Nonequilibrium phenomena are ubiquitous in nature and in a wide range of systems including cold atomic gases and solidstate materials. While these phenomena are challenging to describe both theoretically and experimentally, they are essential for the fundamental understanding of many-body systems and practical devices. In the context of spintronics, when a magnetic insulator (MI) is subjected to a thermal gradient, a pure spin current is generated in the form of magnons without the presence and dissipation of a charge current—attractive for reducing energy consumption and central to the emerging field of spin caloritronics. However, the experimental methods for directly quantifying a spin current in insulators, and for probing local phonon-magnon nonequilibrium and the associated magnon chemical potential are largely missing Here, we apply a heating laser to generate by a thermal gradient in the MI yttrium iron garnet (YIG): Y${}_3$Fe${}_5$O${}_{12}$ and evaluate two components of the spin current, driven by temperature and chemical potential gradients respectively. The experimental method and theory approach for evaluating quasiparticle chemical potential can be applied for analogous phenomena in other many-body systems. {I. Introduction} Magnetic insulators (MIs) provide a unique model system for exploring nonequilibrium phenomena and developing spintronic applications {….()…()}[1–3]. What is appealing to both fields is the fact that properties of MIs are determined by only two sub-systems, i.e. two types of collective excitations: phonons and magnons, leading to longer energy and spin relaxation times/lengths than those in metallic systems. In particular, thermally driven nonequilibria and the interplay between these phonons and magnons result in a broad range of newly discovered spin caloritronic phenomena, such as spin Seebeck effect [4–6]. Understanding these phenomena requires simultaneous descriptions of nonequilibrium energy (heat) and spin transport ….()()..()()()()……()…. ()()().()()()().()……..[7–12]. Theoretical and experimental advances are both necessary to address the outstanding challenges in this emerging frontier of spintronics and nonequilibrium systems in general. In this paper, we measure thermally generated spin current in YIG and quantitatively evaluate its two components driven by temperature and magnon chemical potential gradients. More specifically, a heating laser is used to introduce a large temperature gradient …..()()………[9]. Along this gradient, micro Brillouin light scattering (BLS) was used to measure the local lattice temperature and nonequilibrium magnon density, from which the spatially varying magnon chemical potential is explicitly determined. Based on the magnon temperature and chemical potential profiles, we quantify two components of the spin current and calculate the magnon nonequilibrium spectral density. This new method for measuring spin current in MIs without any interfacial effects, as well as quantitative evaluation of the magnon …

中文翻译：

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非平衡磁绝缘子中的纯自旋电流和磁振子化学势

非平衡现象在自然界和广泛的系统中无处不在，包括冷原子气体和固态材料。尽管从理论上和实验上都难以描述这些现象，但它们对于基本了解多体系统和实际设备至关重要。在自旋电子学中，当磁绝缘体（MI）经受热梯度作用时，会以磁振子的形式生成纯自旋电流，而不会存在和耗散充电电流，这对于降低能耗是很有吸引力的，并且对旋转中心至关重要自旋量热电子学的新兴领域。但是，用于直接量化绝缘子中的自旋电流以及探测局部声子-磁振子非平衡以及相关的磁振子化学势的实验方法在这里大为缺失。${}_3$铁${}_5$Ø${}_{12}$并评估旋转电流的两个分量，分别由温度和化学势梯度驱动。用于评估准粒子化学势的实验方法和理论方法可以应用于其他多体系统中的类似现象。{一世。简介}磁绝缘体（MI）提供了一个独特的模型系统，用于探索非平衡现象并开发自旋电子学应用{…。（）…（）} [1-3]。对这两个领域都有吸引力的是，MI的性质仅由两个子系统（即两种类型的集体激发：声子和磁振子）决定，与金属系统相比，它导致更长的能量和自旋弛豫时间/长度。尤其是，热驱动的非平衡以及这些声子和磁振子之间的相互作用导致了许多新发现的自旋量热电子现象，例如自旋塞贝克效应[4-6]。理解这些现象需要同时描述非平衡能量（热）和自旋输运…。（）（）..（）（）（）（）……（）...。（）（）（）。（）（）（）（）。（）…….. [7-12]。理论上和实验上的进步对于解决自旋电子学和非平衡系统这一新兴领域中的巨大挑战都是必要的。在本文中，我们测量了YIG中热产生的自旋电流，并定量评估了由温度和磁振子化学势梯度驱动的两个分量。更具体地说，使用加热激光器来引入较大的温度梯度……..（）（）……[9]​​。沿着这个梯度，微型布里渊光散射（BLS）用于测量局部晶格温度和非平衡磁振子密度，从而明确确定空间变化的磁振子化学势。基于磁振子温度和化学势分布，我们量化了自旋电流的两个分量，并计算了磁振子非平衡谱密度。这种测量MI中自旋电流而没有任何界面效应的新方法，以及对磁振子的定量评估…… 我们量化了自旋电流的两个分量，并计算了磁振子非平衡谱密度。这种测量MI中自旋电流而没有任何界面效应的新方法，以及对磁振子的定量评估…… 我们量化了自旋电流的两个分量，并计算了磁振子非平衡谱密度。这种测量MI中自旋电流而没有任何界面效应的新方法，以及对磁振子的定量评估……