Hybrid Ising superconductor-ferromagnetic insulator heterostructures provide a unique opportunity to explore the interplay between proximity-induced magnetism, spin-orbit coupling, and superconductivity. Here we use a combination of first-principles calculations of NbSe2/CrBr3 heterostructures and an analytical theory of Ising superconductivity to analyze the existing experiments and provide a complete explanation of highly nontrivial and largely counterintuitive effects: an increase in the magnitude of the superconducting gap accompanied by the broadening of the tunneling peaks; hysteretic behavior of the tunneling conductance that sets in ≈2 K below Tc; and nematic symmetry breaking in the superconducting state. The microscopic reason in all three cases appears to be the interplay between the proximity-induced exchange splitting and intrinsic defects. Finally, we predict additional interesting effects that at the moment cannot be addressed experimentally: spin-filtering when tunneling across CrBr3 and tunneling "hot spots"in momentum space that are anticorrelated with regions where the spin-orbit splitting is maximum.
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