Dynamics of spatially inhomogeneous spin polarization of nonequilibrium conduction electrons in magnetic transitions

The equation of the dynamics of the magnetic moment motion that has been averaged over the ensemble of nonequilibrium spin-injected electrons in a ferromagnetic transition in the presence of exchange interaction, interaction with an external electromagnetic field, and a thermostat has been obtained taking into account the spatial inhomogeneity of the charge carrier distribution. It has been shown that taking into account the spatial inhomogeneity of the charge carrier distribution in the equation of the dynamics of the magnetic moment motion allows for describing the various processes of electron transfer in the magnetic transition. The probability of quantum transitions of electrons with opposite spin directions, which determine spin relaxation in interaction with a thermostat, has been estimated. It has been shown that the anisotropy of the radiation medium is determined not only by the anisotropy of the $sd$-exchange tensor, but also by the additional anisotropy that is caused by the electron impulse derivatives of this tensor. The considered phenomena have a great potential for the detection of new effects and development of new devices based on them, including compact tunable radiation sources in the terahertz frequency range, which is obviously difficult to generate.