Quantum scattering theory of spin transfer torque, spin pumping, and fluctuations

Spin transfer torque and spin pumping are central reciprocal phenomena in spintronics. The author demonstrates a way to understand these effects within quantum out-of-equilibrium path-integral model. At finite temperature, frequency, or accumulation, the magnet also experiences fluctuating torques. In regime, transport coefficients related electron shot noise caused by discrete angular momentum of electrons govern fluctuations at low temperatures. results open path for exploring low-temperature magnetization dynamics caloritronics.