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Abstract The spin current model of electric polarization in multiferroics is justifiedvia the quantum hydrodynamic method and the mean-field part of the spin-orbit interaction.The spin current model is applied to derive the electric polarization proportional to the scalar product of the spins of the nearby ions,which appears to be caused by the Dzylaoshinskii-Moriya interaction.The symmetric tensor spin structure of the polarization is discussed as well.We start our derivations for the ferromagnetic multiferroic materialsand present further generalizations for the antiferromagnetic multiferroic materials.We rederive the operator of the electric dipole moment,which provides the macroscopic polarization obtained via the spin current model.Finally, we use the quantum average of the found electric dipole moment operator to derivethe polarization evolution equation for the antiferromagnetic multiferroic materials.The possibility of spiral spin structures is analyzed.
Andreev et al. (Thu,) studied this question.