  Hybrid semiconducting nanowire devices combining epitaxial superconductor and
ferromagnetic insulator layers have been recently explored experimentally as an
alternative platform for topological superconductivity at zero applied magnetic
field. In this proof-of-principle work we show that the topological regime can
be reached in actual devices depending on some geometrical constraints. To this
end, we perform numerical simulations of InAs wires in which we explicitly
include the superconducting Al and magnetic EuS shells, as well as the
interaction with the electrostatic environment at a self-consistent mean-field
level. Our calculations show that both the magnetic and the superconducting
proximity effects on the nanowire can be tuned by nearby gates thanks to their
ability to move the wavefunction across the wire section. We find that the
topological phase is achieved in significant portions of the phase diagram only
in configurations where the Al and EuS layers overlap on some wire facet, due
to the rather local direct induced spin polarization and the appearance of an
extra indirect exchange field through the superconductor. While of obvious
relevance for the explanation of recent experiments, tunable proximity effects
are of interest in the broader field of superconducting spintronics.
