International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 1.5, pp. 106-153
https://doi.org/10.1107/97809553602060000904

Chapter 1.5. Magnetic properties

A. S. Borovik-Romanov,a H. Grimmerb,c* and M. Kenzelmannc*

aP. L. Kapitza Institute for Physical Problems, Russian Academy of Sciences, Kosygin Street 2, 119334 Moscow, Russia,bLabor für Neutronenstreuung, ETH Zurich, Switzerland, and cPaul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
Correspondence e-mail:  hans.grimmer@psi.ch, michel.kenzelmann@psi.ch

References

Aizu, K. (1970). Possible species of ferromagnetic, ferroelectric and ferroelastic crystals. Phys. Rev. B, 2, 754–772.
Akulov, N. (1928). Über die Magnetostriktion der Eisenkristalle. Z. Phys. 52, 389–405.
Alcantara Bonfim, O. F. de & Gehring, G. A. (1980). Magnetoelectric effect in antiferromagnetic crystals. Adv. Phys. 29, 731–769.
Anderson, J. C., Birss, R. R. & Scott, R. A. M. (1964). Linear magnetostriction in hematite. In Proc. Int. Conf. Magnetism, Nottingham, pp. 597–599. London: Institute of Physics and the Physical Society.
Andratskii, V. P. & Borovik-Romanov, A. S. (1966). Piezomagnetic effect in α-Fe2O3. (In Russian.) Zh. Eksp. Teor. Fiz. 51, 1030–1036. [English translation: Sov. Phys. JETP, 24 (1967), 687–691.]
Andreev, A. F. & Marchenko, V. I. (1976). Macroscopic theory of spin waves. (In Russian.) Zh. Eksp. Teor. Fiz. 70, 1522–1538. (English translation: Sov. Phys. JETP, 43, 794–803.)
Andreev, A. F. & Marchenko, V. I. (1980). Symmetry and the macroscopic dynamics of magnetic materials. (In Russian.) Usp. Fiz. Nauk, 130, 39–63. (English translation: Sov. Phys. Usp. 23, 21–34.)
Ascher, E. (1966). Some properties of spontaneous currents. Helv. Phys. Acta, 39, 40–48.
Ascher, E. (1968). Higher-order magneto-electric effects. Philos. Mag. 17, 149–157.
Ascher, E. (1970). The interactions between magnetization and polarization: phenomenological symmetry considerations on boracites. J. Phys. Soc. Jpn, 28 Suppl., 7–14.
Ascher, E., Rieder, H., Schmid, H. & Stössel, H. (1966). Some properties of ferromagnetoelectric nickel–iodine boracite, Ni3B7O13I. J. Appl. Phys. 37, 1404–1405.
Astrov, D. N. (1960). The magnetoelectric effect in antiferromagnetics. (In Russian.) Zh. Eksp. Teor. Fiz. 38, 984–985. (English translation: Sov. Phys. JETP, 11, 708–709.)
Astrov, D. N. (1961). Magnetoelectric effect in chromium oxide. (In Russian.) Zh. Eksp. Teor. Fiz. 40, 1035–1041. (English translation: Sov. Phys. JETP, 13, 729–733.)
Astrov, D. N., Al'shin, B. I., Zorin, R. V. & Drobyshev, L. A. (1968). Spontaneous magnetoelectric effect. (In Russian.) Zh. Eksp. Teor. Fiz. 55, 2122–2127. [English translation: Sov. Phys. JETP, 28 (1969), 1123–1125.]
Barbara, B., Gignoux, D. & Vettier, C. (1988). Lectures on Modern Magnetism. Beijing: Science Press.
Bazhan, A. N. & Bazan, Ch. (1975). Weak ferromagnetism in CoF2 and NiF2. (In Russian.) Zh. Eksp. Teor. Fiz. 69, 1768–1781. (English translation: Sov. Phys. JETP, 42, 898–904.)
Becker, R. & Döring, W. (1939). Ferromagnetismus. Berlin: Springer.
Belov, N. V., Belova, E. N. & Tarkhova, T. N. (1964). Polychromatic plane groups. In Shubnikov & Belov (1964)[link]. Colored Symmetry, edited by W. T. Holser, pp. 228–237. Oxford: Pergamon.
