The properties of antiferromagnetic materials with violated space-time parity are considered. Particular attention is given to the bismuth ferrite BiFeO 3 ferroelectric magnet. This material is distinguished from other antiferromagnets in that the inversion center is absent in its crystal and magnetic structures. This circumstance gives rise to the diversified and unusual properties, namely, to the appearance of a spatially modulated spin structure and to the unique possibility of the linear magnetoelectric effect coexisting with a weak ferromagnetic moment. The magnetic-induced phase transitions accompanied by the suppression of the modulated spin structure and appearance of a number of new and unusual effects are considered. These are the linear magnetoelectric effect and the appearance of a toroidal moment and a weak ferromagnetic moment of the magnetoelectric nature.

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The magnetic, electric, magnetoelectric, and magnetoelastic properties of rare-earth ferroborates RFe3(BO3)4 (R=Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er) as well as yttrium ferroborate YFe3(BO3)4 have been studied comprehensively. A strong dependence not only of the magnetic but also magnetoelectric properties on the type of rare-earth ion, specifically, on its anisotropy, which determines the magnetic structure and the large contribution to the electric polarization, has been found. This is manifested in the strong temperature dependence of the polarization below the Néel point TN and its specific field dependence, which is determined by the competition between the external and exchange f-d fields. A close correlation has been found between the magnetoelastic properties of ferroborates and the magnetoelastic and magnetic anomalies at magnetic-field induced phase transitions. It is found that in easy-plane ferroborates, together with magnetic-field induced electric polarization spontaneous polarization also arises below the Néel point. The ferroelectric ordering in ferroborates is of extrinsic character, giving rise to strong magnetoelectric coupling below TN. Aside from the antiferromagnetic phase transition, the particulars of the structural phase transition accompanied by anomalies of the dielectric and magnetoelectric properties are examined for the first time. The character of the dielectric anomalies at a structural transition is analyzed for the first time on the basis of Landau’s approach.