Spin-torque ferromagnetic resonance (ST-FMR), particularly using magnetic insulators and heavy metals possessing a giant spin Hall effect (SHE), has received a lot of attention for the development of spintronic devices. To devise complex functional devices, it is necessary to construct the equivalent spin-circuit representations of different phenomena. Such representations are useful for translating physical equations into circuit elements, benchmarking experiments, and then developing creative and efficient designs. We utilize the superposition principle in circuit theory to separate the spin Hall magnetoresistance and spin-pumping contributions in ST-FMR experiments. We show that the proposed spin-circuit representation reproduces the standard results found in the literature. We further consider multilayers like a spin-valve structure with a SHE layer sandwiched by two magnetic layers and show how the corresponding spin-circuit representation can be constructed by simply writing a vector netlist and then solving using circuit theory.

中文翻译：

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自旋扭矩铁磁谐振的自旋电路表示

自旋扭矩铁磁共振（ST-FMR），特别是使用磁绝缘体和具有巨自旋霍尔效应（SHE）的重金属，在自旋电子器件的发展中受到了很多关注。为了设计复杂的功能器件，有必要构建不同现象的等效自旋电路表示。这种表示对于将物理方程转换为电路元件、基准实验以及开发创造性和高效的设计非常有用。我们利用电路理论中的叠加原理来分离 ST-FMR 实验中的自旋霍尔磁阻和自旋泵浦贡献。我们表明，所提出的自旋电路表示再现了文献中发现的标准结果。