Theoretical description of the ferromagnetic $\pi $-junctions near the critical temperature

TL;DR

This paper develops a theoretical framework for understanding ferromagnetic π-junctions near their critical temperature, focusing on the proximity effect and Josephson current oscillations in the dirty limit.

Contribution

It introduces a modified Usadel equation to accurately describe the proximity effect in ferromagnets near the critical temperature, including interface transparency effects.

Findings

Oscillations of Josephson critical current with ferromagnetic layer thickness.

Modified Usadel equation effectively models the proximity effect.

Dependence of critical current on interface transparency.

Abstract

The theory of ferromagnetic Pi-junction near the critical temperature is presented. It is demonstrated that in the dirty limit the modified Usadel equation adequately describes the proximity effect in ferromagnets. To provide the description of an experimentally relevant situation, oscillations of the Josephson critical current are calculated as a function of ferromagnetic layer thickness for different transparencies of the superconductor-ferromagnet interfaces.