Valley spin-splitting in pristine and Cr- and Ni-doped HfN2 monolayers

Abstract

Using first-principles calculations, we systematically studied the spin–orbit coupling (SOC)-induced valley spin splitting in a pristine HfN₂ monolayer (HfN₂-ML) and in Cr- and Ni-doped systems. The pristine HfN₂-ML is revealed to host a direct band gap at the K and K′ points of the Brillouin zone. The valley spin splitting reaches 350 meV for the conduction bands and 83.5 meV for the valence bands. Furthermore, the exciton binding energy of the HfN₂-ML is estimated to be approximately 0.90 eV. The exciton ground states belong to the Wannier–Mott type, which are governed by the electron and hole band edge states. More importantly, the valley spin at the K and K′ points could substantially change the effects when Cr or Ni is doped into the HfN₂-ML. Consequently, the Cr-doped HfN₂ monolayer exhibits a pronounced Zeeman splitting of approximately 300 meV. These findings highlight the promise of the HfN₂-ML and related two-dimensional (2D) materials for prospective applications in valleytronic and spintronic devices.