Dynamic equations for individual spins in materials with magnetic order: The ideal ferromagnet

The time and temperature dependence of individual spins is studied in an ideal ferromagnet. Starting from the Heisenberg Hamiltonian in a magnetic field and, building on linear-response theory, we derive the linearized microscopic analogy to the macroscopic Landau-Lifshitz equations of motion for magnetization. The dynamical equations take into account the influence of spin correlations in addition to the molecular field. In order to illustrate the validity of our approach, we calculate the temperature-dependent spin-wave spectrum and Landau damping by employing a finite-temperature perturbation theory for spin operators. The latter is adapted to suit higher-order spin-correlation functions which can be described by simple quasiparticle interactions with the spin system. Our results agree with those established on the thermodynamics of the Heisenberg model. In addition, we provide a method of how to deduce macroscopic equations of the Landau-Lifshitz type from first principles, including temperature dependence and damping. [S0163-1829(99)06141-X].