Magnetization dynamics of electron-impurity systems at paramagnetic resonance

Abstract

The equation for the magnetization is obtained on the basis of the kinetic equation for an isotropic distribution function of electrons scattering on massive impurity centers in the presence of magnetic and electric fields. The analytical solution of the Cauchy problem for a given initial distribution of the magnetization under conditions of paramagnetic resonance is obtained. The exact solutions are found for magnetization dynamics in samples having the forms of an ellipsoid of revolution and a cylinder, as well. The influence of magnetic exchange on the surface of the cylinder (III boundary value problem) is taken into account. The dependence of the magnetization on the static electric field is exponentially decreasing with time, with an exponent proportional to the electric field squared times the diffusion coefficient. For a fixed instant of time the magnetization depends nonlocally on the magnitude and direction of the electric field. The estimated dynamic shift of the forced precession has a nonlocal and nonlinear dependence on the nonuniform distribution of the initial magnetization. This shift is estimated with boundary conditions taken into account and is caused by a field similar to the Suhl-Nakamura field in a paramagnetic medium. The dynamic shift of the free precession has only a nonlocal character. The time and space dependence of the internal field is obtained. All results are expressed in terms of the initial distribution of the magnetization without specifying its functional form and in terms of the propagation function, which depends on the shape of the sample. These results may be used for analysis of spin diffusion in natural and manmade materials and also in magnetometry.