First-principles study of spin-orbital coupling induced ferroelectricity in NiBr2

Two-dimensional multiferroic materials have attracted wide interest due to their intriguing physical properties and strong electromagnetic coupling. Among them, ${\mathrm{NiBr}}_{2}$ is unique with a temperature dependent magnetic modulation vector $\mathbf{Q}$ which is linearly related to the electric polarization. In this work, we perform first-principles calculations on the ${\mathrm{NiBr}}_{2}$ monolayer. Density functional theory calculations with appropriate Hubbard correction reproduce the electric polarization and its linear dependence on the magnitude of $\mathbf{Q}$. The calculated polarization decreases as the Hubbard parameter $U$ increases which enlarges the electronic band gap. Our results suggest the spin-orbital coupling effect of Br ions play a crucial role in generating the polarization. Wannier function analysis proves that the major contributor to electric polarization is the Br atomic orbitals which are strongly hybridized with Ni orbitals. The atomic position relaxation has a negligible contribution to the polarization.