Irreversible thermodynamics of non-uniform insulating ferromagnets

Two types of damping are commonly applied to describe ferromagnets at the phenomenological level: one by Landau and Lifshitz, and the other by Gilbert. This work successively applies the methods of irreversible thermodynamics to insulators, insulating paramagnets, and uniform insulating ferromagnets, in the last case uniquely obtaining Landau-Lifshitz damping. These methods are then applied to non-uniform insulating ferromagnets, for which new, non-current-related, spin fluxes and spin torques appear. These may be relevant to the dynamics of magnets in confined geometries, where boundary conditions impose complex non-trivial textures. Study of systems with very large damping might help distinguish between the two proposed forms of damping.