The Spin Pumping Effect in a Ferromagnetic Insulator/Normal Metal System: A Simple Quantum Mechanical Model

Abstract

A simple quantum mechanical model of the spin pumping effect upon the excitation of a ferromagnetic resonance in a magnetic dielectric having a flat interface with a nonmagnetic metal is constructed. The model is based on the solution of the Schrödinger equation for conduction electrons in metal. It is shown that the reflection of electrons from the insulator with an oscillating magnetization with a spin flip gives rise to both a direct and alternating (oscillating with the frequency of the resonance-exciting microwave field) spin fluxes from the ferromagnet to the insulator. In this case, the effect of direct current is small compared to the effect of the alternating current; the role of a small parameter is played by the ratio of the exchange constant of a ferromagnet to the potential barrier between the metal and the dielectric (which is higher than the Fermi energy). The result obtained is consistent with known experimental data. The model constructed provides a simple and clear picture of the origination of the phenomenon and enable one to analyze the dependence of the effect on the system parameters.