## In the spin polarized transport through

Fig. 1. (Color online.) Schematic illustration of the spin valve with SMM attached on the nonmagnetic metal region. A spin-polarized current flows along the x-axis, and the magnetic configuration of the two ferromagnet leads is antiparallel.Figure optionsDownload full-size imageDownload as PowerPoint slide

Starting with the linear response theory, one finds that the spin current takes the form [8]equation(6)jm→(r,t)=(μB/e)P(r)je→−ξ∂m→(r)∂r, where je→ is the current density, P(r)P(r) is the spin polarization, and ξ is the average LY3039478 constant weighted by conductivities. Taking the spin flip into account, we assume the spin polarization P(r)P(r) fluctuates around constant P0P0, P(r)=P0+acos?rP(r)=P0+acos?r, where a is a small constant. By inserting the spin current density (6) into Eq. (5), the spin diffusion equation can be further expressed asequation(7)∂mx∂t=ξ∇2mx+ajesin?r−J?(mysz−mzsy)−mxτ,∂my∂t=ξ∇2my+ajesin?r−J?(mzsx−mxsz)−myτ,∂mz∂t=ξ∇2mz+ajesin?r−J?(mxsy−mysx)−mzτ. It should be solved self-consistently with Eq. (4).