Belov, N. V., Neronova, N. N. & Smirnova, T. S. (1957). Shubnikov groups. (In Russian.) Kristallografiya, 2, 315–325. (English translation: Sov. Phys. Crystallogr. 2, 311–322.)
Bertaut, E. F. (1963). Spin configurations of ionic structures: theory and practice. In Magnetism, Vol. III, edited by G. T. Rado & H. Suhl, pp. 149–209. New York: Academic Press.
Bertaut, E. F., Mercier, M. & Pauthenet, R. (1964). Ordre magnétique et propriétés magnétiques de MnYO3. J. Phys. 25, 550–557.
Bickford, L. R. Jr, Pappis, J. & Stull, J. L. (1955). Magnetostriction and permeability of magnetite and cobalt-substituted magnetite. Phys. Rev. 99, 1210–1214.
Birss, R. R. (1964). Symmetry and Magnetism. Amsterdam: North-Holland.
Birss, R. R. & Anderson, J. C. (1963). Linear magnetostriction in antiferromagnetics. Proc. Phys. Soc. 81, 1139–1140.
Bloembergen, N. (1962). In Proc. Int. Conf. High Magnetic Fields, edited by B. Lax, p. 454. New York: John Wiley.
Borovik-Romanov, A. S. (1959a). Investigation of weak ferromagnetism in the MnCO3 single crystal. (In Russian.) Zh. Eksp. Teor. Fiz. 36, 766–781. (English translation: Sov. Phys. JETP, 9, 539–549.)
Borovik-Romanov, A. S. (1959b). Piezomagnetism in the antiferromagnetic fluorides of cobalt and manganese. (In Russian.) Zh. Eksp. Teor. Fiz. 36, 1954–1955. (English translation: Sov. Phys. JETP, 9, 1390–1391.)
Borovik-Romanov, A. S. (1960). Piezomagnetism in the antiferromagnetic fluorides of cobalt and manganese. (In Russian.) Zh. Eksp. Teor. Fiz. 38, 1088–1098. (English translation: Sov. Phys. JETP, 11, 786–793.)
Borovik-Romanov, A. S. & Orlova, M. P. (1956). Magnetic properties of cobalt and manganese carbonates. (In Russian.) Zh. Eksp. Teor. Fiz. 31, 579–582. [English translation: Sov. Phys. JETP, 4 (1957), 531–534.]
Borovik-Romanov, A. S. & Ozhogin, V. I. (1960). Weak ferromagnetism in an antiferromagnetic CoCO3 single crystal. (In Russian.) Zh. Eksp. Teor. Fiz. 39, 27–36. (English translation: Sov. Phys. JETP, 12, 18–24.)
Borovik-Romanov, A. S. & Yavelov, B. E. (1963). Linear magnetostriction in antiferromagnetic CoF2. In Proc. 3rd Regional Conf. Prague, 81–83.
Brown, P. J. & Chatterji, T. (2006). Neutron diffraction and polarimetric study of the magnetic and crystal structures of HoMnO3 and YMnO3. J. Phys. Condens. Matter, 18, 10085–10096.
Burzo, E. (1993). Magnetic properties of non-metallic inorganic compounds based on transition elements. Boron containing oxides. Landolt-Börnstein III 27 h, Berlin: Springer.
Cardwell, M. J. (1969). Measurements of the magnetic field dependent electric susceptibility of yttrium iron garnet. Phil. Mag. 20, 1087–1089.
Chapon, L. C., Radaelli, P. G., Blake, G. R., Park, S. & Cheong, S. W. (2006). Ferroelectricity induced by acentric spin-density waves in YMn2O5. Phys. Rev. Lett. 96, 097601.
Chappert, J. (1965). Etude par effet Mössbauer de la substitution partielle par le fer du manganèse dans les manganites de terres rares. Phys. Lett. 18, 229–230.
Clark, A. E., DeSavage, B. F., Tsuya, N. & Kawakami, S. (1966). Magnetostriction of dysprosium, holmium, and erbium iron garnets. J. Appl. Phys. 37, 1324–1326.
Cox, D. E. (1974). Spin ordering in magnetoelectrics. Int. J. Magn. 6, 67–75. [Reprinted in Freeman & Schmid (1975)[link], pp. 111–119.]
Cox, D. E., Frazer, B. C., Newnham, R. E. & Santoro, R. P. (1969). Neutron diffraction investigation of the spiral magnetic structure in Cr2BeO4. J. Appl. Phys. 40, 1124–1125.
