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 leads to a suppression of the superconducting order parameter and appearance of spin splitting of the local electronic density of states (LDOS). In classical thin-film heterostructures with a large number of atomic layers it has been well studied. However, with the discovery of 2D materials that open up unprecedented opportunities for the design of new functional materials, an intensive study of proximity effects in van der Waals (vdW) S/F heterostructures has begun. In particular, it was shown that in monolayer S/monolayer F heterostructures the physical mechanism of the proximity effect is determined by the hybridization of their electronic states, what makes its observable manifestations completely different from the classical results and allows for effective control over the proximity effect using gate voltage. Here we demonstrate that the hybridization mechanism of the proximity effect clearly manifests itself in the evolution of the magnetic proximity effect in vdW S/F heterostructures with varying number of the superconducting layers. In particular, the number of superconducting layers determines the number of minima in the dependence of the order parameter on the ferromagnetic exchange field and gating. The spin splitting of the LDOS is very unusual and in general cannot be described by an effective Zeeman field. Physical reasons of such a behavior and possible experimental manifestations are discussed in details.