Abstract
A quantum anomalous Hall (QAH) insulator is a topological phase in which the interior is insulating but electrical current flows along the edges of the sample in either a clockwise or counterclockwise direction, as dictated by the spontaneous magnetization orientation. Such a chiral edge current eliminates any backscattering, giving rise to quantized Hall resistance and zero longitudinal resistance. Here we fabricate mesoscopic QAH sandwich Hall bar devices and succeed in switching the edge current chirality through thermally assisted spin–orbit torque (SOT). The well-quantized QAH states before and after SOT switching with opposite edge current chiralities are demonstrated through four- and three-terminal measurements. We show that the SOT responsible for magnetization switching can be generated by both surface and bulk carriers. Our results further our understanding of the interplay between magnetism and topological states and usher in an easy and instantaneous method to manipulate the QAH state.
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Data availability
The datasets generated during and/or analysed during this study are available from the corresponding author upon reasonable request.
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Acknowledgements
We thank Y.-T. Cui, Y.-B. Fan, I. Garate, L.-Q. Liu, A. H. MacDonald, N. Samarth, J. Shi, W.-D. Wu, D. Xiao and X.-D. Xu for helpful discussions. This work is primarily supported by an ARO Award (W911NF2210159) (C.-Z.C.), including sample synthesis and device fabrication. The PPMS measurements are supported by an AFOSR grant (FA9550-21-1-0177) (C.-Z.C.) and an NSF-CAREER award (DMR-1847811) (C.-Z.C.). The theoretical calculations and simulations are supported by the Penn State MRSEC for Nanoscale Science (DMR-2011839) (C.-X.L. and C.-Z.C.) and an NSF grant (DMR-2241327) (C.-X.L. and C.-Z.C.). C.-Z.C. acknowledges the support from the Gordon and Betty Moore Foundation EPiQS Initiative (GBMF9063 to C.-Z.C.).
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C.-Z.C. conceived and designed the experiment. Y.-F.Z. and D.Z. grew the QAH sandwich samples. L.-J.Z. fabricated the Hall bar devices using electron-beam lithography. W.Y., L.-J.Z., R.Z., Z.Y., Y.W., H.Y., M.H.W.C. and M.K. performed the electrical-transport measurements. K.Y., R.M. and C.-X.L. carried out the numerical simulations and provided theoretical support. W.Y., K.Y., C.-X.L. and C.-Z.C. analysed the data and wrote the manuscript with inputs from all authors.
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Extended data
Extended Data Fig. 1 QAH state in Device A (w = 5 μm).
a, The optical photograph of Device A. The effective area of the Hall bar device is 20 μm × 5 μm. b, Temperature dependence of ρyx(0) (blue squares) and ρxx(0) (red circles) at Vg = Vg0. All measurements are taken at μ0H = 0 T after magnetic field training. The critical temperature of the QAH state in Device A is ~5.3 K. c, d, μ0H dependence of ρyx and ρxx measured at different temperatures and Vg = Vg0.
Extended Data Fig. 2 SOT-induced magnetization switching under different in-plane magnetic fields in Device A.
a, Current pulse Ipulse dependence of ρyx under different μ0H|| at T = 20 mK. The corresponding current pulse density Jpulse is shown on the upper horizontal axis. The hysteresis loops reflect the reversal of magnetization direction. All these SOT switching measurements are done at ρyx ~ 0.27 h/e2. The data curves are vertically shifted for clarity. b, μ0H|| dependence of the Hall resistance change Δρyx at T = 20 mK. Δρyx is maximized near μ0H|| = +0.05 T, so we choose |μ0H||| = 0.05 T for the SOT-induced magnetization switching in Device A.
