  The significant experimental advances of the last few decades in dealing with
the interaction of spin currents and nanomagnets, at the device level, has
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 non-collinear spin-transport in Section-2 using a lumped
"4-component spin-circuit formalism" that describes the interaction of
non-collinear magnets (required for modeling spin torque), by computing
4-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-3 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 Appendix 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.
