  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
quasiclassical Green's function method, we show that the magnetization becomes
finite inside 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 proximity effect in the S/F1/N/F2/S junction. We find that
the 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 between
two 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 phase
coherence between two Ss in Josephson junctions. The q dependence thus allows
us to control the magnetization in N by tuning q for a fixed d. We show that
MI(d) weakly decreases with increasing d, while the q dependent magnetization
MII(d,q) rapidly decays with d. Moreover, we find that the time-averaged
magnetization <MII(d,q)> exhibits discontinuous peak at each resonance DC
voltage 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 is
because MII(d,q) oscillates generally in time t (AC magnetization) with
dq/dt=2e[V+v_ac(t)]/h and thus <MII(d,q)>=0, but can be converted into the
time-independent DC magnetization for DC voltage at Vn. We also discuss that
the magnetization induced in 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 two Ss in Josephson
junctions. Our results also provide a basic concept for tunable magnetization
in superconducting spintronics devices.
