Spin pumping in a ferromagnetic insulator / normal metal system: a simple quantum-mechanical model

We suggest a simple quantum-mechanical model of the spin pumping effect that appears when the ferromagnetic resonance is excited in a magnetic insulator that has a flat contact with a nonmagnetic metal. The model is based on the solution of Schrodinger equation for conductance electrons in the metal. We show that electron reflection with spin flip at the boundary with the insulator leads to the dc and ac (oscillating with the frequency of microwave field exciting the resonance) spin flow from ferromagnet to insulator. The dc effect is small compared to the ac effect; the small parameter here is the ratio of exchange constant in the ferromagnet to the energy of potential barrier between the metal and insulator which is greater than the Fermi energy. The obtained result agrees to known experimental data. The developed model provides a simple and spectacular insight into the phenomenon roots and allows to make analysis of the effect dependence on the parameters of considered system.