Josephson coupling through ferromagnetic heterojunctions with noncollinear magnetizations

TL;DR

This paper investigates how the Josephson current in superconductor-ferromagnet heterojunctions depends on the relative magnetization angle, revealing conditions for monotonic and non-monotonic behavior and the influence of triplet correlations.

Contribution

It provides a comprehensive theoretical analysis of the Josephson effect considering arbitrary magnetization orientations and interface transparencies, highlighting the role of magnetic configuration on current behavior.

Findings

Critical current varies monotonically with magnetization angle for weak ferromagnets.

For stronger ferromagnets, angle variation causes 0-$\

Transitions between 0 and $\

Abstract

We study the Josephson effect in clean heterojunctions that consist of superconductors connected through two metallic ferromagnets with insulating interfaces. We solve the scattering problem based on the Bogoliubov--de Gennes equation for any relative orientation of in-plane magnetizations, arbitrary transparency of interfaces, and mismatch of Fermi wave vectors. Both spin singlet and triplet superconducting correlations are taken into account, and the Josephson current is calculated as a function of the ferromagnetic layers thicknesses and of the angle $\alpha$ between their magnetizations. We find that the critical Josephson current $I_c$ is a monotonic function of $\alpha$ when the junction is far enough from $0-\pi$ transitions. This holds when ferromagnets are relatively weak. For stronger ferromagnets, variation of $\alpha$ induces switching between 0 and $\pi$ states and $I_c(\alpha)$ is non-monotonic function, displaying characteristic dips at the transitions. However, the non-monotonicity is the effect of a weaker influence of the exchange potential in the case of non-parallel magnetizations. No substantial impact of spin-triplet superconducting correlations on the Josephson current has been found in the clean limit. Experimental control of the critical current and $0-\pi$ transitions by varying the angle between magnetizations is suggested.