# Anomalous current in diffusive ferromagnetic Josephson junctions

## TL;DR

This paper reveals that diffusive superconductor/ferromagnet/superconductor junctions can exhibit a finite anomalous Josephson current at zero phase difference, contingent on specific magnetic configurations and boundary conditions.

## Contribution

It introduces a method to break magnetization inversion symmetry in quasiclassical theory, enabling the prediction of anomalous Josephson currents in diffusive magnetic systems.

## Key findings

- Anomalous Josephson current can occur at zero phase difference.
- Broken magnetization symmetry is essential for the effect.
- Optimal conditions involve non-coplanar magnetization and specific boundary conditions.

## Abstract

We demonstrate that in diffusive superconductor/ferromagnet/superconductor (S/F/S) junctions a finite, {\it anomalous}, Josephson current can flow even at zero phase difference between the S electrodes. The conditions for the observation of this effect are non-coplanar magnetization distribution and a broken magnetization inversion symmetry of the superconducting current. The latter symmetry is intrinsic for the widely used quasiclassical approximation and prevent previous works, based on this approximation, from obtaining the Josephson anomalous current. We show that this symmetry can be removed by introducing spin-dependent boundary conditions for the quasiclassical equations at the superconducting/ferromagnet interfaces in diffusive systems. Using this recipe we considered generic multilayer magnetic systems and determine the ideal experimental conditions in order to maximize the anomalous current.