Energy Repartition of Magnons in Nonequilibrium Steady States

Magnetic insulators with weakly damped dynamics are ideal model systems to study the thermodynamics of nonequilibrium steady states (NESS). We study the properties of thermal magnons in a classical Heisenberg spin chain by analytical solutions of the stochastic Landau-Lifshitz-Gilbert equation with Markovian damping in contact with local Langevin heat baths. Fluctuations are goverened by a set of normal-mode temperatures, independent of material parameters and the external magnetic field, but depending only on the bath temperature profile and the boundary conditions. The non-equilibrium magnon accumulation can be parameterized by a magnon temperature and chemical potential. We predict new regimes for the spin Seebeck effect at low temperatures that cannot be described by magnon diffusion.