The contribution of the magnetoelectric effect in ferromagnetic and antiferromagnetic materials to the Landau–Lifshitz–Gilbert equation has been considered in the case where the polarization of the medium is caused by the parallel component of neighboring spins. This contribution has been compared to the contribution of the magnetoelectric effect to the Landau–Lifshitz–Gilbert equation when the polarization of the medium is caused by the perpendicular component of spins. The dispersion relation of spin waves in antiferromagnets with a cycloidal equilibrium spin order has been derived. The permittivity of antiferromagnetic multiferroics has been analytically obtained in the case where the magnetoelectric effect is caused by the collinear component of the spins.
P. Andreev (Thu,) studied this question.