Magnetic proximity effect induced spin splitting in two-dimensional antimonene/Fe3GeTe2 van der Waals heterostructures

Recently, two-dimensional van der Waals (vdW) magnetic heterostructures have attracted intensive attention since they can show remarkable properties due to the magnetic proximity effect. In this work, the spin-polarized electronic structures of antimonene/Fe3GeTe2 vdW heterostructures were investigated through the first-principles calculations. Owing to the magnetic proximity effect, the spin splitting appears at the conduction-band minimum (CBM) and the valence-band maximum (VBM) of the antimonene. A low-energy effective Hamiltonian was proposed to depict the spin splitting. It was found that the spin splitting can be modulated by means of applying an external electric field, changing interlayer distance or changing stacking configuration. The spin splitting energy at the CBM monotonously increases as the external electric field changes from -5 V/nm to 5 V/nm, while the spin splitting energy at the VBM almost remains the same. Meanwhile, as the interlayer distance increases, the spin splitting energies at the CBM and VBM both decrease. The different stacking configurations can also induce different spin splitting energies at the CBM and VBM. Our work demonstrates that the spin splitting of antimonene in this heterostructure is not singly dependent on the nearest Sb-Fe distance, which indicates that magnetic proximity effect in heterostructures may be modulated by multiple factors, such as hybridization of electronic states and the local electronic environment. The results enrich the fundamental understanding of the magnetic proximity effect in two-dimensional vdW heterostructures.