LAUSR

We examine a modified drift-diffusion formalism to describe spin transport near an ultrathin magnet whose thickness is similar to or less than the spin dephasing length. Most of the 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 adopt the concept of transmitted mixing conductance, whose application to the drift-diffusion formalism has been limited. For a concise description of physical consequences, we introduce an effective spin transparency. Interestingly, for an ultrathin magnet with a finite dephasing rate, the spin transparency can be even enhanced and there arises a non-negligible 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.