  We investigate the mutual proximity effect in a normal metal contacted to a
superconductor through a magnetic interface. Analytical and self-consistent
numerical results are presented, and we consider both the diffusive and
ballistic regimes. We focus on the density of states in both the normal and
superconducting region, and find that the presence of spin-dependent
phase-shifts occurring at the interface qualitatively modifies the density of
states. In particular, we find that the proximity-induced pairing amplitudes in
the normal metal region undergo a conversion at the Fermi level from pure
even-frequency to odd-frequency. Above a critical value of the interface
spin-polarization (or, equivalently, for fixed interface spin-polarization,
above a critical interface resistance), only odd frequency correlations remain.
This is accompanied by the replacement of the familiar proximity minigap or
pseudogap in the normal layer by an enhancement of the density of states above
its normal state value for energies near the chemical potential. The robustness
of this effect towards inelastic scattering, impurity scattering, and the
depletion of the superconducting order parameter close to the interface is
investigated. We also study the inverse proximity effect in the diffusive
limit. We find that the above-mentioned conversion persists also for thin
superconducting layers comparable in size to the superconducting coherence
length $\xi_\text{S}$, as long as the inverse proximity effect is relatively
weak. Concomitantly, we find a shift in the critical interface resistance where
the pairing conversion occurs. Our findings suggest a robust and simple method
for producing purely odd-frequency superconducting correlations, that can be
tested experimentally.