Extended Data Fig. 3 More magneto-transport properties of Device A.
a, μ0H dependence of ρyx without tuning Vg after SOT switching at ρyx(0) ~ 0.27 h/e2 and T = 20 mK. After SOT-induced switching, ρyx(0) is ~ −0.225 h/e2. After applying μ0H ~ 0.5 T to align the magnetization, ρyx(0) ~ 0.268 h/e2. Therefore, the SOT magnetization switching ratio at ρyx(0) ~ 0.27 h/e2 by applying |Ipulse|~200 μA under μ0H|| = +0.05 T is ~ 0.225/0.268 = 83.9%. Here the switching ratio is defined as the absolute value of the zero magnetic field Hall resistance ratio before and after magnetic training. When the sample magnetization is fully aligned, the negligible ρyx difference suggests the gating effect induced by the injection of Ipulse is much weaker when the SOT switching is done at |ρyx(0)| ~0.27 h/e2. The red dashed curve corresponds to the initial magnetization process after SOT switching. b, μ0H|| dependence of ρyx at T = 20 mK when the sample is tuned to ρyx(0) ~ 0.27 h/e2. We find that the anisotropy field K is ~0.7 T and thus the sample magnetization almost points upward and downward under |μ0H||| = 0.05 T.
Extended Data Fig. 4 Electrical switching of edge current chirality in Device A through bulk and surface carriers generated SOT.
a, Gate (Vg − Vg0) dependence of ρyx(0) (blue) and ρxx(0) (red) of the QAH insulator after the fourth switch with Ipulse ~ −200 μA under μ0H|| = −0.05 T. The SOT switching is done at ρyx(0) ~ −0.27 h/e2 and T = 20 mK. b, μ0H dependence of ρyx at Vg = Vg0 and T = 20 mK after the fourth switch. The red dashed curve corresponds to the initial magnetization process after the SOT switching. c, Summary of all four switches of CEC chirality at T = 20 mK. The CEC chirality can be switched by changing the direction of either the in-plane magnetic field or the current pulse. Note that the SOT switching is independent of the initial direction of magnetization M (Supplementary Figs. 11 and 12). Therefore, the reversed magnetization should be independent of the number of switching times.
Extended Data Table. 5 Electrical switching of edge current chirality in Device A at T = 2 K.
a-c, Gate (Vg − Vg0) dependence of ρyx(0) (blue) and ρxx(0) (red) of the QAH insulator with right-handed CEC (that is the initial state) (a), after the first (b) and second (c) switches. d, μ0H dependence of ρyx (blue) and ρxx (red) at Vg = Vg0 and T = 2 K. e, f, μ0H dependence of ρyx at Vg = Vg0 and T = 2 K after the first (e) and second (f) switches, respectively. The red dashed curves correspond to the initial magnetization process after each switch.
Extended Data Fig. 6 QAH state in Device B (w = 2 μm).
a, The optical photograph of Device B. The effective area of the Hall bar device is 8 μm × 2 μm. b, Temperature dependence of ρyx(0) (blue squares) and ρxx(0) (red circles) at Vg = Vg0. All measurements are taken at μ0H = 0 T after magnetic field training. The critical temperature of the QAH state in Device B is ~6.8 K. c, d, μ0H dependence of ρyx and ρxx measured at different temperatures and Vg = Vg0.
Extended Data Fig. 7 Electrical switching of edge current chirality in Device B through bulk and surface carriers generated SOT.
a-c, Gate (Vg − Vg0) dependence of ρyx(0) (blue) and ρxx(0) (red) of the QAH insulator with the right-handed CEC (that is the initial state) (a), after the first switch with Ipulse ~ −100 μA (b) and the second switch with Ipulse ~ 100 μA (c) under μ0H|| ~ +0.05 T. Both SOT switches are done at |ρyx(0)| ~ 0.27 h/e2 and T = 20 mK. d, μ0H dependence of ρyx (blue) and ρxx (red) at Vg = Vg0 and T = 20 mK. e, f, μ0H dependence of ρyx at Vg = Vg0 and T = 20 mK after the first (e) and second (f) switches. The red dashed curves correspond to the initial magnetization process after each switch. Vg0s are +1.0 V, +22.5 V, and +35.5 V for the initial state, after 1st switch, and after 2nd switch, respectively.