Cracknell, A. P. (1975). Magnetism in Crystalline Materials. Oxford: Pergamon.
Curie, P. (1894). Sur la symétrie dans les phénomènes physiques, symétrie d'un champ électrique et d'un champ magnétique. J. Phys., 3rd series III, 393–415.
Dzyaloshinskii, I. E. (1957a). Thermodynamic theory of `weak' ferromagnetism in antiferromagnetic substances. (In Russian.) Zh. Eksp. Teor. Fiz. 32, 1547–1562. (English translation: Sov. Phys. JETP, 5, 1259–1272.)
Dzyaloshinskii, I. E. (1957b). The problem of piezomagnetism. (In Russian.) Zh. Eksp. Teor. Fiz. 33, 807–808. [English translation: Sov. Phys. JETP, 6 (1958), 621–622.]
Dzyaloshinskii, I. E. (1957c). The magnetic structure of fluorides of the transition metals. (In Russian.) Zh. Eksp. Teor. Fiz. 33, 1454–1456. [English translation: Sov. Phys. JETP, 6 (1958), 1120–1122.]
Dzyaloshinskii, I. E. (1959). On the magneto-electrical effect in antiferromagnets. (In Russian.) Zh. Eksp. Teor. Fiz. 37, 881–882. [English translation: Sov. Phys. JETP, 10 (1960), 628–629.]
Dzyaloshinskii, I. E. (1964). Theory of helicoidal structures in antiferromagnets. (In Russian.) Zh. Eksp. Teor. Fiz. 46, 1420–1437, 47, 336–348 and 992–1002. [English translation: Sov. Phys. JETP, 19, 960–971, 20 (1965), 223–231 and 665–671.]
Dzyaloshinskii, I. E. & Man'ko, V. I. (1964). Nonlinear effects in antiferromagnets. `Latent' antiferromagnetism. (In Russian.) Zh. Eksp. Teor. Fiz. 46, 1352–1359. (English translation: Sov. Phys. JETP, 19, 915–919.)
Eremenko, V. V., Kharchenko, N. F., Litvinenko, Yu. G. & Naumenko, V. M. (1989). Magneto-optics and spectroscopy of antiferromagnets. (In Russian.) Kiev: Naukova Dumka. [English translation (1992): New York: Springer.]
Faber, J., Lander, G. H. & Cooper, B. R. (1975). Neutron-diffraction study of UO2: observation of an internal distortion. Phys. Rev. Lett. 35, 1770–1773.
Ferré, J. & Gehring, G. A. (1984). Linear optical birefringence of magnetic crystals. Rep. Prog. Phys. 47, 513–611.
Fiebig, M. (2005). Revival of the magnetoelectric effect. J. Phys. D Appl. Phys. 38, R123–R152.
Fiebig, M. & Spaldin, N. A. (2009). Topical issue on Magnetic Interaction Phenomena in Crystals. Eur. Phys. J. B, 71, Issue 3, 293–427.
Folen, V. J., Rado, G. T. & Stalder, E. W. (1961). Anisotropy of the magnetoelectric effect in Cr2O3. Phys. Rev. Lett. 6, 607–608.
Foner, S. (1963). Antiferromagnetic and ferrimagnetic resonance. In Magnetism, Vol. I, edited by G. T. Rado & H. Suhl, pp. 383–447. New York: Academic Press.
Freeman, A. J. & Schmid, H. (1975). Magnetoelectric Interaction Phenomena in Crystals. London: Gordon and Breach.
Gallego, S. V., Tasci, E. S., de la Flor, G., Perez-Mato, J. M. & Aroyo, M. I. (2012). Magnetic symmetry in the Bilbao Crystallographic Server: a computer program to provide systematic absences of magnetic neutron diffraction. J. Appl. Cryst. 45, 1236–1247.
Gijsman, H. M., Poulis, N. J. & Van den Handel, J. (1959). Magnetic susceptibilities and phase transitions of two antiferromagnetic manganese salts. Physica, 25, 954–968.
Gorbatsevich, A. A. & Kopaev, Yu. V. (1994). Toroidal order in crystals. Ferroelectrics, 161, 321–334.
Grimmer, H. (1991). General connections for the form of the property tensors in the 122 Shubnikov point groups. Acta Cryst. A47, 226–232.
