Phenomenological description of the magnetization relaxation (abstract)

Abstract

The dynamics and relaxation of magnetization M(r,t) is usually described phenomenologically by the Landau–Lifshitz (LL) equation with relaxation term M=−γ[M×F]+R, where γ is the gyromagnetic ratio (γ≳0), F is the effective field, and R describes the relaxation of the magnetization toward its equilibrium value. It is already well known that the relaxation term of either the LL or Gilbert form does not give a correct description of the dependence of spin-wave damping on the wave vector at small wave vectors for the models of an isotropic and easy plane ferromagnet. The correct behavior of the spin wave damping may be obtained by taking into account the spatial dispersion of the relaxation caused by the exchange interaction and correct symmetry structure of the relativistic part of the relaxation term which now has to be represented as a sum of the exchange and relativistic parts by R=Rex+Rτ. A review of the recent results on the relaxation obtained in the frames of the LL equation with the relaxation term suggested by Bar’yakhtar is presented. Comparison of the spin wave damping calculated in the frames of the phenomenological and microscopic approaches has been carried out. In particular it is shown that, in the case of yttrium iron garnet or substituted garnets, the estimation of the value of phenomenological constant of the exchange relaxation has to be carried out by properly taking into account the many sublattice magnetic structure of these magnets. Numerical estimations of the phenomenological relaxation constants for the yttrium iron garnet are given.