Nonequilibrium Transport Properties of Magnons in Steady States in Magnetic Insulators

Abstract Understanding nonequilibrium transport phenomena in bosonic systems is highly challenging. Magnons, as bosons, exhibit distinct transport behavior compared with fermionic electron spins. This study focused on the key factors influencing the nonequilibrium transport of magnons in steady states within magnetic insulators, exemplified by Y3Fe5O12 (YIG). By incorporating the Bose-Einstein distribution function with a non-zero chemical potential μ_m into the Boltzmann transport equation, analytical expressions for transport parameters in powers of α (=-μm/kB T) were obtained, assuming the condition α<1. Our theory establishes a nonlinear relationship between the chemical potential and the nonequilibrium particle density for magnons. Owing to this nonlinear relationship, the magnon diffusion equation markedly differs from that governing electron spin，which evolved into more complex nonlinear differential equation. Our theoretical and numerical findings greatly contribute to a profound understanding of the nonequilibrium magnon transport characteristics in magnetic insulators.