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

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, $M(d,\theta )=M^{\mathrm{I}}(d)+M^{\mathrm{II}}(d,\theta )$, 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.

18 pages, 5 figures. arXiv admin note: text overlap with arXiv:1507.03763

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