Unified drift-diffusion theory for transverse spin currents in spin valves, domain walls, and other textured magnets

Spins transverse to the magnetization of a ferromagnet only survive over a short distance. We develop a drift-diffusion approach that captures the main features of transverse spin effects in systems with arbitrary spin textures (e.g., vortices and domain walls) and generalizes the Valet-Fert theory. In addition to the standard characteristic lengths (mean free path for majority and minority electrons, and spin diffusion length), the theory introduces two length scales, the transverse spin coherence length ℓ(⊥) and the (Larmor) spin precession length ℓ(L). We show how ℓ(L) and ℓ(⊥) can be extracted from ab initio calculations or measured with giant magnetoresistance experiments. In long (adiabatic) domain walls, we provide an analytic formula that expresses the so-called "nonadiabatic" (or fieldlike) torque in terms of these length scales. However, this nonadiabatic torque is no longer a simple material parameter but depends on the actual spin texture: in thin (<10  nm) domain walls, we observe very significant deviations from the adiabatic limit.