The effects of magnons in spin pumping

Spin pumping theory conventionally models a precessing magnetization as time-dependent classical vector that generates an effective spin chemical potential, or spin battery, driving a spin current into an adjacent conductor. Here, we develop a quantum correction of spin pumping by treating the magnetization as a time-dependent magnonic system at finite temperature. In this approach, the additional spin pumping current is obtained from the conversion of non-equilibrium magnons associated with the precessing magnetization to the electron spin current at the interface. We show that the resulting magnon-driven spin pumping is a significant addition to the classical value at finite temperature. We calculate the magnon contributions both for 2D and 3D magnets.