Spin transparency for an interface of an ultrathin magnet within the spin dephasing length

Abstract

We examine a modified drift-diffusion formalism to describe spin transport near a ultrathin magnet whose thickness is similar to or less than the spin dephasing length. Previous theories on spin torque assume the transverse component of a injected spin current dephases perfectly thus are fully absorbed into the ferromagnet. However, in the state-of-art multilayer systems under consideration of recent studies, the thicknesses of ferromagnets are on the order of or less than a nanometer, thus one cannot safely assume the spin dephasing to be perfect. To describe the effects of a finite dephasing rate, we introduce an effective spin transparency, which determines the spin torque efficiency. Interestingly, for an ultrathin magnet with a finite dephasing rate, the spin transparency can be even enhanced and there arises a nonnegligible field-like spin-orbit torque even in the absence of the imaginary part of the spin mixing conductance. The effective spin transparency provides a simple extension of the drift-diffusion formalism which is accessible to experimentalists analyzing their results.