  Spin-torque ferromagnetic resonance (ST-FMR) particularly using magnetic
insulators and heavy metals possessing a giant spin Hall effect (SHE) has
gotten 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 representation is
useful to translate physical equations into circuit elements, benchmarking
experiments, and then proposing creative and efficient designs. We utilize the
superposition principle in circuit theory to separate the spin Hall
magnetoresistance and spin pumping contributions in the ST-FMR experiments. We
show that the proposed spin-circuit representation reproduces the standard
results in literature. We further consider multilayers like a spin-valve
structure with an 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 solved using circuit theory.
