Nematic versus ferromagnetic spin filtering of triplet Cooper pairs in superconducting spintronics

TL;DR

This paper compares nematic and magnetic Josephson junctions with magnetic layers that filter triplet Cooper pairs, revealing distinct behaviors in charge and spin currents based on the type of filter and their orientations.

Contribution

It introduces a detailed theoretical analysis of how nematic and magnetic filters differently influence triplet Cooper pair transport in superconducting spintronics.

Findings

Nematic JJs' currents are independent of filter axis orientation.

Magnetic JJs' currents vanish with antiparallel filter axes.

A duality exists between phase difference and exchange field angle.

Abstract

We consider two types of magnetic Josephson junctions~(JJ). They are formed by two singlet superconductors~S and magnetic layers between them so that the JJ is a heterostructure of the S$_{\text{m}}$/n/S$_{\text{m}}$ type, where~S$_{\text{m}}$ includes two magnetic layers with non-collinear magnetization vectors. One layer is represented by a weak ferromagnet and another one---the spin filter---is either conducting strong ferromagnet (nematic or N\nobreakdash-type JJ) or magnetic tunnel barrier with spin-dependent transparency (magnetic or M\nobreakdash-type JJ). Due to spin filtering only fully polarized triplet component penetrates the normal n~wire and provides the Josephson coupling between the superconductors~S. Although both filters let to pass triplet Cooper pairs with total spin~$\mathbf{S}$ parallel to the filter axes, the behavior of nematic and magnetic JJs is completely different. Whereas in the nematic case the charge and spin currents,~$I_{\text{Q}}$ and~$I_{\text{sp}}$, do not depend on mutual orientation of the filter axes, both currents vanish in magnetic~JJ in case of antiparallel filter axes, and change sign under reversing the filter direction. The obtained expressions for~$I_{\text{Q}}$ and~$I_{\text{sp}}$ show clearly a duality between the superconducting phase~$\varphi$ and the angle~$\alpha$ between the exchange fields in the weak magnetic layers.