Abstract
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.
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