Resistance of a domain wall in the quasiclassical approach

TL;DR

This paper derives a kinetic equation for a matrix distribution function to analyze how a domain wall affects conductance in a mesoscopic ferromagnetic structure, revealing that finite width and magnetization rotation influence conductance.

Contribution

It introduces a microscopic model and kinetic equation approach to study domain wall effects on conductance, providing new insights into the influence of domain wall width and magnetization rotation.

Findings

Finite domain wall width increases conductance.

Large exchange energy yields conductance similar to a single domain.

Magnetization rotation causes a negative correction to conductance.

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 $G_{2d}=4\sigma_{\uparrow}\sigma_{\downarrow }/(\sigma_{\uparrow}+\sigma_{\downarrow})L$. 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 $% G_{1d}=(\sigma_{\uparrow}+\sigma_{\downarrow})/L$. 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.