Giant proximity exchange and valley splitting in transition metal dichalcogenide/hBN/(Co, Ni) heterostructures

Abstract

We investigate the proximity-induced exchange coupling in transition-metal dichalcogenides (TMDCs), originating from spin injector geometries composed of hexagonal boron-nitride (hBN) and ferromagnetic (FM) cobalt (Co) or nickel (Ni), from first principles. We employ a minimal tight-binding Hamiltonian that captures the low energy bands of the TMDCs around K and K′ valleys, to extract orbital, spin-orbit, and exchange parameters. The TMDC/hBN/FM heterostructure calculations show that due to the hBN buffer layer, the band structure of the TMDC is preserved, with an additional proximity-induced exchange splitting in the bands. We extract proximity exchange parameters in the 1-10 meV range, depending on the FM. The combination of proximity-induced exchange and intrinsic spin-orbit coupling (SOC) of the TMDCs, leads to a valley polarization, translating into magnetic exchange fields of tens of Tesla. The extracted parameters are useful for subsequent exciton calculations of TMDCs in the presence of a hBN/FM spin injector. Our calculated absorption spectra show large splittings for the exciton peaks; in the case of MoS2/hBN/Co we find a value of about 8 meV, corresponding to about 50 T external magnetic field in bare TMDCs. The reason lies in the band structure, where a hybridization with Co d orbitals causes a giant valence band exchange splitting of more than 10 meV. Structures with Ni do not show any d level hybridization features, but still sizable proximity exchange and exciton peak splittings of around 2 meV are present in the TMDCs.