Two-Dimensional Room-Temperature Ferromagnetic Semiconductors with Quantum Anomalous Hall Effect

To obtain room-temperature ferromagnetic semiconductors and to realize the room-temperature quantum anomalous Hall effect (QAHE) have been big challenges for a long time. Here we report that, on the basis of first-principles calculations, ${\mathrm{Pd}\mathrm{Br}}_3$, ${\mathrm{Pt}\mathrm{Br}}_3$, ${\mathrm{Pd}\mathrm{I}}_3$, and ${\mathrm{Pt}\mathrm{I}}_3$ monolayers are ferromagnetic semiconductors that could exhibit a high-temperature QAHE. The Curie temperatures estimated by Monte Carlo simulations are 350 and 375 K for ${\mathrm{Pd}\mathrm{Br}}_3$ and ${\mathrm{Pt}\mathrm{Br}}_3$ monolayers, respectively. The band gaps of ${\mathrm{Pd}\mathrm{Br}}_3$ and ${\mathrm{Pt}\mathrm{Br}}_3$ are found to be 58.7 and 28.1 meV, respectively, with the generalized-gradient approximation and 100.8 and 45 meV, respectively, with the HSE06 method, being quite well in favor of observing the room-temperature QAHE. It is shown that the large band gaps are induced from multiorbital electron correlations. By carefully studying the stabilities of the four aforementioned monolayers, we unveil that they could be feasible for use in experiments. The present work sheds light on the development of spintronic devices by use of room-temperature ferromagnetic semiconductors and the implementation of dissipationless devices by application of the room-temperature QAHE.

Figure 1

Stable structures of 2D ${\mathrm{Pd}\mathrm{Br}}_3$ and ${\mathrm{Pt}\mathrm{Br}}_3$ monolayers with a honeycomb lattice. (a) Top and side views of the ${\mathrm{Pd}\mathrm{Br}}_3$ (${\mathrm{Pt}\mathrm{Br}}_3$) monolayer as well as the first Brillouin zone with high-symmetry points labeled. $\mathrm{Pd}$ ($\mathrm{Pt}$) atoms form a honeycomb lattice, and a unit cell contains four $\mathrm{Pd}$ ($\mathrm{Pt}$) atoms. Phonon spectra of (b) ${\mathrm{Pd}\mathrm{Br}}_3$ and (c) ${\mathrm{Pt}\mathrm{Br}}_3$ monolayers.

Figure 2

The calculated temperature-dependent free energy of ${\mathrm{Pd}\mathrm{Br}}_3$, ${\mathrm{Pt}\mathrm{Br}}_3$, ${\mathrm{Pd}\mathrm{I}}_3$, and ${\mathrm{Pt}\mathrm{I}}_3$ monolayers, where ${\mathrm{Pd}\mathrm{Cl}}_3$ is included for comparison.

Figure 3

Half-ferromagnetic ${\mathrm{Pd}\mathrm{Br}}_3$ and ${\mathrm{Pt}\mathrm{Br}}_3$ monolayers with Curie temperatures above room temperature. (a) Total energy of the ${\mathrm{Pd}\mathrm{Br}}_3$ monolayer as a function of the lattice constant for FM and AFM configurations. (b) Band structure of the ${\mathrm{Pd}\mathrm{Br}}_3$ monolayer without inclusion of SOC, where the bands for spin-down electrons are too far from the Fermi level to be included. (c) Possible configurations of $\mathrm{Pd}$ ($\mathrm{Pt}$) spins on the honeycomb lattice: FM, NAFM, SAFM, and ZAFM. (d) Temperature dependence of the normalized magnetic moment of ${\mathrm{Pd}\mathrm{Br}}_3$ and ${\mathrm{Pt}\mathrm{Br}}_3$ monolayers by Monte Carlo simulations.

Figure 4

Room-temperature QAHE in ${\mathrm{Pd}\mathrm{Br}}_3$ and ${\mathrm{Pt}\mathrm{Br}}_3$ monolayers. The band structure of (a) ${\mathrm{Pd}\mathrm{Br}}_3$ and (b) ${\mathrm{Pt}\mathrm{Br}}_3$ monolayers with SOC, where the Chern number $C$ of nontrivial bands near the Fermi level is indicated, where the band gaps are 58.7 and 28.1 meV for the ${\mathrm{Pd}\mathrm{Br}}_3$ and ${\mathrm{Pt}\mathrm{Br}}_3$ monolayers, respectively. Anomalous Hall conductivity of (c) ${\mathrm{Pd}\mathrm{Br}}_3$ and (d) ${\mathrm{Pt}\mathrm{Br}}_3$ monolayers as a function of energy near the Fermi level. The surface states of (e) ${\mathrm{Pd}\mathrm{Br}}_3$ and (f) ${\mathrm{Pt}\mathrm{Br}}_3$ monolayers. Warmer colors represent higher local density of states, and blue regions indicate the bulk band gap. The results are obtained by GGA plus SOC plus $U$ calculations.