Spin current through a normal-metal/insulating-ferromagnet junction

We study the spin current across the interface between a normal metal and an insulating ferromagnet in a junction. At the interface, conduction electrons in the normal metal interact with localized moments of the ferromagnet via the sd-type exchange interaction. In the presence of spin accumulation in the normal metal, the spin accumulation decays by spin-flip scattering of conduction electrons at the interface, thereby emitting magnons through the exchange interaction at the interface. Using the linear response theory, we obtain the spin current through the interface, which is proportional to spin accumulation as well as the population of magnons.