Large-gap quantum anomalous Hall effect in monolayer halide perovskite

We theoretically propose a family of structurally stable monolayer halide perovskite ${\mathrm{A}}_3{\mathrm{B}}_2{\mathrm{C}}_9$ (A = Rb, Cs; B = Pd, Pt; C = Cl, Br) with easy magnetization planes. The family materials are all half metals with large spin gaps beyond 1 eV accompanying a single spin Dirac point located at K point. When the spin-orbit coupling is switched on, we further show that ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9, {\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$, and ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$ monolayers can open up large band gaps from 63 to 103 meV to harbor quantum anomalous Hall effect with Chern numbers of $\mathcal{C}=\pm 1$ whenever the mirror symmetry is broken by the in-plane magnetization, and the corresponding Berezinskii-Kosterlitz-Thouless transition temperatures are over 248 K. Our findings provide a potentially realizable platform to explore quantum anomalous Hall effect and spintronic applications at high temperatures.

Figure 1

(a) Top view and side view of monolayer ${\text{A}}_3{\text{B}}_2{\text{C}}_9$, with the transition metal atoms forming a buckled honeycomb lattice. (b) First Brillouin zone with high symmetry points, with the solid lines representing three vertical mirror planes. (c) Phonon spectra of ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$.

Figure 2

(a) Four possible magnetic configurations: FM, NAFM, SAFM, and ZAFM. (b) The magnetic anisotropic energy (MAE) of monolayer ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$, with red and black curves corresponding to the relative energy in $x\text{−}z$ and $x\text{−}y$ planes with respect to that along the $x$ direction. (c) The normalized magnetic moment of monolayers ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9, {\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$, and ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$ as a function of temperature by Monte Carlo simulations.

Figure 3

(a) Orbital projected ($3d$ orbitals of Pt) band structure of monolayer ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$ without spin-orbit coupling where the ($d_{xz}, d_{yz}$) orbitals dominate the bands near the Fermi level. (b)–(d) Band structures with spin-orbit coupling when the magnetization direction is along $\varphi =0^{\circ },{45}^{\circ }$ and $z$ direction, respectively.

Figure 4

Energy spectra of a semi-infinite ribbon of monolayer ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$ with the in-plane magnetization along $\varphi ={45}^{\circ }$ (a) and $-{45}^{\circ }$ (c). The corresponding anomalous Hall conductivity with $\varphi ={45}^{\circ }$ (b) and $-{45}^{\circ }$ (d).

Figure 5

(a) Five atomic layers of monolayer ${\text{A}}_3{\text{B}}_2{\text{C}}_9$. (b) Internal and external bond length between transition metal atom and halogen atom in monolayer ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$. (c) Schematic diagram of energy level splitting for $d$ orbitals in a distorted octahedra crystal field of monolayer ${\text{A}}_3{\text{B}}_2{\text{C}}_9$.

Figure 6

(a)–(d) Phonon spectrum of monolayers (a) ${\mathrm{Rb}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$, (b) ${\mathrm{Rb}}_3{\mathrm{Pd}}_2{\mathrm{Br}}_9$, (c) ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$, and (d) ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Br}}_9$. (e)–(h) The phonon spectrum of monolayers (e) ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$, (f) ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Br}}_9$, (g) ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$, and (h) ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Br}}_9$. No imaginary frequency mode emerges along the high symmetry path for all monolayers ${\text{A}}_3{\text{B}}_2{\text{C}}_9$.

Figure 7

(a)–(h) Magnetic anisotropy energy (MAE) of monolayers (a) ${\mathrm{Rb}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$, (b) ${\mathrm{Rb}}_3{\mathrm{Pd}}_2{\mathrm{Br}}_9$, (c) ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$, (d) ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Br}}_9$, (e) ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$, (f) ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Br}}_9$, (g) ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$, and (h) ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Br}}_9$. There is an extremely small MAE (6.41 $\mu \mathrm{eV}$) of ${\mathrm{Rb}}_3{\mathrm{Pd}}_2{\mathrm{Br}}_9$ in the $x\text{−}y$ plane.

Figure 8

(a),(b) Normalized magnetic moment of monolayers (a) ${\mathrm{Rb}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9, {\mathrm{Rb}}_3{\mathrm{Pd}}_2{\mathrm{Br}}_9$, and ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Br}}_9$ and (b) ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Br}}_9$ and ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Br}}_9$ as a function of temperature by Monte Carlo simulations.

Figure 9

(a)–(h) Band structure of (a) ${\mathrm{Rb}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$, (b) ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$, (c) ${\mathrm{Rb}}_3{\mathrm{Pd}}_2{\mathrm{Br}}_9$, (d) ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Br}}_9$, (e) ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$, (f) ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Br}}_9$, (g) ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$, and (h) ${\mathrm{Cs}}_3{\mathrm{Pt}}_2{\mathrm{Br}}_9$ without and with spin-orbit coupling.

Figure 10

(a)–(c) Band structure of ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$ without spin-orbit coupling. The band structure and anomalous Hall conductivity of ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$ with spin-orbit coupling when magnetization is along $\varphi ={45}^{\circ }$. The band structure and anomalous Hall conductivity of ${\mathrm{Rb}}_3{\mathrm{Pt}}_2{\mathrm{Cl}}_9$ with spin-orbit coupling when magnetization is along $z$ direction; (d)–(f) the band structure of ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$ without spin-orbit coupling. The band structure and anomalous Hall conductivity of ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$ with spin-orbit coupling when magnetization is along $\varphi ={45}^{\circ }$. The band structure and anomalous Hall conductivity of ${\mathrm{Cs}}_3{\mathrm{Pd}}_2{\mathrm{Cl}}_9$ with spin-orbit coupling when magnetization is along $z$ direction.