NONLINEAR DAMPING IN SPIN SYSTEMS - LONG-RANGE SPIN-SPIN INTERACTIONS

The effective field theory of nonlinear damping for strongly interacting spins driven by external fields and weakly coupled to a bath is derived starting from the microscopic dynamics. The use of a block-spin model with long range spin-spin interactions makes it possible to treat the spin dynamics exactly and to eliminate the microscopic degrees of freedom. The results are presented in form of a nonlinear integro-differential equation for the time and space dependent magnetization. This equation is of memory type, applies to spin-spin interactions of any symmetry and is valid for inhomogeneous external fields of arbitrary strength and time dependence. For an isotropic ferromagnet in weak and slow external fields the general integro-differential equation is shown to reduce to a differential equation of motion of Landau-Lifshitz-Bloch type.