Unified theory of spin and charge in a ferromagnet

We derive a unified theory of spin and charge degrees of freedom in a ferromagnet. The spin-transfer torque and spin electromotive force are examined from the coarse-grained perspective of collective coordinates. The resulting equations of motion reflect a balance of conservative, gyroscopic (Berry-phase), and dissipative forces. We then expand the space of collective coordinates by adding the electric charge. The adiabatic spin-transfer torque and spin electromotive force (emf) turn out to be a gyroscopic force; their nonadiabatic counterparts are a dissipative force.

Automated summary

We propose a unified theory for the spin and charge degrees of freedom in a ferromagnet. The spin-transfer torque and spin electromotive force are analyzed from the macroscopic perspective of collective coordinates. The resulting equations of motion demonstrate a balance between conservative, gyroscopic (Berry-phase), and dissipative forces. Furthermore, by introducing the electric charge, we expand the space of collective coordinates. The adiabatic spin-transfer torque and spin electromotive force are found to be gyroscopic forces, while their nonadiabatic counterparts act as dissipative forces.