Stability and magnetism of strongly correlated single-layerVS2

Single-layer transition metal dichalcogenides exhibit a variety of atomic structures and associated exotic electronic and magnetic properties. Density-functional calculations using the LDA+$U$ approximation show that single-layer ${\mathrm{VS}}_{2}$ is a strongly correlated material, where the stability, phonon spectra, and magnetic moments of the octahedral ($1T$) and the trigonal prismatic ($2H$) structures significantly depend on the effective Hubbard $U$ parameter, ${U}_{\mathrm{eff}}$. Comparison with the HSE06 hybrid density functional used as a benchmark indicates that ${U}_{\mathrm{eff}}=2.5$ eV, which consistently shows that the $2H$ structure is more stable than the $1T$ structure and a ferromagnetic semiconductor. The magnetic moments are localized on the V atoms and coupled ferromagnetically due to the superexchange interactions mediated by the S atoms. Calculations of the magnetic anisotropy show an easy plane for the magnetic moment. Assuming a classical $\mathit{XY}$ model with nearest neighbor coupling, we determine the critical temperature, ${T}_{\mathrm{c}}$, for the Berezinsky-Kosterlitz-Thouless transition of $2H$ single-layer ${\mathrm{VS}}_{2}$ to be about 90 K. Applying biaxial tensile strains can increase ${T}_{\mathrm{c}}$. Using Wannier interpolation, we evaluate the Berry curvature and anomalous Hall conductivity of $2H$ single-layer ${\mathrm{VS}}_{2}$. The coexistence of quasi-long-range ferromagnetic ordering and semiconducting behavior enables $2H$ single-layer ${\mathrm{VS}}_{2}$ to be a promising candidate for spintronics applications.