Crossed Andreev reflection at ferromagnetic domain walls

TL;DR

This paper explores how ferromagnetic domain walls influence superconducting hybrid structures, revealing conditions under which crossed Andreev reflection and Josephson currents occur or are suppressed.

Contribution

It provides a detailed theoretical analysis of crossed Andreev reflection in ferromagnetic domain walls, highlighting the impact of inelastic scattering and domain wall size on transport phenomena.

Findings

Josephson current requires ferromagnetic region smaller than elastic mean free path.

Crossed Andreev reflection enables finite dc current despite suppressed Josephson effect.

Transport properties are similar in S/DW/N and S/DW/S junctions with inelastic scattering.

Abstract

We investigate several factors controlling the physics of hybrid structures involving ferromagnetic domain walls (DWs) and superconducting (S) metals. We discuss the role of non collinear magnetizations in S/DW junctions in a spin $\otimes$ Nambu $\otimes$ Keldysh formalism. We discuss transport in S/DW/N and S/DW/S junctions in the presence of inelastic scattering in the domain wall. In this case transport properties are similar for the S/DW/S and S/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 to crossed Andreev reflection cannot be observed under usual experimental conditions. Nevertheless a finite dc current can circulate across the S/DW/S junction due to crossed Andreev reflection associated to sequential tunneling.