Crossed Andreev reflection at ferromagnetic domain walls

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.

18 pages, 8 figures, references added at the end of the introduction

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• Crossed conductance in FSF double junctions: role of out-of-equilibrium populations
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• Long range statistical fluctuations of the crossed Josephson current
• Cooper pair splitting in diffusive magnetic SQUIDs
• Interface effects in d-wave superconductor-ferromagnet junctions
• Cooper pair splitting in ballistic ferromagnetic SQUIDs
• Subgap tunneling via quantum-interference effect: insulators and charge density waves
• Long-range Cooper pair splitting by chiral Majorana edge states