Extended Data Fig. 8 More magneto-transport properties of Device B after SOT switching.
a-d, μ0H dependence of ρyx without tuning Vg after SOT switching at ρyx(0) ~ 0.185 h/e2 (a), ~0.275 h/e2 (b), ~0.625 h/e2 (c), and ~0.999 ± 0.001 h/e2 (d), respectively. After SOT-induced switching, the corresponding ρyx(0) is ~ −0.142 h/e2 (a), ~ −0.240 h/e2 (b), ~ −0.489 h/e2 (c), and ~ −0.620 h/e2 (d), respectively. After applying μ0H ~ 0.5 T to align the magnetization, ρyx(0) becomes ~0.184 h/e2 (a), ~0.277 h/e2 (b), ~0.523 h/e2 (c), and ~0.653 h/e2 (d), respectively. The red dashed curve corresponds to the initial magnetization process after each switch. e-g, Three ratios \({\rho }_{yx}^{{\rm{a}}}(0)/{\rho }_{yx}^{{\rm{a}}}\) (0, trained) (e), \({\rho }_{yx}^{{\rm{a}}}(0)/{\rho }_{yx}^{{\rm{b}}}\)(0) (f), \({\rho }_{yx}^{{\rm{a}}}\) (0, trained)/ \({\rho }_{yx}^{{\rm{b}}}\)(0) (g) as a function of ρyxb(0), where the SOT switching is done. ρyxb(0): the zero magnetic field Hall resistance before SOT switching. ρyxa(0): the zero magnetic field Hall resistance after SOT switching. \({\rho }_{yx}^{{\rm{a}}}\)(0, trained): the zero magnetic field Hall resistance after SOT switching and μ0H ~ 0.5 T training. All measurements are taken at T = 20 mK. For the SOT switching done near the QAH regime, the \({\rho }_{yx}^{{\rm{a}}}(0)/{\rho }_{yx}^{{\rm{b}}}(0)\) ratio cannot be used to estimate the magnetization switching ratio since ρyx ∝ M becomes invalid.
Extended Data Fig. 9 SOT-induced magnetization switching under different in-plane magnetic fields in Device B (w = 2 μm).
a, Current pulse Ipulse dependence of ρyx under μ0H|| = +0.05 T (top) and μ0H|| = −0.05 T (bottom) at T = 20 mK. b, Ipulse dependence of ρyx under different μ0H|| at T = 20 mK. The corresponding current pulse density Jpulse in (a) and (b) is shown on the upper horizontal axis. All these SOT switching measurements in (a) and (b) are done at ρyx ~ 0.27 h/e2. The data curves in (b) are vertically shifted for clarity. c, μ0H|| dependence of the Hall resistance change Δρyx at T = 20 mK. Δρyx is maximized near μ0H|| = +0.05 T, so we chose |μ0H||| = 0.05 T for the SOT-induced magnetization switching in Device B. We find that the optimal μ0H|| for the SOT-induced magnetization switching is independent of the width of the QAH Hall bar device.
Extended Data Fig. 10 Electrical switching of edge current chirality in more QAH insulator devices at T = 2 K.
a-f, Gate (Vg − Vg0) dependence of ρyx(0) before (blue) and after (red) SOT magnetization switching in Device C (w = 10 μm) (a), Device D (w = 5 μm) (b), Device B (w = 2 μm) (c), Device E (w = 2 μm) (d), Device F (w = 1 μm) (e), and Device G (w = 1 μm) (f), respectively. The SOT-induced magnetization switching is all done at ρyx(0) ~ 0.155 h/e2 and T = 2 K under μ0H|| ~ +0.05 T. The current pulse Ipulse used for SOT magnetization switching becomes smaller by reducing the width of the QAH Hall bar device.
Supplementary information
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Supplementary Figs. 1–12, Tables 1 and 2 and Sections 1–13.
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Yuan, W., Zhou, LJ., Yang, K. et al. Electrical switching of the edge current chirality in quantum anomalous Hall insulators. Nat. Mater. 23, 58–64 (2024). https://doi.org/10.1038/s41563-023-01694-y
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DOI: https://doi.org/10.1038/s41563-023-01694-y
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