Charge and Spin Currents in Ferromagnetic Josephson junctions

TL;DR

This paper investigates charge and spin currents in ferromagnetic Josephson junctions with various magnetic configurations, revealing how magnetization orientations and phase differences influence supercurrent behavior and spin transfer torques.

Contribution

It provides a self-consistent analysis of charge and spin currents in ballistic ferromagnetic Josephson junctions, including effects of magnetic inhomogeneity and interface scattering.

Findings

Charge supercurrent can reverse or vanish with magnetization orientation changes.

Multiple harmonics in current-phase relations depend on interface scattering and magnetic geometry.

Spin currents induce torques that can switch directions based on magnetic configuration.

Abstract

We determine, using a self consistent method, the charge and spin currents in ballistic Josephson junctions consisting of ferromagnetic ($F$) layers sandwiched between superconducting ($S$) electrodes ($SFS$-type junctions). When there are two $F$ layers, we also consider the experimentally relevant configuration where a normal ($N$) nonmagnetic spacer layer separates them. We study the current-phase relationships as functions of geometrical parameters that are accessible experimentally including the angles that characterize the relative orientation of the magnetization in the $F$ layers. Our self-consistent method ensures that the proper charge conservation laws are satisfied. As we vary the phase difference $\Delta\varphi$ between the two outer $S$ electrodes, multiple harmonics in the current phase relations emerge, their extent depends on the interface scattering strength and the relative $F$ layer widths and magnetization orientations. By manipulating the relative $F$ layer magnetization orientations, we find that the charge supercurrent can reverse directions or vanish altogether. These findings are discussed in the context of the generation and long-range nature of triplet pair correlation. We also investigate the spin currents and associated spin transfer torques throughout the junction. For noncollinear relative magnetizations, the non-conserved spin currents in a given $F$ region gives rise to net torques that can switch directions at particular magnetic configurations or $\Delta\varphi$ values. The details of the spin current behavior are shown to depend strongly on the degree of magnetic inhomogeneity in the system.