Grimmer, H. (1992). The piezomagnetoelectric effect. Acta Cryst. A48, 266–271.
Harris, A. B. (2007). Landau analysis of the symmetry of the magnetic structure and magnetoelectric interaction in multiferroics. Phys. Rev. B, 76, 054447.
Heesch, H. (1930). Über die vierdimensionalen Gruppen des dreidimensionalen Raumes. Z. Kristallogr. 73, 325–345.
Hehl, F. W., Obukhov, Y. N., Rivera, J.-P. & Schmid, H. (2009). Magnetoelectric Cr2O3 and relativity theory. Eur. Phys. J. B, 71, 321–329.
Hou, S. L. & Bloembergen, N. (1965). Paramagnetoelectric effects in NiSO4·6H2O. Phys. Rev. A, 138, 1218–1226.
Hur, N., Park, S., Sharma, P. A., Ahn, J. S., Guha, S. & Cheong, S. W. (2004). Electric polarization reversal and memory in a multiferroic material induced by magnetic fields. Nature (London), 429, 392–395.
Iida, S. (1967). Magnetostriction constants of rare earth iron garnets. J. Phys. Soc. Jpn, 22, 1201–1209.
Indenbom, V. L. (1959). Relation of the antisymmetry and color symmetry groups to one-dimensional representations of the ordinary symmetry groups. Isomorphism of the Shubnikov and space groups. (In Russian.) Kristallografiya, 4, 619–621. [English translation: Sov. Phys. Crystallogr. 4 (1960), 578–580.]
International Tables for Crystallography (2005). Vol. A. Space-Group Symmetry, edited by Th. Hahn. Heidelberg: Springer.
Izyumov, Yu. A. & Naish, V. E. (1979). Symmetry analysis in neutron diffraction studies of magnetic structures. J. Magn. Magn. Mater. 12, 239–248.
Izyumov, Yu. A., Naish, V. E. & Petrov, S. B. (1979). Symmetry analysis in neutron diffraction studies of magnetic structures. J. Magn. Magn. Mater. 13, 267–274, 275–282.
Izyumov, Yu. A., Naish, V. E. & Syromiatnikov, V. N. (1979). Symmetry analysis in neutron diffraction studies of magnetic structures. J. Magn. Magn. Mater. 12, 249–261.
Jackson, J. D. (1999). Classical Electrodynamics, 3rd ed. New York: Wiley.
Joshua, S. J. (1991). Symmetry Principles and Magnetic Symmetry in Solid State Physics. Graduate Student Series in Physics. Bristol: Hilger.
Kadomtseva, A. M., Agafonov, A. P., Lukina, M. M., Milov, V. N., Moskvin, A. S. & Semenov, V. A. (1981). Characteristic magnetoelastic properties of yttrium orthochromite. (In Russian.) Fiz. Tverd. Tela, 23, 3554–3557. (English translation: Sov. Phys. Solid State, 23, 2065–2067.)
Kadomtseva, A. M., Agafonov, A. P., Milov, V. N., Moskvin, A. S. & Semenov, V. A. (1981). Direct observation of symmetry change induced in orthoferrite crystals by an external magnetic field. (In Russian.) Pis'ma Zh. Eksp. Teor. Fiz. 33, 400–403. (English translation: JETP Lett. 33, 383–386.)
Kenzelmann, M., Harris, A. B., Jonas, S., Broholm, C., Schefer, J., Kim, S. B., Zhang, C. L., Cheong, S. W., Vajk, O. P. & Lynn, J. W. (2005). Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3. Phys. Rev. Lett. 95, 087206.
Kharchenko, N. F., Eremenko, V. V. & Belyi, L. I. (1979). Visual observation of 180-degree antiferromagnetic domains. (In Russian.) Pis'ma Zh. Eksp. Teor. Fiz. 29, 432–435. (English translation: JETP Lett. 29, 392–395.)
Kharchenko, N. F. & Gnatchenko, S. L. (1981). Linear magnetooptic effect and visual observation of antiferromagnetic domains in an orthorhombic crystal of DyFeO3. (In Russian.) Fiz. Nizk. Temp. 7, 475–493. (English translation: Sov. J. Low Temp. Phys. 7, 234–243.)
Khomskii, D. (2009). Classifying multiferroics: Mechanisms and effects. Physics, 2, 20.
