  We study the magnetic and superconducting proximity effects in a
semiconducting nanowire (NW) attached to superconducting leads and a
ferromagnetic insulator (FI). We show that a sizable equilibrium spin
polarization arises in the NW due to the interplay between the superconducting
correlations and the exchange field in the FI. The resulting magnetization has
a nonlocal contribution that spreads in the NW over the superconducting
coherence length and is opposite in sign to the local spin polarization induced
by the magnetic proximity effect in the normal state. For a Josephson-junction
setup, we show that the nonlocal magnetization can be controlled by the
superconducting phase bias across the junction. Our findings are relevant for
the implementation of Majorana bound states in state-of-the-art hybrid
structures.
