Nonequilibrium steady-state transport properties of magnons in ferromagnetic insulators

Abstract

Understanding nonequilibrium transport phenomena in bosonic systems is highly challenging. Magnons, as bosons, exhibit different transport behavior from fermionic electron spins. This study focuses on the key factors influencing the nonequilibrium transport of magnons in steady states within magnetic insulators by taking Y3Fe5O12 (YIG) for example. 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 power of α (= −µm/(kBT)) are obtained under the condition α<1. It is the biggest different from previous researches 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 a 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 evolves into more complex nonlinear differential equation. We specifically focus on the ferrimagnetic insulator YIG by making a comparison of the spatial distribution of the nonequilibrium magnon density δnm and chemical potential µm between two extreme temperature gradients, namely, ∇T ∼ 1 K/mm and 104 K/mm, which correspond to µm values on the order of −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 is in good agreement with the experimental result. Our theoretical and numerical findings greatly contribute to a profound understanding of the nonequilibrium magnon transport characteristics in magnetic insulators.

玻色子体系中的非平衡输运过程研究是极具挑战性的工作. 磁振子是玻色子, 具有与电子等费米子截然不同的自旋输运行为. 本文以钇铁石榴石(YIG)铁磁绝缘体为研究对象, 聚焦影响稳态下YIG中磁振子非平衡输运过程的关键因素. 通过将具有非零化学势μm的玻色-爱因斯坦统计函数引入到玻尔兹曼输运方程中, 获得了以α为幂次的输运方程严格解析表达式(当α(=−μm/(kBT))<1时). 结果显示, 当α≪1时, 我们得到了与以往研究不同的化学势μm与非平衡粒子浓度δnm之间的非线性关系δnm∝−α1/2∝−(−μm)1/2; α较大时, 则还须考虑其高阶项. 正因这种非线性关系, 导致磁振子扩散方程显著不同于电子自旋扩散特性, 其由线性微分方程演变为更复杂的非线性微分方程. 本文重点研究了在两种极端温度梯度(即∇T∼1K/mm和104K/mm)下非平衡磁振子浓度δnm和化学势μm的空间分布, 它们分别对应于μm的值约为−0.1μeV和−6.2meV, 均满足前提条件α < 1. 在远离平衡态的大温度梯度分布下, 本文理论计算与实验结果吻合很好. 这些理论研究结果将加深人们对铁磁绝缘体中磁振子非平衡输运行为的认识.