First order $0$ - $\pi$ phase transitions in superconductor/ferromagnet/superconductor trilayers

TL;DR

This paper investigates the thermodynamics and phase transitions in superconductor/ferromagnet/superconductor trilayers, revealing a first order $0$-$oldsymbol{\pi}$ transition with observable effects on magnetic penetration depth and Josephson junction behavior.

Contribution

It introduces a self-consistent Ginzburg--Landau framework for SFS trilayers, capturing the first order $0$-$oldsymbol{\pi}$ transition and strong anharmonicity near the transition point.

Findings

First order $0$-$oldsymbol{\pi}$ transition as temperature varies.

Strong anharmonicity in the Josephson current-phase relation.

Coexistence of stable and metastable $0$ and $oldsymbol{\pi}$ states in rf SQUIDs.

Abstract

We study the thermodynamics of the diffusive SFS trilayer composed of thin superconductor (S) and ferromagnet (F) layers. On the basis the self-consistent solutions of nonlinear Usadel equations in the F and S layers we obtain the Ginzburg--Landau expansion and compute the condensation free energy and entropy of the $0$ (even) and $\pi$ (odd) order parameter configurations. The first order $0-\pi$ transition as a function of temperature $T$ occurs, which is responsible for a jump of the averaged magnetic field penetration depth $\lambda(T)$ recently observed on experiments [N.Pompeo, et. al., Phys. Rev. B 90, 064510 (2014)]. The generalized Ginzburg-Landau functional was proposed to describe SFS trilayer for arbitrary phase difference between the superconducting order parameters in the S layers. The temperature dependence of the SFS Josephson junction critical current demonstrates the strong anharmonicity of the corresponding current--phase relation in the vicinity of the $0-\pi$ transition. In rf SQUID, coexistence of stable and metastable $0$ and $\pi$ states provides integer and half--integer fluxoid configurations.