Crossed Andreev reflection at ferromagnetic domain walls

Abstract

We investigate several factors controlling the physics of hybrid structures involving ferromagnetic domain walls (DW's) and superconducting (S) metals. We discuss the role of noncollinear magnetizations in $S/\mathrm{DW}$ junctions in a $\mathrm{spin}\ensuremath{\bigotimes}\mathrm{Nambu}\ensuremath{\bigotimes}\mathrm{Keldysh}$ formalism. We discuss transport in S/DW/normal metal (N) and $S/\mathrm{DW}/S$ junctions in the presence of inelastic scattering in the domain wall. In this case transport properties are similar for the $S/\mathrm{DW}/S$ and $S/\mathrm{DW}/N$ junctions and are controlled by sequential tunneling of spatially separated Cooper pairs across the domain wall. In the absence of inelastic scattering we find that a Josephson current circulates only if the size of the ferromagnetic region is smaller than the elastic mean free path meaning that the Josephson effect associated with the crossed Andreev reflection cannot be observed under usual experimental conditions. Nevertheless, a finite dc current can circulate across the $S/\mathrm{DW}/S$ junction due to crossed Andreev reflection associated with sequential tunneling.