Anomalous Josephson current through a ferromagnetic trilayer junction

TL;DR

This paper investigates the anomalous Josephson current in ferromagnetic trilayer junctions with noncoplanar magnetizations, demonstrating tunable phase differences and supercurrent amplitudes, and providing a physical explanation based on spin precession.

Contribution

It introduces a detailed analysis of the anomalous Josephson effect in ferromagnetic trilayers, including a physical model linking spin precession to the observed phenomena.

Findings

Achieved a $C6/2$ junction with equilibrium phase difference C6/2.

Demonstrated that the supercurrent amplitude and phase difference are tunable via structure parameters.

Provided a physical picture connecting spin precession to the anomalous Josephson effect.

Abstract

We studied the anomalous Josephson current appearing at zero phase difference in junctions coupled with a ferromagnetic trilayer which has noncoplanar magnetizations. A $\pi/2$ junction with an equilibrium phase difference $\pi/2$ is obtained under suitable conditions. The equilibrium phase difference and the amplitude of the supercurrent are all tunable by the structure parameters. In addition to calculating the anomalous current using the Bogoliubov-de Gennes equation, we also developed a clear physical picture explaining the anomalous Josephson effect in the structure. We show that the triplet proximity correlation and the phase shift in the anomalous current-phase relation all stem from the spin precession in the first and third ferromagnet layers.