Chern Number Tunable Quantum Anomalous Hall Effect in Monolayer Transitional Metal Oxides via Manipulating Magnetization Orientation

Although much effort has been made to explore quantum anomalous Hall effect (QAHE) in both theory and experiment, the QAHE systems with tunable Chern numbers are yet limited. Here, we theoretically propose that ${\mathrm{NiAsO}}_3$ and ${\mathrm{PdSbO}}_3$, monolayer transitional metal oxides, can realize QAHE with tunable Chern numbers via manipulating their magnetization orientations. When the magnetization lies in the $x\text{−}y$ plane and all mirror symmetries are broken, the low-Chern-number (i.e., $\mathcal{C}=\pm 1$) phase emerges. When the magnetization exhibits nonzero $z$-direction component, the system enters the high-Chern-number (i.e., $\mathcal{C}=\pm 3$) phase, even in the presence of canted magnetization. The global band gap can approach the room-temperature energy scale in monolayer ${\mathrm{PdSbO}}_3$ (23.4 meV), when the magnetization is aligned to $z$ direction. By using Wannier-based tight-binding model, we establish the phase diagram of magnetization induced topological phase transition. Our work provides a high-temperature QAHE system with tunable Chern number for the practical electronic application.

Figure 1

(a) Top and side views of monolayer ${\mathrm{NiAsO}}_3/{\text{PdSbO}}_3$. (b) The first Brillouin zone with high symmetry points, the blue solid lines representing three vertical mirror planes. (c) The bond angle and the schematics of the Ni(Pd)-O-Ni(Pd) superexchange mechanism in the ${\mathrm{NiAsO}}_3$ and ${\mathrm{PdSbO}}_3$ via the $(d_{xz},{\mathrm{d}}_{yz})\text{−}p\text{−}(d_{xz},{\mathrm{d}}_{yz})$ orbitals.

Figure 2

Spin-polarized band structure of monolayer ${\mathrm{NiAsO}}_3$ (a) and ${\mathrm{PdSbO}}_3$ (c). (b) Band structure of monolayer ${\mathrm{NiAsO}}_3$ (b) and ${\mathrm{PdSbO}}_3$ (d) with spin-orbit coupling when the magnetization along $x$ and $z$ direction, respectively.

Figure 3

(a),(c): Bulk band structure of monolayer ${\mathrm{PdSbO}}_3$ along high symmetry line and corresponding anomalous Hall conductivity in the presence of spin-orbit coupling and magnetization lying in $x\text{−}y$ plane for different $\varphi =0°$ (a) and $\varphi =60°$ (c), respectively. (b),(d): Corresponding energy spectra of semi-infinite ribbon of monolayer ${\mathrm{PdSbO}}_3$ for different $\varphi =0°$ (b) and $\varphi =60°$ (d), respectively. Note that there is one gapless edge mode at $k=0$ in (b) and (d). (e)–(h) are similar to those in (a)–(d) but with magnetization along $z$ and $-z$ direction, respectively. Note that there are three gapless edge modes near $k=0$, $\pi$ and $-\pi$ in (f) and (h). (i) The distribution of the Berry curvatures for monolayer ${\mathrm{PdSbO}}_3$ with in-plane magnetization along $x$ direction and (k) out-of-plane magnetization along $z$ direction, respectively. (j) Phase diagram of Chern number as a function of azimuthal angle $\varphi$ for in-plane magnetization. (l) Phase diagram of Chern number as a function of polar angle $\theta$ for the out-of-plane magnetization. The polar radius indicates the value of band gap (in meV).

Figure 4

(a),(b) Magnetocrystalline anisotropic energy of monolayer ${\mathrm{NiAsO}}_3$ and ${\mathrm{PdSbO}}_3$ as a function of applied biaxial strain. (c),(d) Band structure along high symmetry lines, anomalous hall conductivity, and energy spectra of semi-infinite ribbon of ${\mathrm{PdSbO}}_3\text{−}{\text{MoS}}_2$ heterostructure with magnetization along $z$ direction.