Disturbance of spin equilibrium by current through the interface of noncollinear ferromagnets

TL;DR

This paper derives boundary conditions for spin current penetration at interfaces between non-collinear ferromagnets, analyzing how spin accumulation and potential shifts depend on interface properties and magnetization angles.

Contribution

It introduces a new set of boundary conditions for spin current and chemical potential differences at non-collinear ferromagnetic interfaces, considering arbitrary magnetization angles.

Findings

Spin accumulation depends on interface resistance and magnetization angle.

Spin current causes a shift in potential drop at the interface.

No spin scattering assumed at the boundary.

Abstract

Boundary conditions are derived that determine the penetration of spin current through an interface of two non-collinear ferromagnets with an arbitrary angle between their magnetization vectors. We start from the well-known transformation properties of an electron spin wave functions under the rotation of a quantization axis. It allows directly find the connection between partial electric current densities for different spin subbands of the ferromagnets. No spin scattering is assumed in the near interface region, so that spin conservation takes place when electron intersects the boundary. The continuity conditions are found for partial chemical potential differences in the situation. Spatial distribution of nonequilibrium electron magnetizations is calculated under the spin current flowing through a contact of two semi-infinite ferromagnets. The distribution describes the spin accumulation effect by current and corresponding shift of the potential drop at the interface. These effects appear strongly dependent on the relation between spin contact resistances at the interface.