Inverse proximity effect in thin-film superconductor/magnet heterostructures with metallic and insulating magnets

Proximity effect in thin-film superconductor (S)/magnet heterostructures with different types of magnets including ferromagnets, antiferromagnets and altermagnets is widely considered in the framework of an effective model, where the heterostructure is replaced by a homogeneous superconductor in the presence of a homogeneous exchange field of a corresponding type. Here we study the extent to which such a model is actually applicable to ballistic thin-film superconductor/magnetic heterostructures. In particular, a comparative analysis of thin-film superconductor/magnetic metal and superconductor/magnetic insulator heterostructures is performed. Metallic and insulating ferromagnets (FM, FI) and altermagnets (AM, AI) are considered. It is shown that in the S/FI and S/AI heterostructures the the proximity effect creates a well-defined spin splitting of the electronic spectra in the S layer. Thus, they are well described by the effective model. At the same time, the proximity effect in S/FM and S/AM heterostructures also creates a spin splitting of the spectra of the S layer, but it has a chaotic spectral and spatial distribution and unpredictable amplitude and, in general, cannot be detected via the spin splitting of the superconducting density of states. Thus, the effective model is not applicable to such heterostructures. Nevertheless, we demonstrate that they support well-pronounced triplet correlations and, thus, can be used for spintronics applications.