Magnetic proximity effect in superconductor/ferromagnet van der Waals heterostructures: Dependence on the number of superconducting monolayers

The magnetic proximity effect in superconductor/ferromagnet (S/F) heterostructures with a large number of atomic layers leads to a suppression of the superconducting order parameter and appearance of Zeeman-like spin splitting of the local density of states (LDOS). Here we study the magnetic proximity effects in van der Waals S/F heterostructures with a few atomic layers and demonstrate that the corresponding physics is very different from the classical results. We find that the dependence of the superconducting order parameter exhibits dips as a function of the ferromagnetic exchange field and gating. The number of dips is determined by the number of monolayers in the heterostructure and, in general, the superconductivity is not suppressed by large values of the exchange field. The spin splitting of the LDOS cannot be described by an effective Zeeman field and manifests a multiple peak structure, where each peak is connected to a unique spin splitting of one of the superconducting bands, which also can be tuned by gating.