Quantum anomalous Hall effect in monolayers Ti<sub>2</sub>X<sub>2</sub> (X = P, As, Sb, Bi) with tunable Chern numbers by adjusting magnetization orientation

doi:10.15302/frontphys.2025.024203

2025, Vol. 20

Issue (2) : 24203 https://doi.org/10.15302/frontphys.2025.024203

Quantum anomalous Hall effect in monolayers Ti₂X₂ (X = P, As, Sb, Bi) with tunable Chern numbers by adjusting magnetization orientation

Keer Huang¹, Lei Li^1,^2,³(

), Wu Zhao⁴, Xuewen Wang^1,^2,³

¹. Frontiers Science Center for Flexible Electronics (FSCFE) & Institute of Flexible Electronics (IFE), Northwestern Polytechnical University, Xi’an 710072, China
². MIIT Key Laboratory of Flexible Electronics (KLoFE), Northwestern Polytechnical University, Xi’an 710072, China
³. Shaanxi Key Laboratory of Flexible Electronics (KLoFE), Northwestern Polytechnical University, Xi’an 710072, China
⁴. School of Information Science and Technology, Northwest University, Xi’an 710072, China

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Abstract

Despite extensive research, the achievement of tunable Chern numbers in quantum anomalous Hall (QAH) systems remains a challenge in the field of condensed matter physics. Here, we theoretically proposed that Ti₂X₂ (X = P, As, Sb, Bi) can realize tunable Chern numbers QAH effect by adjusting their magnetization orientations. In the case of Ti₂P₂ and Ti₂As₂, if the magnetization lies in the x−y plane, and all C₂ symmetries are broken, a low-Chern-number phase with C = 1 will manifest. Conversely, if the magnetization is aligned to the z-axis, the systems enter a high-Chern number phase with C = 3. As for Ti₂Sb₂ and Ti₂Bi₂, by manipulating the in-plane magnetization orientation, these systems can periodically enter topological phases (C = ±1) over a 60° interval. Adjusting the magnetization orientation from +z to −z will result in the systems’ Chern number alternating between ±1. The non-trivial gap in monolayer Ti₂X₂ (X = P, As, Sb, Bi) can reach values of 23.4, 54.4, 60.8, and 88.2 meV, respectively. All of these values are close to the room-temperature energy scale. Furthermore, our research has revealed that the application of biaxial strain can effectively modify the magnetocrystalline anisotropic energy, which is advantageous in the manipulation of magnetization orientation. This work provides a family of large-gap QAH insulators with tunable Chern numbers, demonstrating promising prospects for future electronic applications.

Keywords tunable Chern number ferromagnetic quantum anomalous Hall effect Ti₂X₂ (X = P, As, Sb, Bi) first-principles

Corresponding Author(s): Lei Li

Issue Date: 01 November 2024

Cite this article:

Keer Huang,Lei Li,Wu Zhao, et al. Quantum anomalous Hall effect in monolayers Ti₂X₂ (X = P, As, Sb, Bi) with tunable Chern numbers by adjusting magnetization orientation[J]. Front. Phys. , 2025, 20(2): 24203.

URL:

https://academic.hep.com.cn/fop/EN/10.15302/frontphys.2025.024203
https://academic.hep.com.cn/fop/EN/Y2025/V20/I2/24203

Fig.1 (a) Top, side, and oblique views of the Ti₂X₂ monolayers. (b) First Brillouin zone with marked high symmetry points.

b 1

and

b 2

are reciprocal lattice vectors. (c) Schematic diagram of the d-orbital distribution of Ti atoms in the Ti₂X₂ (X = P, As, Sb, Bi) monolayers.

	a (Å)	d (Å)	$α$ ( $∘$ )	D (meV)	$J 1$ (meV)	$J 2$ (meV)
Ti₂P₂	4.117	3.056	114.014	0.292	55.734	−1.762
Ti₂As₂	4.198	3.070	111.426	0.744	80.901	5.495
Ti₂Sb₂	4.383	3.094	105.374	−0.122	99.214	10.830
Ti₂Bi₂	4.425	3.090	102.676	−4.490	100.679	17.704

Tab.1 Calculated optimized lattice constants (a), nearest Ti-Ti distances (d), Ti−X−Ti angles [

α

; see Fig.1(a)], magnetocrystalline anisotropic energy (D), magnetic coupling parameters of

J 1

and

J 2

for the Ti₂X₂ (X = P, As, Sb, Bi) monolayers.

Fig.2 (a−d) Band structures of the Ti₂P₂, Ti₂As₂, Ti₂Sb₂, and Ti₂Bi₂ monolayers without SOC, respectively. The red and blue colors indicate the spin-up and spin-down bands, respectively. (e−h) d-orbital resolved band structures of the Ti₂P₂, Ti₂As₂, Ti₂Sb₂, and Ti₂Bi₂ monolayers without SOC, respectively.

Fig.3 (a) Bulk band structure of monolayer Ti₂As₂ along high symmetry line K−

Γ

and corresponding anomalous Hall conductivity considering SOC and magnetization lying in x−y plane for

φ = 30 ∘

. (b) Corresponding energy spectra of semi-infinite ribbon of monolayer Ti₂As₂ for

φ = 30 ∘

. Note that there is one gapless edge mode in the gap. (e, f) are similar to those in (a, b) but with magnetization along z-axis. Note that there are three gapless edge modes in the gap. (d) The distribution of the Berry curvatures for monolayer Ti₂As₂ with in-plane magnetization along

φ = 30 ∘

direction and (h) out-of-plane magnetization along z-axis, respectively. (c) Phase diagram of Chern number as a function of azimuthal angle (

φ

) for in-plane magnetization. (g) Phase diagram of Chern number as a function of polar angle (

θ

) for the out-of-plane magnetization along

φ = 30 ∘

path. The polar radius indicates the value of band gap (in meV).

Fig.4 (a) Bulk band structure of monolayer Ti₂Sb₂ along high symmetry line M−K−

Γ

considering SOC and magnetization lying in x−y plane for

φ = 30 ∘

. (b) Corresponding energy spectra of semi-infinite ribbon of monolayer Ti₂Sb₂ for

φ = 30 ∘

. (c) Phase diagram of Chern number as a function of azimuthal angle (

φ

) for in-plane magnetization. (d, e) are similar to those in (a, b) but with magnetization along the z direction. (f) Phase diagram of Chern number as a function of polar angle (

θ

) for the out-of-plane magnetization along

φ = 30 ∘

path.

Fig.5 Magnetocrystalline anisotropic energy of monolayers (a) Ti₂P₂, (b) Ti₂As₂, (c) Ti₂Sb₂, and (d) Ti₂Bi₂ as a function of applied biaxial strain, respectively.

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