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Quasiparticle density of states and triplet correlations in superconductor/ferromagnetic-insulator structures across a sharp domain wall

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.