Theoretical study of magnetism induced by proximity effect in a ferromagnetic Josephson junction with a normal metal

TL;DR

This paper provides a theoretical analysis of how proximity-induced magnetism in a normal metal within a ferromagnetic Josephson junction can be controlled via the superconducting phase difference, revealing new insights into phase-dependent magnetization.

Contribution

It introduces a theoretical framework for understanding and controlling proximity-induced magnetism in a ferromagnetic Josephson junction through phase difference manipulation.

Findings

Magnetization arises in the normal metal due to specific Cooper pair correlations.

The magnetization can be decomposed into phase-independent and phase-dependent parts.

The phase difference between superconductors allows control over the magnetization amplitude.

Abstract

We theoretically study the magnetism induced by the proximity effect in the normal metal of ferromagnetic Josephson junction composed of two $s$-wave superconductors separated by ferromagnetic metal/normal metal/ferromagnetic metal junction (${S}/{F}/{N}/{F}/{S}$ junction). We calculate the magnetization in the $N$ by solving the Eilenberger equation. We show that the magnetization arises in the ${N}$ when the product of anomalous Green's functions of the spin-triplet even-frequency odd-parity Cooper pair and spin-singlet odd-frequency odd-parity Cooper pair in the ${N}$ has a finite value. The induced magnetization $M(d,\theta)$ can be decomposed into two parts, $M(d,\theta)=M^{\rm I}(d)+M^{\rm II}(d,\theta)$, where $d$ is the thickness of $N$ and $\theta$ is superconducting phase difference between two ${S}$s. Therefore, $\theta$ dependence of $M(d,\theta)$ allows us to control the amplitude of magnetization by changing $\theta$. The variation of $M(d,\theta)$ with $\theta$ is indeed the good evidence of the magnetization induced by the proximity effect, since some methods of magnetization measurement pick up total magnetization in the ${S}/{F}/{N}/{F}/{S}$ junction.