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We investigate the proximity-induced exchange coupling in transition-metaldichalcogenides (TMDCs), originating from spin injector geometries composed ofhexagonal boron-nitride (hBN) and ferromagnetic (FM) cobalt (Co) or nickel(Ni), from first-principles. We employ a minimal tight-binding Hamiltonian thatcaptures the low energy bands of the TMDCs around K and K' valleys, to extractorbital, spin-orbit, and exchange parameters. The TMDC/hBN/FM heterostructurecalculations show that due to the hBN buffer layer, the band structure of theTMDC is preserved, with an additional proximity-induced exchange splitting inthe bands. We extract proximity exchange parameters in the 1--10 meV range,depending on the FM. The combination of proximity-induced exchange andintrinsic spin-orbit coupling (SOC) of the TMDCs, leads to a valleypolarization, translating into magnetic exchange fields of tens of Tesla. Theextracted parameters are useful for subsequent exciton calculations of TMDCs inthe presence of a hBN/FM spin injector. Our calculated absorption spectra showlarge splittings for the exciton peaks; in the case of MoS$_2$/hBN/Co we find avalue of about 8 meV, corresponding to about 50 Tesla external magnetic fieldin bare TMDCs. The reason lies in the band structure, where a hybridizationwith Co $d$ orbitals causes a giant valence band exchange splitting of morethan 10 meV. Structures with Ni do not show any $d$ level hybridizationfeatures, but still sizeable proximity exchange and exciton peak splittings ofaround 2 meV are present in the TMDCs.

Giant proximity exchange and valley splitting in transition metal dichalcogenide/$h\mathrm{BN}$/(Co, Ni) heterostructures