Giant proximity exchange and valley splitting in transition metal dichalcogenide/<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>h</mml:mi><mml:mi>BN</mml:mi></mml:mrow></mml:math>/(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 ($h\mathrm{BN}$) 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 ${K}^{\ensuremath{'}}$ valleys, to extract orbital, spin-orbit, and exchange parameters. The TMDC/$h\mathrm{BN}$/FM heterostructure calculations show that due to the $h\mathrm{BN}$ 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 $h\mathrm{BN}$/FM spin injector. Our calculated absorption spectra show large splittings for the exciton peaks; in the case of ${\mathrm{MoS}}_{2}/h\mathrm{BN}$/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.

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