Spin-mixing conductances of thin magnetic films from first principles

Abstract

We present a first-principles theory of the spin-mixing conductance for a thin ferromagnetic film embedded epitaxially between two nonmagnetic metallic electrodes. The complex spin-mixing conductance is formulated as a linear response of the spin torque experienced by the film due to the spin accumulation in one of the electrodes. The derivation is based on nonequilibrium Green's functions; the obtained result for the torque response is in agreement with the response of spin fluxes on both sides of the ferromagnet as well as with expressions derived within the Landauer-B\"uttiker scattering theory. Numerical implementation of the developed formalism employs the tight-binding linear muffin-tin orbital method and calculations are performed for selected metallic and half-metallic ferromagnetic films relevant for spintronics applications. The spin-mixing conductance of the $\mathrm{Cu}∕\mathrm{Ni}∕\mathrm{Cu}(100)$ system is found to exhibit pronounced oscillations as a function of Ni thickness; their period is explained by spin-resolved Fermi-surface properties of nickel. Investigated half-metallic films include the full-Heusler ${\mathrm{Co}}_{2}\mathrm{Mn}\mathrm{Si}$ compound and the diluted (Ga,Mn)As magnetic semiconductors attached to nonmagnetic Cr(100) leads; the imaginary part of their spin-mixing conductance has a magnitude comparable to the real part. This unusual feature has been qualitatively explained in terms of a free-electron model.