Josephson current and $\pi-$state in ferromagnet with embedded superconducting nanoparticles

TL;DR

This paper investigates Josephson effects in superconductor/ferromagnet/superconductor systems with embedded nanostructures, revealing the possibility of $ ext{π}$-states and 0-$ ext{π}$ transitions driven by spacer thickness and temperature.

Contribution

It demonstrates the realization of $ ext{π}$-states in S/F/S junctions with embedded nanostructures despite spatial dispersion, and explores temperature-induced transitions.

Findings

$ ext{π}$-state can occur despite dispersion of electrode distances

Critical current oscillates with ferromagnetic spacer thickness

Transitions between 0 and $ ext{π}$ states can be temperature-controlled

Abstract

On the basis of Usadel equations we investigate superconductor/ferromagnet/superconductor (S/F/S) hybrid systems which consist of superconducting nanostructures (spheres, rods) embedded in ferromagnetic metal. The oscillations of the critical current of the S/F/S Josephson junctions with the thickness of ferromagnetic spacer between superconducting electrodes are studied. We demonstrate that the $\pi $ state can be realized in such structures despite of a dispersion of the distances between different parts of the electrodes. The transitions between 0 and $\pi $ states at some thickness of ferromagnetic spacer can be triggered by temperature variation.