Nonequilibrium Steady States Transport Properties of Magnons in Magnetic Insulators

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 μm into the Boltzmann transport equation, analytical expressions for transport parameters in powers of α(=-μm/kB T) were obtained, assuming the condition α<1. Compared with the previous works, the biggest difference is that our theory establishes a nonlinear relationship between the chemical potential and the nonequilibrium particle density δnm∝-α1/2∝-(-μm)1/2 for magnons under α≪1. For large chemical potential, higher-order terms of α must be taken into account. Owing to this nonlinear relationship, the magnon diffusion equation markedly differs from that governing electron spin，which evolved into more complex nonlinear differential equation. We specifically focused on the ferrimagnetic insulator YIG, comparing the spatial distribution of the nonequilibrium magnon density δnm and chemical potential μm under two extreme temperature gradients, namely, ∇T~1 K/mm and 104 K/mm. These correspond to μm values in the order of approximately -0.1 μeV and -6.2 meV, respectively, while still satisfying the prerequisite α<1. Given the known temperature gradient distribution, the nonequilibrium magnon density δnm calculated based on our theory agree well with the experimental results. Our theoretical and numerical findings greatly contribute to a profound understanding of the nonequilibrium magnon transport characteristics in magnetic insulators.