  A ferromagnetic insulator (FI) in contact with a superconductor (S) is known
to induce a spin splitting of the BCS density of states at the FI/S interface.
This spin splitting causes the Cooper pairs to reduce their singlet-state
correlations and acquire odd-in-frequency triplet correlations. We consider a
diffusive FI/S bilayer with a sharp magnetic domain wall in the FI and study
the local quasiparticle density of states and triplet superconducting
correlations. In the case of collinear alignment of the domains, we obtain
analytical results by solving the Usadel equation. For a small enough exchange
field or weak superconductivity, we also find an analytical expression for
arbitrary magnetic textures, which reveals how the triplet component vector
depends on the local magnetization of the FI. For an arbitrary angle between
the magnetizations and the strength of the exchange field, we numerically solve
the problem of a sharp domain wall. We finally propose two different setups
based on FI/S/F stacks, where F is a ferromagnetic layer, to filter out singlet
pairs and detect the presence of triplet correlations via tunneling
differential conductance measurements.
