Theoretical seminar | 21 February 2023

There is a version of the Landau-Lifshitz equation that takes into account the exchange interaction between atoms. It contains the vector product of the magnetization by the second spatial derivative of the magnetization. We propose a fundamental microscopic derivation of such an equation as part of a system of equations for the evolution of macroscopic characteristics of the medium. Despite the fact that we are considering a crystal lattice in which ions do not move in an ordered manner in space, the resulting equations have the form of the hydrodynamic equations. Based on the Schrodinger-Pauli equation, which describes the dynamics of atoms in the medium, the equations of the evolution of the magnetic moment, which include the contribution of the exchange interaction of particles with spin S=1/2 or S=1, are obtained. Along with the term described above, an additional contribution is obtained from the nematic tensor, which is the average value of the anticommutator of the spin operators for atoms with spin S=1. For magnetic systems with noncollinear spins subject to antisymmetric exchange interactions, we introduce a microscopic expression for the electric polarization vector and derive an equation for the evolution of polarization in an external magnetic field.

Main paper/arXiv, related to the seminar, and other references

1. Andreev Pavel A., Trukhanova Mariya Iv., Dipolar-drift and collective instabilities of skyrmions in crossed nonuniform electric and magnetic fields in a chiral magnetic insulator, Europhysics Letters, 132, № 5, 56002 (2020).

2. Pavel A Andreev, Extended hydrodynamics of degenerate partially spin polarized fermions with short-range interaction up to the third order by interaction radius approximation, Laser Phys., 31, 045501 (2021).

3. Y. Tokura, S. Seki and N. Nagaosa, Multiferroics of spin origin, Reports on Progress in Physics, 77(7), 076501 (2014).

4. H. Katsura, N. Nagaosa and A. V. Balatsky, Spin current and magnetoelectric effect in noncollinear magnets, Phys. Rev. Lett., 95, 057205 (2005).