Modeling multi-magnet networks interacting via spin currents

Abstract

The significant experimental advances of the last few decades in dealing with the interaction of spin currents and nanomagnets, at the device level, have allowed envisioning a broad class of devices that propose to implement information processing using spin currents and nanomagnets. To analyze such spin-magnet logic circuits, in general, we have developed a coupled spin-transport/magnetization- dynamics simulation framework that could be broadly applicable to various classes of spin-valve/spin-torque devices. Indeed, the primary purpose of this chapter is to describe in detail the overall approach we have developed to include a description of spin transport coupled with magnetization dynamics and to show how it was benchmarked against available data on experiments. We address noncollinear spin transport in section "Circuit Representation of Spin Transport" using a lumped "four-component spin-circuit formalism" that describes the interaction of noncollinear magnets (required for modeling spin torque), by computing four-component currents and voltages at every node of a "circuit." For modeling the magnetization dynamics, we use the standard Landau-Lifshitz-Gilbert (LLG) equation with the Slonczewski and the field-like terms included for spin torque. Section "A Coupled Spin-Transport/Magnetization-Dynamics Simulator" describes how this LLG model is coupled with the spin-transport model to analyze spin-torque experiments and spin-magnet circuits in general. We include MATLAB codes in the Additional Information to facilitate a "hands-on" understanding of our model and hope it will enable interested readers to conveniently analyze their own experiments, develop a deeper insight into spin-magnet circuits, or come up with their own creative designs.