Kimura, T., Goto, T., Shintani, H., Ishizaka, K., Arima, T. & Tokura, Y. (2003). Magnetic control of ferroelectric polarization. Nature (London), 426, 55–58.
Kiselev, S. V., Ozerov, R. P. & Zhdanov, G. S. (1962). Detection of magnetic order in ferroelectric BiFeO3 by neutron diffraction. (In Russian.) Dokl. Akad. Nauk SSSR, 145, 1255–1258. [English translation: Sov. Phys. Dokl. 7 (1963), 742–744.]
Kopský, V. (1979a). Tensorial covariants for the 32 crystal point groups. Acta Cryst. A35, 83–95.
Kopský, V. (1979b). A simplified calculation and tabulation of tensorial covariants for magnetic point groups belonging to the same Laue class. Acta Cryst. A35, 95–101.
Koptsik, V. A. (1966). Shubnikov Groups. (In Russian.) Moscow: Izd. MGU.
Koptsik, J. N. & Kuzhukeev, Zh.-N. M. (1972). Derivation of the three-, four- and six-color Belov space groups from tables of irreducible representations. (In Russian.) Kristallografiya, 17, 705–711. [English translation: Sov. Phys. Crystallogr. 17 (1973), 622–627.]
Kouvel, J. S. & Fisher, M. E. (1964). Detailed magnetic behavior of nickel near its Curie point. Phys. Rev. A, 136, 1626–1632.
Kovalev, O. V. (1987). Representations of the Crystallographic Space Groups, 2nd ed. (In Russian.) Moscow: Nauka. [English translation (1993): New York: Gordon and Breach.]
Landau, L. D. (1933). Eine mögliche Erklärung der Feldabhängigkeit der Suszeptibilität bei niedrigen Temperaturen. Phys. Z. Sowjet. 4, 675–679.
Landau, L. D. (1937). Zur Theorie der Phasenumwandlungen. I. Phys. Z. Sowjet. 11, 26–47.
Landau, L. D. & Lifshitz, E. M. (1951). Statistical Physics. (In Russian.) Moscow: Gostekhizdat. [English translation (1958): London: Pergamon.]
Landau, L. D. & Lifshitz, E. M. (1957). Electrodynamics of Continuous Media. (In Russian.) Moscow: Gostekhizdat. [English translation (1960): London: Pergamon.]
Le Gall, H., Leycuras, C., Minella, D., Rudashevskii, E. G. & Merkulov, V. S. (1977). Anomalous evolution of the magnetic and magnetooptical properties of hematite at temperature near and lower than the Morin phase transition. Physica B, 86–88, 1223–1225.
Lebeugle, D., Colson, D., Forget, A., Viret, M., Bataille, A. M. & Gukasov, A. (2008). Electric-field-induced spin flop in BiFeO3 single crystals at room temperature. Phys. Rev. Lett. 100, 227602.
Lee, E. W. (1955). Magnetostriction and magnetomechanical effects. Rep. Prog. Phys. 18, 184–229.
Lee, G., Mercier, M. & Bauer, P. (1970). Mesures magnétoélectriques sur les grenats de Y, de Gd et de Dy aux basses températures. In Les éléments des terres rares, Vol. II, pp. 389–399. Paris: Editions du CNRS.
Levitin, R. Z. & Shchurov, V. A. (1973). In Physics and Chemistry of Ferrites, pp. 162–194. (In Russian.) Moscow: Izd. Mosk. Gos. Univ.
Lifshitz, E. M. (1942). On the theory of phase transitions of the second order. J. Phys. (Moscow), 6, 61–74.
Litvin, D. B. (2009). Tensor distinction of domains in ferroic crystals. Eur. Phys. J. B, 71, 315–320.
Lorenz, B., Wang, Y. Q. & Chu, C. W. (2007). Ferroelectricity in perovskite HoMnO3 and YMnO3. Phys. Rev. B, 76, 104405.
Lyubimov, V. N. (1965). The interaction of polarization and magnetization in crystals. (In Russian.) Kristallografiya, 10, 520–524. [English translation: Sov. Phys. Crystallogr. 10 (1966), 433–436.]
Mason, W. P. (1951). A phenomenological derivation of the first- and second-order magnetostriction and morphic effects for a nickel crystal. Phys. Rev. 82, 715–723.
