Space-time parity violation and magnetoelectric interactions in antiferromagnets

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 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.