Magnetization-tuned topological quantum phase transition in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ devices

Recently, the intrinsic magnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ has attracted enormous research interest due to the great success in realizing exotic topological quantum states, such as the quantum anomalous Hall effect, the axion insulator state, and high-Chern-number and high-temperature Chern insulator (CI) states. One key issue in this field is to effectively manipulate these states and control topological phase transitions. Here, by systematic angle-dependent transport measurements, we reveal a magnetization-tuned topological quantum phase transition from CI to magnetic insulator with gapped Dirac surface states in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ devices. Specifically, as the magnetic field is tilted away from the out-of-plane direction by ∼40–60 °, the Hall resistance deviates from the quantization value, and a colossal, anisotropic magnetoresistance is detected. Theoretical analyses based on modified Landauer-Büttiker formalism show that the field-tilt-driven switching from the ferromagnetic state to the canted antiferromagnetic state induces a topological quantum phase transition from CI to magnetic insulator with gapped Dirac surface states in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ devices. These findings reveal a kind of topological phase transition associated with magnetism and spin-orbit coupling. In this letter, we suggest that ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ is an ideal platform for exploring topological quantum phase transitions, and it provides an efficient means for modulating topological quantum states and topological quantum phase transitions.

Figure 1

(a) Schematic crystal and magnetic structure of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. The orange and cyan arrows denote magnetic moment directions of Mn ions. (b) Schematic diagram of the transport measurements configuration. The magnetic field rotates from the out-of-plane direction to the in-plane direction, and the angle between the magnetic field and the out-of-plane direction is denoted as θ. (c) and (d) $R_{yx}$ and $R_{xx}$ of device D1 (9 SL) and D2 (8 SL) as a function of magnetic field. The dashed lines in (c) denote the quantized values $h/e^2$ and $h/2e^2$, respectively.

Figure 2

(a) A schematic of the configuration highlighting field rotation from out of plane to in plane. (b) and (c) ${\rho }_{yx}$ and ${\rho }_{xx}$ of the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ bulk single crystal as a function of magnetic field at various angles. $B_{\mathrm{AFM}}$ and $B_{\mathrm{FM}}$ represent the transition from the antiferromagnetic (AFM) state to the canted AFM (cAFM) state and the transition from the cAFM state to the ferromagnetic (FM) state, respectively. For clarity, data curves are shifted. (d) Angle-dependent $M\left(B\right)$ curves of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ bulk single crystal measured at 2 K.

Figure 3

(a) and (b) $R_{yx}$ and $R_{xx}$ as a function of $B$ at various angles in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ device D1 (9 SL). The black and red traces represent magnetic field sweeping to the negative and positive directions, respectively. (c) $B$-θ phase diagram of D1. (d)–(f) The schematic of the magnetic structure at different tilted magnetic fields. When $B$ is lower than the spin-flip field $B_{\mathrm{AFM}}, {\mathrm{MnBi}}_2{\mathrm{Te}}_4$ is in the antiferromagnetic (AFM) state. ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ will be in the canted AFM (cAFM) state when $B_{\mathrm{AFM}}<B<B_{\mathrm{FM}}$ and finally enters the ferromagnetic (FM) state when further increasing the magnetic field above $B_{\mathrm{FM}}$.

Figure 4

Theoretical fitting of the $R_{xx}$-θ curve in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ device D1 (9 SL). The red solid line is the theoretical fitting curve based on the modified Landauer-Büttiker formula, wherein the dissipative contribution from the gapped surface states in a magnetic insulator with gapped Dirac surface states is considered. The theoretical fitting shows an evident deviation in the Chern insulator (CI) region (green region, $\theta <{44}^{\circ }$ and $\theta >{136}^{\circ }$). In the blue region (${44}^{\circ }<\theta <{136}^{\circ }$), the experimental data can be well fitted by the modified Landauer-Büttiker formula, indicating that the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ device in this region is tuned into a magnetic insulator with gapped Dirac surface states, which suggests a field-tilt-driven topological quantum phase transition from CI to magnetic insulator with gapped Dirac surface states.