Mason, W. P. (1952). A phenomenological derivation of the first- and second-order magnetostriction and morphic effects for a nickel crystal. Erratum. Phys. Rev. 85, 1065.
Mason, W. P. (1954). Derivation of magnetostriction and anisotropic energies for hexagonal, tetragonal, and orthorhombic crystals. Phys. Rev. 96, 302–310.
Matarrese, L. M. & Stout, J. W. (1954). Magnetic anisotropy of NiF2. Phys. Rev. 94, 1792–1793.
Mercier, R. (1974). Magnetoelectric behaviour in garnets. Int. J. Magn. 6, 77–88. [Reprinted in Freeman & Schmid (1975)[link], pp. 99–110.]
Merkulov, V. S., Rudashevskii, E. G., Le Gall, H. & Leycuras, C. (1981). Linear magnetic birefringence of hematite in the vicinity of the Morin temperature. (In Russian.) Zh. Eksp. Teor. Fiz. 80, 161–170. (English translation: Sov. Phys. JETP, 53, 81–85.)
Michel, Ch., Moreau, J.-M., Achenbach, G. D., Gerson, R. & James, W. J. (1969). The atomic structure of BiFeO3. Solid State Commun. 7, 701–704.
Morin, F. J. (1950). Magnetic susceptibility of α-Fe2O3 and α-Fe2O3 with added titanium. Phys. Rev. 78, 819–820.
Moriya, T. (1960a). Theory of magnetism of NiF2. Phys. Rev. 117, 635–647.
Moriya, T. (1960b). Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98.
Moriya, T. (1963). Weak ferromagnetism. In Magnetism, Vol. I, edited by G. T. Rado & H. Suhl, pp. 85–125. New York: Academic Press.
Néel, L. & Pauthenet, R. (1952). Étude thermomagnétique d'un monocristal de Fe2O3α. C. R. Acad. Sci. 234, 2172–2174.
Neronova, N. N. & Belov, N. V. (1959). Ferromagnetic and ferroelectric space groups. (In Russian.) Kristallografiya, 4, 807–812. (English translation: Sov. Phys. Crystallogr. 4, 769–774.)
Newnham, R. E. (1974). Domains in minerals. Am. Mineral. 59, 906–918.
Newnham, R. E. & Cross, L. E. (1976). Secondary ferroics and domain-divided piezoelectrics. Ferroelectrics, 10, 269–276.
Newnham, R. E., Kramer, J. J., Schulze, W. A. & Cross, L. E. (1978). Magnetoferroelectricity in Cr2BeO4. J. Appl. Phys. 49, 6088–6091.
O'Dell, T. H. (1967). An induced magneto-electric effect in yttrium iron garnet. Philos. Mag. 16, 487–494.
O'Dell, T. H. (1970). The electrodynamics of magneto-electric media. Amsterdam: North-Holland.
Opechowski, W. & Guccione, R. (1965). Magnetic symmetry. In Magnetism, Vol. IIA, edited by G. T. Rado & H. Suhl, pp. 105–165. New York: Academic Press.
Popov, Yu. F., Kazei, Z. A. & Kadomtseva, A. M. (1992). Linear magnetoelectric effect in Cr2O3 in strong magnetic fields. (In Russian.) Pis'ma Zh. Eksp. Teor. Fiz. 55, 238–241. (English translation: JETP Lett. 55, 234–238.)
Prokhorov, A. S. & Rudashevskii, E. G. (1969). Magnetostriction of antiferromagnetic cobalt fluoride. (In Russian.) Pis'ma Zh. Eksp. Teor. Fiz. 10, 175–179. (English translation: JETP Lett. 10, 110–113.)
Prokhorov, A. S. & Rudashevskii, E. G. (1975). Magnetoelastic interactions and the single-domain antiferromagnetic state in cobalt fluoride. (In Russian.) Kratk. Soobshch. Fiz. 11, 3–6. (English translation: Sov. Phys. Lebedev Inst. Rep. 11, 1–4.)
Radaelli, P. G. & Chapon, L. C. (2007). Symmetry constraints on the electrical polarization in multiferroic materials. Phys. Rev. B, 76, 054428.
Rado, G. T. (1961). Mechanism of the magnetoelectric effect in an antiferromagnet. Phys. Rev. Lett. 6, 609–610.
