  The strong coupling between magnetism and ferroelectricity was found in rare
earth manganites, where the electric polarization could be induced by special
magnetic ordering. There is no theoretical model that would allow us to study
the static and dynamic properties of electric polarization in strongly
correlated magnetic dielectrics. In the presented research, we have taken the
main step towards the construction of such a fundamental model, and made a
direct connection between the microscopic Katsura-Nagaosa-Balatsky theory and
Mostovoy's phenomenological model for magnetically induced polarization. A
novel description of the ferroelectricity of spin origin is proposed within the
framework of the many-particle quantum hydrodynamics method. It is applied to
the study of cells of magnetic ions, where the electric dipole moment is
proportional to the vector product of spins. Our approach is based on the
many-particle Pauli equation, where the influence of an external magnetic field
is considered. We define the electric dipole moment operator of the ion cell
and introduce the macroscopic polarization as the quantum mechanical average of
that operator. We formulate a model for the description of nonequilibrium
polarization and derive a new polarization evolution equation. The polarization
switching in ferroelectric magnets with the spiral spin-density-wave state is
considered, and we demonstrate that the proposed model yields known results and
can predict novel effects. The dynamic magnetoelectric effect can be
investigated by employing this novel equation to study the evolution of
polarization.
