Electronic and magnetic properties of van der Waals ferromagnetic semiconductor ${\mathrm{VI}}_3$

Magnetic van der Waals materials with intrinsic magnetic properties provide the ideal platform for exploring magnetism in the low-dimensional limit. In this work, we investigate the electronic and magnetic properties of the ${\mathrm{VI}}_3$ material, a new member of the ferromagnetic van der Waals materials. First-principles results confirm the Mott-insulator state as its electronic ground state. The half-metallic state as reported in the literature is a metastable state, with a total energy 0.2–0.3 eV per ${\mathrm{VI}}_3$ higher than the Mott-insulator state. Magnetocrystalline anisotropy calculations confirm an out-of-plane magnetic easy axis of the ${\mathrm{VI}}_3$ monolayer. We predict the interlayer exchange coupling of the ${\mathrm{VI}}_3$ bilayer to be determined by the interlayer stacking order, ferromagnetic at the most stable and antiferromagnetic at the metastable stacking orders, respectively, reminiscent of the ${\mathrm{CrI}}_3$ material.

Figure 1

The atomic structure of a ${\mathrm{VI}}_3$ monolayer with its unit cell (black lines). The octahedra formed by six neighboring I ions surrounding V ions are shown.

Figure 2

The spin-resolved density of states (DOS) of (a) the Mott-insulating state and (b) the half-metallic state. A Hubbard $U$ of $3.7\mathrm{eV}$ is used in the DOS calculations. (c) The charge density contributed by the states within the narrow conduction band at $1.0\mathrm{eV}$ of the Mott-insulating state.

Figure 3

The calculated energy gap of the Mott-insulating state (circles) and the energy difference between the half-metallic state and the Mott-insulating state (squares) vs the value of the Hubbard $U$ parameter.

Figure 4

The calculated magnetocrystalline anisotropy energy (MAE) of ${\mathrm{VI}}_3$ monolayer. (a) The calculated MAE using the experimental and the relaxed structure vs the value of Hubbard $U$. The experimental lattice constant is used. (b) The calculated MAE as a function of lattice constant by using different Hubbard $U$. The optimal lattice constant is about $7.15\AA$.

Figure 5

Stacking-order-dependent interlayer magnetic exchange coupling in ${\mathrm{VI}}_3$ bilayer. Top view of ${\mathrm{VI}}_3$ bilayer with (a) the $AB$ stacking order and (b) the $A{B}^{\prime }$ stacking order; only V ions are shown for clarity. (c) The calculated total energies and the interlayer magnetic coupling energies of the ${\mathrm{VI}}_3$ bilayer with $AB$ and $A{B}^{\prime }$ stacking orders. The interlayer distance is measured as the distance between I ions across the van der Waals gap.