Quantum theory of spin transfer and spin pumping in collinear antiferromagnets and ferrimagnets

Antiferromagnets are promising candidates as active components in spintronic applications. They share features with ferrimagnets in that opposing spin orientations exist in two or more sublattices. Spin-transfer torque and spin pumping are essential ingredients in antiferromagnetic and ferrimagnet spintronics. This paper develops an out-of-equilibrium quantum theory of the spin dynamics of collinear magnets containing many spins coupled to normal metal reservoirs. At equilibrium, the spins are parallel or antiparallel to the easy axis. The theory, therefore, covers collinear antiferromagnets and ferrimagnets. We focus on the resulting semiclassical spin dynamics. The dissipation in the spin dynamics is enhanced due to spin pumping. Spin accumulations in the normal metals induce deterministic spin-transfer torques on the magnet. Additionally, each electron's discrete spin angular momentum causes stochastic fluctuating torques on the antiferromagnet or ferrimagnet. We derive these fluctuating torques. The fluctuation-dissipation theorem holds at high temperatures, including the effects of spin pumping. At low temperatures, we derive shot noise contributions to the fluctuations.