Abstract
We extended McMillan’s Green’s function method to study the equilibrium spin current(ESC) in a ferromagnet/ferromagnet (FM/FM) tunnelling junction, in which the magneticmoments in both FM electrodes are not collinear. The single-electron Green’s function ofthe junction system is directly constructed from the elements of the scattering matrix,which can be obtained by matching wavefunctions at boundaries. The ESC is found to bedetermined only by the Andreev-type reflection amplitudes as in the Josephson effect. Theobtained expression of ESC is an exact result and at the strong barrier limit gives the sameexplanation for the origin of ESC as the linear response theory, that is, ESC comes fromthe exchange coupling between the magnetic moments of the two FM electrodes,J∼hl × hr. In the weak barrier region, ESC cannot form spontaneously in a noncollinear FM/FMjunction when there is no tunnelling barrier between the two FM electrodes.
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