Rado, G. T. (1962). Statistical theory of magnetoelectric effects in antiferromagnets. Phys. Rev. 128, 2546–2556.
Rado, G. T. (1964). Observation and possible mechanisms of magnetoelectric effects in a ferromagnet. Phys. Rev. Lett. 13, 335–337.
Rado, G. T. (1969). Magnetoelectric evidence for the attainability of time-reversed antiferromagnetic configurations by metamagnetic transitions in DyPO4. Phys. Rev. Lett. 23, 644–647, 946.
Rado, G. T. & Ferrari, J. M. (1973). Magnetoelectric effects in TbPO4. AIP Conf. Proc. 10, 1417.
Rado, G. T., Ferrari, J. M. & Maisch, W. G. (1984). Magnetoelectric susceptibility and magnetic symmetry of magnetoelectrically annealed TbPO4. Phys. Rev. B, 29, 4041–4048.
Rado, G. T. & Folen, V. J. (1961). Observation of the magnetically induced magnetoelectric effect and evidence for antiferromagnetic domains. Phys. Rev. Lett. 7, 310–311.
Rado, G. T. & Folen, V. J. (1962). Magnetoelectric effects in antiferromagnetics. J. Appl. Phys. 33 Suppl., 1126–1132.
Rivera, J.-P. (1994). On definitions, units, measurements, tensor forms of the linear magnetoelectric effect and on a new dynamic method applied to Cr–Cl boracite. Ferroelectrics, 161, 165–180.
Rivera, J.-P. (2009). A short review of the magnetoelectric effect and related experimental techniques on single phase (multi-) ferroics. Eur. Phys. J. B, 71, 299–313.
Rivera, J.-P. & Schmid, H. (1994). Search for the piezomagnetoelectric effect in LiCoPO4. Ferroelectrics, 161, 91–97.
Schlenker, M. & Baruchel, J. (1978). Neutron techniques for the observation of ferro- and antiferromagnetic domains. J. Appl. Phys. 49, 1996–2001.
Schmid, H. (1965). Die Synthese von Boraziten mit Hilfe chemischer Transportreaktionen. J. Phys. Chem. Solids, 26, 973–988.
Schmid, H. (1967). Twinning and sector growth in nickel boracites grown by transport reactions. (In Russian.) Rost Krist. 7, 32–65. (English translation: Growth Cryst. USSR, 7, 25–52.)
Schmid, H. (1973). On a magnetoelectric classification of materials. Int. J. Magn. 4, 337–361. [Reprinted in Freeman & Schmid (1975)[link] pp. 121–146.]
Schmid, H. (1994a). Introduction to the proceedings of the 2nd international conference on magnetoelectric interaction phenomena in crystals, MEIPIC-2. Ferroelectrics, 161, 1–28.
Schmid, H. (1994b). Multi-ferroic magnetoelectrics. Ferroelectrics, 162, 317–338.
Schmid, H. (2008). Some symmetry aspects of ferroics and single phase multiferroics. J. Phys. Condens. Matter, 20, 434201.
Schwarzenberger, R. L. E. (1984). Colour symmetry. Bull. London Math. Soc. 16, 209–240.
Scott, R. A. M. & Anderson, J. C. (1966). Indirect observation of antiferromagnetic domains by linear magnetostriction. J. Appl. Phys. 37, 234–237.
Shubnikov, A. V. (1951). Symmetry and antisymmetry of finite figures. (In Russian.) Moscow: Acad. Sci. USSR. [English translation in Shubnikov & Belov (1964) pp. 3–172 and 249–252.]
Shubnikov, A. V. & Belov, N. V. (1964). Colored Symmetry, edited by W. T. Holser. Oxford: Pergamon.
Shubnikov, A. V. & Koptsik, V. A. (1972). Symmetry in Science and Art. (In Russian.) Moscow: Nauka. [English translation (1974): New York: Plenum.]
Shuvalov, L. A. & Belov, N. V. (1962). The symmetry of crystals in which ferromagnetic and ferroelectric properties appear simultaneously. (In Russian.) Kristallografiya, 7, 192–194. (English translation: Sov. Phys. Crystallogr. 7, 150–151.)
Sirotin, Y. I. & Shaskol'skaya, M. P. (1979). Fundamentals of Crystal Physics. (In Russian.) Moscow: Nauka. [English translation (1982): Moscow: Mir.]
