Spin dynamics in magnets: Equation of motion and finite temperature effects

General equations of motion are introduced for the evaluation of spin dynamics in magnetic materials. The theory uses the adiabatic separation of diagonal and off-diagonal components of the spin density matrix. This adiabatic approach considers the orientation of the local magnetic moments to be slowly varying relative to their magnitudes. The angles of the magnetization density are introduced as {ital collective} variables in density functional theory. The equations and technique can be simultaneously combined with those of first-principles molecular dynamics for the consistent treatment of spin-lattice interactions. Stochastic and deterministic approaches for treating finite temperature effects are introduced for such dynamics. The method is implemented within the local density approximation and applied to {gamma}-Fe, a frustrated system where we obtain additional low-energy magnetic configurations. {copyright} {ital 1996 The American Physical Society.}