Magnetic multilayers for current flowing perpendicular to the interfaces can also exhibit an effect called spin transfer. Description of the spin transfer and their consequences depends on a hierarchy of models. Quantum mechanical calculations describe the behavior of spins when they scatter from interfaces. In these approaches, the spin-dependent reflection amplitudes to compute the behavior of electrons that have spins that are not collinear with the magnetization of the ferro magnet are used. When electrons in a non-magnet scatter from an interface with a ferro magnet, the two spinor components of the electron's spin along the magnetization separate spatially because the reflection amplitudes are different for the majority and minority electrons. In the process, angular momentum is effectively transferred from the electron spin to the ferromagnetic magnetization. This transfer of angular momentum can be described as a torque from the electron spin on the magnetization.
In this work we applied a effective theory for theoretical description of interactions and behavior of spins when they scatter from interfaces. The result of the quantum mechanical calculations, that the transverse spin current is absorbed by the ferromagnetic magnetization at the interface, enters into transport calculations as a boundary condition. We have used the effective theory for obtaining amplitude and the diffusion equation to compute the torque for various system geometries and magnetic configurations. This calculation reveals the importance of spin flip scattering in determining the polarization of the currents for magnetic multilayers and spin-transfer in magnetic nanostructures.
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