Smolenskii, G. A., Agranovskaia, A. I., Popov, S. N. & Isupov, V. A. (1958). New ferroelectrics of complex composition. (In Russian.) Zh. Tekh. Fiz. 28, 2152–2153. (English translation: Sov. Phys. Tech. Phys. 3, 1981–1982.)
Smolenskii, G. A., Yudin, V. M., Sher, E. S. & Stolypin, Yu. E. (1962). Antiferromagnetic properties of some perovskites. (In Russian.) Zh. Eksp. Teor. Fiz. 43, 877–880. [English translation: Sov. Phys. JETP, 16 (1963), 622–624.]
Sosnovska, I., Peterlin-Neumaier, T. & Steichele, E. (1982). Spiral magnetic ordering in bismuth ferrite. J. Phys. C, 15, 4835–4846.
Spaldin, N. A., Fiebig, M. & Mostovoy, M. (2008). The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect. J. Phys. Condens. Matter, 20, 434203.
Tavger, B. A. (1958). The symmetry of ferromagnetics and antiferromagnetics. (In Russian.) Kristallografiya, 3, 339–341. (English translation: Sov. Phys. Crystallogr. 3, 341–343.)
Tavger, B. A. & Zaitsev, V. M. (1956). Magnetic symmetry of crystals. (In Russian.) Zh. Eksp. Teor. Fiz. 30, 564–568. (English translation: Sov. Phys. JETP, 3, 430–436.)
Townsend Smith, T. (1916). The magnetic properties of hematite. Phys. Rev. 8, 721–737.
Turov, E. A. (1963). Physical Properties of Magnetically Ordered Crystals. (In Russian.) Moscow: Akad. Nauk SSSR. [English translation (1965): New York: Academic Press.]
Van Aken, B. B., Rivera, J. P., Schmid, H. & Fiebig, M. (2007). Observation of ferrotoroidic domains. Nature (London), 449, 702–705.
Venevtsev, Yu. N., Gagulin, V. V. & Zhitomirsky, I. D. (1987). Material science aspects of seignette-magnetism problem. Ferroelectrics, 73, 221–248.
Voigt, W. (1928). Lehrbuch der Kristallphysik. Leipzig: Teubner.
Waerden, B. L. van der & Burckhardt, J. J. (1961). Farbgruppen. Z. Kristallogr. 115, 231–234.
White, J. S., Honda, T., Kimura, K., Kimura, T., Niedermayer, C., Zaharko, O., Poole, A., Roessli, B. & Kenzelmann, M. (2012). Coupling of magnetic and ferroelectric hysteresis by a multicomponent magnetic structure in Mn2GeO4. Phys. Rev. Lett. 108, 077204.
White, R. L. (1974). Microscopic origins of piezomagnetism and magnetoelectricity. Int. J. Magn. 6, 243–245. [Reprinted in Freeman & Schmid (1975)[link], pp. 41–43.]
Wijn, H. P. J. (1994). Magnetic properties of non-metallic inorganic compounds based on transition elements. Perovskites. II. Oxides with corundum, ilmenite and amorphous structures. Landolt-Börnstein III, 27, f3, Berlin: Springer.
Yamasaki, Y., Miyasaka, S., Kaneko, Y., He, J. P., Arima, T. & Tokura, Y. (2006). Magnetic reversal of ferroelectric polarization in a multiferroic spinel oxide. Phys. Rev. Lett. 96, 207204.
Zalessky, A. V. (1981). Magnetic properties of crystals. In Modern Crystallography, Vol. IV, edited by L. A. Shuvalov. (In Russian.) Moscow: Nauka. [English translation (1988): Berlin: Springer.]
Zamorzaev, A. M. (1957). Generalization of Fedorov groups. (In Russian.) Kristallografiya, 2, 15–20. (English translation: Sov. Phys. Crystallogr. 2, 10–15.)
Zvezdin, A. K., Zorin, I. A., Kadomtseva, A. M., Krynetskii, I. B., Moskvin, A. S. & Mukhin, A. A. (1985). Linear magnetostriction and antiferromagnetic domain structure in dysprosium orthoferrite. (In Russian.) Zh. Eksp. Teor. Fiz. 88, 1098–1102. (English translation: Sov. Phys. JETP, 61, 645–647.)