Quantum anomalous Hall effect in monolayer transition-metal trihalides

Abstract

We present systematic first-principles results for the electronic and magnetic properties of two-dimensional transition-metal trihalide monolayers MX3 (M = V, Cr, Mn, Fe, Ni, Pd; X = F, Cl, Br, I), focusing on their potential to host the quantum anomalous Hall effect. In particular, MnF3 and PdF3 exhibit a spin-polarized Dirac cone at the K point, spin-orbit coupling opens a sizable gap with a nonzero Chern number. Nanoribbon slab calculations reveal gap-crossing chiral edge states, establishing the nontrivial topological character. Beyond these case studies, our systematic screening clarifies general trends across the MX3 family and provides insight into how electronic configuration and spin-orbit coupling cooperate to produce magnetic and topological phases in two-dimensional magnets.

Figures (5)

• Figure 1: (a) Top view of $MX_3$ monolayer structure. The black line shows the hexagonal unit cell. Transition-metal atoms form a honeycomb-pattern layered lattice. (b) Schematic illustration of the $MX_6$ octahedron, where each $M^{3+}$ ion is coordinated by six $X^-$ ions.
• Figure 2: Bandstructure obtained for monolayer with SOC taken into account in GGA+$U$ calculation. The spin polarization along the $z$ direction ($S_z$) is shown by red (up spin) and blue (down spin) colors. The Fermi energy $E_{\rm F}$ is set as origin of energy.
• Figure 3: (a) Orbital projection of Pd 3$d$ contributions to the bandstructure in PdF$_3$ without SOC. Purple (green) color band presents $d_{z^2}$ ($d_{x^2-y^2}$) orbital projection. (b) $k$-dependent crystal orbital Hamilton population (COHP) of Pd 3$d$$e_g$ state. (c) COHP diagrams for Pd-Pd neighboring atoms. The Fermi level is set as the energy reference at zero. The COHP curves of the up-spin (down-spin) state are shown in red (blue). The negative regions represent the bonding interactions, while the positive regions denote antibonding interactions. (d) The wavefunctions (real part) at the $\Gamma$ point corresponding to 31st to 34th bands (b31-b34) with odd/even parity. The positive and negative sign is shown by yellow and cyan colors VASPKIT.
• Figure 4: (a) The bandstructure of monolayer PdF$_3$ with $s_z$ polarization in color, red for up spin and blue for down spin. Fermi energy is set to zero. (b) The calculated anomalous Hall conductivity of monolayer PdF$_3$ as a function of energy near the Fermi level.
• Figure 5: Bandstructure of (a) the zigzag and (b) the armchair edges of the PdF$_3$ nanoribbon, with the edge states connecting the 2D valence and conduction bands. (c) The charge density distribution in the zigzag edge of PdF$_3$ nanoribbon.