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We theoretically study the magnetization inside a normal metal induced in ans-wave superconductor/ferromagnetic metal/normal metal/ferromagneticmetal/s-wave superconductor (S/F1/N/F2/S) Josephson junction. Usingquasiclassical Green's function method, we show that the magnetization becomesfinite inside N. The origin of this magnetization is due to odd-frequencyspin-triplet Cooper pairs formed by electrons of equal and opposite spins,which are induced by proximity effect in the S/F1/N/F2/S junction. We find thatthe magnetization M(d,q) in N can be decomposed into two parts,M(d,q)=MI(d)+MII(d,q), where q is the superconducting phase difference betweentwo Ss and d is the thickness of N. MI(d) exists generally in S/F junctions,while MII(d,q) carries all q dependence and represents the fingerprint of phasecoherence between two Ss in Josephson junctions. The q dependence thus allowsus to control the magnetization in N by tuning q for a fixed d. We show thatMI(d) weakly decreases with increasing d, while the q dependent magnetizationMII(d,q) rapidly decays with d. Moreover, we find that the time-averagedmagnetization <MII(d,q)> exhibits discontinuous peak at each resonance DCvoltage Vn=nhw_S/2e(n: integer) when DC voltage V as well as AC voltage v_ac(t)with frequency w_S are both applied to the S/F1/N/F2/S junction. This isbecause MII(d,q) oscillates generally in time t (AC magnetization) withdq/dt=2e[V+v_ac(t)]/h and thus <MII(d,q)>=0, but can be converted into thetime-independent DC magnetization for DC voltage at Vn. We also discuss thatthe magnetization induced in N can be measurably large in realistic systems.Therefore, the measurement of the induced magnetization serves as analternative way to detect the phase coherence between two Ss in Josephsonjunctions. Our results also provide a basic concept for tunable magnetizationin superconducting spintronics devices.

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