Resistance of a domain wall in the quasiclassical approach

Abstract

Starting from a simple microscopic model, we have derived a kinetic equation for the matrix distribution function. We employed this equation to calculate the conductance $G$ in a mesoscopic F'/F/F' structure with a domain wall (DW). In the limit of a small exchange energy $J$ and an abrupt DW, the conductance of the structure is equal to $G_{2d}=4σ_{\uparrow}σ_{\downarrow }/(σ_{\uparrow}+σ_{\downarrow})L$. Assuming that the scattering times for electrons with up and down spins are close to each other we show that the account for a finite width of the DW leads to an increase in this conductance. We have also calculated the spatial distribution of the electric field in the F wire. In the opposite limit of large $J$ (adiabatic variation of the magnetization in the DW) the conductance coincides in the main approximation with the conductance of a single domain structure $% G_{1d}=(σ_{\uparrow}+σ_{\downarrow})/L$. The account for rotation of the magnetization in the DW leads to a negative correction to this conductance. Our results differ from the results in papers published earlier.