  The properties of antiferromagnetic materials with violated space-time parity
are considered. Particular attention is given to the bismuth ferrite BiFeO3
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.
