Magnetization induced by odd-frequency spin-triplet Cooper pairs in a Josephson junction with metallic trilayers

Abstract

We theoretically study the magnetization inside a normal metal induced in an s-wave superconductor/ferromagnetic metal/normal metal/ferromagnetic metal/s-wave superconductor (S/F1/N/F2/S) Josephson junction. Using the quasiclassical Green's function method, we show that the magnetization becomes finite inside the N. The origin of this magnetization is due to odd-frequency spin-triplet Cooper pairs formed by electrons of equal and opposite spins, which are induced by the proximity effect in the S/F1/N/F2/S junction. We find that the magnetization M(d,θ) in the N can be decomposed into two parts, M(d,θ)=MI(d)+MII(d,θ), where θ is the superconducting phase difference between the two Ss and d is the thickness of N. The θ-independent magnetization MI(d) exists generally in S/F junctions, while MII(d,θ) carries all θ dependence and represents the fingerprint of the phase coherence between the two Ss in Josephson junctions. The θ dependence thus allows us to control the magnetization in the N by tuning θ for a fixed d. We show that the θ-independent magnetization MI(d) weakly decreases with increasing d, while the θ-dependent magnetization MII(d,θ) rapidly decays with d. Moreover, we find that the time-averaged magnetization 〈MII(d,θ)〉 exhibits a discontinuous peak at each resonance dc voltage Vn=nℏωS/2e (n: integer) when dc voltage V as well as ac voltage vac(t) with frequency ωS are both applied to the S/F1/N/F2/S junction. This is because MII(d,θ) oscillates generally in time t (ac magnetization) with dθ/dt=2e[V+vac(t)]/ℏ and thus 〈MII(d,θ)〉=0, but can be converted into the time-independent dc magnetization for the dc voltage at Vn. We also discuss that the magnetization induced in the N can be measurably large in realistic systems. Therefore, the measurement of the induced magnetization serves as an alternative way to detect the phase coherence between the two Ss in Josephson junctions. Our results also provide a basic concept for tunable magnetization in superconducting spintronics devices.

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