Quantum Statistical Derivation of Ferromagnetic-Resonance Equations

From the quantum equation for the density matrix, equations are derived which characterize the behavior of magnetization and mean exchange-interaction energy of ferromagnets in an external magnetic field for a wide temperature region. In the limiting case $T\gg T_C$ ($T_C$ is the Curie temperature), these equations lead to the Bloch-type ferromagnetic-resonance equations (for sufficiently weak magnetic field). In the low-temperature region $T\ll T_C$ these equations lead to the well-known Landau-Lifshitz equations. Expressions for the relaxation times are obtained which connect these parameters with the microscopic properties of ferromagnetic substances.