Topological states of matter and two-dimensional (2D) magnetism are two fascinating topics attracting tremendous interest in current research. In this work, we explore their interplay in a single 2D material system by proposing a different topological quantum state of matter—the 2D Weyl half-semimetal (WHS), which features 2D Weyl points at the Fermi level belonging to a single spin channel, such that the low-energy electrons are described by fully spin polarized 2D Weyl fermions. We provide the condition to realize this state, which requires an in-plane magnetization and a preserved vertical mirror symmetry. Remarkably, we prove that the WHS state is a critical state sitting at the topological phase transition between two quantum anomalous Hall (QAH) insulator phases with opposite Chern numbers, such that a switching of the QAH states as well as the direction of chiral edge channels can be readily achieved by rotating the magnetization direction. Furthermore, we predict a concrete 2D material, monolayer ${\mathrm{PtCl}}_3$, as a candidate for realizing the 2D WHS state and the above intriguing effects. Our findings open up a new direction of research at the confluent point of topology and magnetism in two dimensions, and the revealed route towards switchable QAH phases will enable new designs of topological nanoelectronic devices.

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.

Tuning the topological and magnetic properties of materials by applying an electric field is widely used in spintronics. In this work, we find a topological phase transition from topologically trivial to nontrivial states at an external electric field of about 0.1 V/Å in a ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ monolayer that is a topologically trivial ferromagnetic semiconductor. It is shown that when electric field increases from 0 to 0.15 V/Å, the magnetic anisotropy energy (MAE) increases from about 0.1 to 6.3 meV, and the Curie temperature $T_C$ increases from 13 to about 61 K. The increased MAE mainly comes from the enhanced spin-orbit coupling due to the applied electric field. The enhanced $T_C$ can be understood from the enhanced $p\text{−}d$ hybridization and decreased energy difference between $p$ orbitals of Te atoms and $d$ orbitals of Mn atoms. Moreover, we propose two Janus materials, ${\mathrm{MnBi}}_2{\mathrm{Se}}_2{\mathrm{Te}}_2$ and ${\mathrm{MnBi}}_2{\mathrm{S}}_2{\mathrm{Te}}_2$ monolayers with different internal electric polarizations, which can realize the quantum anomalous Hall effect (QAHE) with Chern numbers $C=1$ and $C=2$, respectively. Our study not only exposes the electric field induced exotic properties of the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ monolayer but also proposes materials to realize QAHE in ferromagnetic Janus semiconductors with electric polarization.

In two-dimensional (2D) magnetic systems, large magnetic anisotropy is needed to stabilize the magnetic order according to Mermin-Wagner theorem. Based on density-functional theory (DFT) calculations, we propose that the magnetic anisotropic energy (MAE) of 2D ferromagnetic (FM) semiconductors can be strongly enhanced in van der Waals heterostructures by attaching a nonmagnetic semiconductor monolayer with large spin-orbit coupling. We studied ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6/{\mathrm{PtSe}}_2$ bilayer heterostructures, where each layer has been realized in recent experiments. The DFT calculations show that the MAE of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6/{\mathrm{PtSe}}_2$ is enhanced by 70%, and the Curie temperature $T_C$ is increased far beyond room temperature. A model Hamiltonian is suggested to analyze the DFT results, showing that both the Dzyaloshinskii-Moriya interaction and single-ion anisotropy contribute to the enhancement of the MAE. Based on the superexchange picture, we find that the decreased energy difference between $3d$ orbitals of Cr and $5p$ orbitals of Te contributes partially to the increase of $T_C$. Our present work indicates a promising way to enhance the MAE and $T_C$ by constructing van der Waals semiconductor heterostructures, which will inspire further studies on the 2D magnetic semiconductor systems.