Mapping the phase diagram of the quantum anomalous Hall and topological Hall effects in a dual-gated magnetic topological insulator heterostructure

We use magnetotransport in dual-gated magnetic topological insulator heterostructures to map out a phase diagram of the topological Hall and quantum anomalous Hall effects as a function of the chemical potential (primarily determined by the back gate voltage) and the asymmetric potential (primarily determined by the top gate voltage). A theoretical model that includes both surface states and valence band quantum well states allows the evaluation of the variation of the Dzyaloshinskii-Moriya interaction and carrier density with gate voltages. The qualitative agreement between experiment and theory provides strong evidence for the existence of a topological Hall effect in the system studied, opening up a route for understanding and manipulating chiral magnetic spin textures in real space.

Figure 1

The quantum anomalous Hall (QAH) effect in dual-gated magnetic topological insulator (TI) heterostructures. (a) A schematic structure of the magnetic TI heterostructure. (b) Cross-sectional transmission electron microscope (TEM) image of a dual-gated device. (c) Temperature dependence of the magnetic field dependence of Hall resistance. (d) Demonstration of the QAH effect at $T$ = 60 mK with gate voltages $V_b=100$ V and $V_t=0$ V.

Figure 2

The topological Hall effect (THE) observed in dual-gated magnetic topological insulator (TI) heterostructures. (a) The deviation from the quantum anomalous Hall (QAH) regime using the bottom gate. (b) Top gate-voltage-driven THE. The bottom gate voltage $V_b$ is fixed at $-200$ V. By applying a positive top gate voltage $V_t$, the THE becomes more pronounced. On the other hand, applying a negative $V_t$ can make the THE vanish. (c) Top gate-voltage dependence of the magnitude of the THE ${\rho }_{yx}^{\text{THE}}$. The data are obtained by subtracting a constant high-field Hall resistance.

Figure 3

The gate voltage dependence of the topological Hall effect (THE). (a) Capacitance model of the gating effect. The top gate mainly tunes the chemical potential of the top surface, while the bottom gate mainly tunes the chemical potential of the bottom surface. Dual gates can induce an asymmetric potential between top and bottom surfaces. (b) The THE phase diagram. THE is absent in the quantum anomalous Hall (QAH) effect regime (dark blue area). Away from the QAH regime, when the top- and back-gate voltages have different signs, the THE becomes more obvious (red area). When dual gates have the same sign, the THE is quenched (lower left corner). The actual measurement points are shown as black dots, and the rest of the plot is the result of linear interpolation.

Figure 4

(a) The energy dispersion of the surface states and bulk quantum well bands in a magnetic topological insulator (TI). Here, $U=0.02\text{eV}$. (b) Spin susceptibility ${\chi }_{xz}$ as a function of chemical potential $\mu$ and asymmetric potential $U$. The blue and red dashed lines correspond to the blue and red plots in (c). (c) Spin susceptibility ${\chi }_{xz}$ as a function of $U$ for the chemical potential $\mu =0.02\text{eV}$ (blue line) and $\mu =-0.02\text{eV}$ (red line). (d) Electron or hole carrier concentration $\rho$ as a function of chemical potential $\mu$ and asymmetric potential $U$. Here, $\rho$ is in the unit of ${\text{Å}}^{-2}$. The topological Hall (TH) resistance is expected to be proportional to $|{\chi }_{xz}{|}^2\rho$, whose dependence on $\mu$ and $U$ is shown in (e). Here, we choose $q_x=0.005{\text{Å}}^{-1}$ and $q_y=0$.