions in the 2D triangular lattice compound RbFe(MoO4)2. J. Phys. Condens. Matter 23:446003 [Google Scholar]
  83. Abakumov AM, Tsirlin AA, Perez-Mato JM, Petříček V, Rosner H. 83.  et al. 2011. Spiral ground state against ferroelectricity in the frustrated magnet BiMnFe2O6. Phys. Rev. B 83:214402 [Google Scholar]
  84. Urcelay-Olabarria I, Perez-Mato JM, Ribeiro JL, García-Muñoz JL, Ressouche E. 84.  et al. 2013. Incommensurate magnetic structures of multiferroic MnWO4 studied within the superspace formalism. Phys. Rev. B 87:014419 [Google Scholar]
  85. Terada N, Khalyavin DD, Perez-Mato JM, Manuel P, Prabhakaran D. 85.  et al. 2014. Magnetic and ferroelectric orderings in multiferroic α-NaFeO2. Phys. Rev. B 89:184421 [Google Scholar]
  86. Prokeš K, Petříček V, Ressouche E, Hartwig S, Ouladdiaf B. 86.  et al. 2014. (3 + 1)-dimensional crystal and antiferromagnetic structures in CeRuSn. J. Phys. Condens. Matter 26:122201 [Google Scholar]
  87. Orlandi F, Righi L, Ritter C, Pernechele C, Solzi M. 87.  et al. 2014. Superspace application on magnetic structure analysis of the Pb2MnWO6 double perovskite system. J. Mater. Chem. C 2:9215–23 [Google Scholar]
  88. Herpin A, Meriel P. 88.  1961. Étude de l'antiferromagnétisme helicoidal de MnAu2 par diffraction de neutrons. J. Phys. Radium. 22:337–48 [Google Scholar]
  89. Brown ID, McMahon B. 89.  2002. CIF: the computer language of crystallography. Acta Crystallogr. Sect. B 58:317–24 [Google Scholar]
  90. Laffargue D, Fourgeot F, Bourée F, Chevalier B, Roisnel T. 90.  et al. 1996. The antiferromagnetic-ferromagnetic transition of Ce2Pd2.04Sn0.96 stannide. Solid State Commun. 100:575–79 [Google Scholar]
  91. Rodríguez-Carvajal J, Bourée F. 91.  2012. Symmetry and magnetic structures. EPJ Web Conf. 22:00010 [Google Scholar]
  92. Biffin A, Johnson RD, Choi S, Freund F, Manni S. 92.  et al. 2014. Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in β-Li2IrO3: full solution via magnetic resonant X-ray diffraction. Phys. Rev. B 90:205116 [Google Scholar]
  93. Kenzelmann M, Lawes G, Harris AB, Gasparovic G, Broholm C. 93.  et al. 2007. Direct transition from a disordered to a multiferroic phase on a triangular lattice. Phys. Rev. Lett. 98:267205 [Google Scholar]

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