Magnetism typically arises from the joint effect of Fermi statistics and repulsive Coulomb interactions, which favours ground states with non-zero electron spin. As a result, controlling spin magnetism with electric fields—a longstanding technological goal in spintronics and multiferroics1,2—can be achieved only indirectly. Here we experimentally demonstrate direct electric-field control of magnetic states in an orbital Chern insulator3,4,5,6, a magnetic system in which non-trivial band topology favours long-range order of orbital angular momentum but the spins are thought to remain disordered7,8,9,10,11,12,13,14. We use van der Waals heterostructures consisting of a graphene monolayer rotationally faulted with respect to a Bernal-stacked bilayer to realize narrow and topologically non-trivial valley-projected moiré minibands15,16,17. At fillings of one and three electrons per moiré unit cell within these bands, we observe quantized anomalous Hall effects18 with transverse resistance approximately equal to h/2e2 (where h is Planck’s constant and e is the charge on the electron), which is indicative of spontaneous polarization of the system into a single-valley-projected band with a Chern number equal to two. At a filling of three electrons per moiré unit cell, we find that the sign of the quantum anomalous Hall effect can be reversed via field-effect control of the chemical potential; moreover, this transition is hysteretic, which we use to demonstrate non-volatile electric-field-induced reversal of the magnetic state. A theoretical analysis19 indicates that the effect arises from the topological edge states, which drive a change in sign of the magnetization and thus a reversal in the favoured magnetic state. Voltage control of magnetic states can be used to electrically pattern non-volatile magnetic-domain structures hosting chiral edge states, with applications ranging from reconfigurable microwave circuit elements to ultralow-power magnetic memories.
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Localization-enhanced moiré exciton in twisted transition metal dichalcogenide heterotrilayer superlattices
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We acknowledge discussions with J. Checkelsky, S. Chen, C. Dean, M. Yankowitz, D. Reilly, I. Sodemann and M. Zaletel. Work at UCSB was primarily supported by the ARO under MURI W911NF-16-1-0361. Measurements of twisted bilayer graphene (Extended Data Fig. 8) and measurements at elevated temperatures (Extended Data Fig. 3) were supported by a SEED grant and made use of shared facilities of the UCSB MRSEC (NSF DMR 1720256), a member of the Materials Research Facilities Network (www.mrfn.org). A.F.Y. acknowledges the support of the David and Lucille Packard Foundation under award 2016-65145. A.H.M. and J.Z. were supported by the National Science Foundation through the Center for Dynamics and Control of Materials, an NSF MRSEC under Cooperative Agreement number DMR-1720595, and by the Welch Foundation under grant TBF1473. C.L.T. acknowledges support from the Hertz Foundation and from the National Science Foundation Graduate Research Fellowship Program under grant 1650114. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant Number JPMXP0112101001, JSPS KAKENHI grant numbers JP20H00354 and the CREST(JPMJCR15F3), JST.
The authors declare no competing interests.
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Extended data figures and tables
a, Optical image of a typical graphene flake containing both MLG and BLG domains. b, The same image as in a but in greyscale and with enhanced contrast to clearly show the graphene flake. Dashed lines show the lines along which the flake was cut using atomic force microscopy. c–f, Optical images of completed tMBG devices D1 (c), D2 (d), D3 (e) and D4 (f). All scale bars, 10 μm.
a–d, Longitudinal resistance Rxx of devices D1 with θ ≈ 1.25(1)° (a), D2 with θ ≈ 1.25(1)° (b), D3 with θ = 1.385(5)° (c) and D4 with θ ≈ 0.90(1)° (d). The numbers in parentheses indicate the uncertainty in the final digit. All measurements are performed at zero magnetic field and T ≈ 20 mK.
a, Temperature-dependent resistance measured at D = 0.43 V nm−1 in device D1. b, c, Temperature-dependent resistance at selected carrier densities, marked by the arrows in a, for n < 0 (b) and n > 0 (c).
a, Longitudinal resistance Rxx of the correlated region at B = 0 T. b–e, Hall resistance Ryx measured at n and D marked by the dots in a. The colour of the dots in a corresponds to the colour of curves in b–e. Panels b and c show curves taken at small negative and positive dopings of ν = 1. Panels d and e show curves taken at small negative and positive dopings of ν = 2. f, Zoom-in of Rxx around ν = 1. g–i, Ryx measured along the line cuts I (g), II (h) and III (i). Ryx in the plots are shifted by an offset.
a, Longitudinal resistance Rxx of the correlated region at B = 0 T. b, Hall resistance Ryx of the same region as in a. c, Temperature dependence of Ryx at ν = 1. The anomalous Hall effect disappears at 4.2 K. d, Rxx of the correlated region measured at B = 2 T. e–i, Ryx along the line cuts I (e), II (f), III (g), IV (h) and V (i).
a, b, Temperature dependence of the Hall resistance Ryx measured at ν = 1 (a) and ν = 3 (b). Insets show the temperature dependence of the height of the hysteresis loop height, as defined in Fig. 3a.
Extended Data Fig. 7 n and B dependence of the measured anomalous Hall effect, plotted at selected temperatures for D = 0.4 V nm−1 in device D1.
Temperatures are labelled on the individual panels.
a, Anomalous Hall resistance ΔRyx associated with tBLG ferromagnetism, extracted by subtracting Ryx(B) as B is increased from Ryx(B) as B is decreased. The tBLG device is the same as in ref. 4. The colour scale is fixed to the von Klitzing constant in the top of the plot to show the range of filling factors for which a robust quantum anomalous Hall effect is observed. The colour scale axis is dramatically reduced in the bottom plot to illustrate weak features in ΔRyx(ν). For ν < 3, the coercive field of the ferromagnetic order increases dramatically, peaking at ν = 2.82 electrons per moiré unit cell. For ν < 2.82, ΔRyx switches sign, indicating that the valley polarization of the ground state of the system at finite magnetic field has switched. b, A robust C = 1 quantum anomalous Hall effect at ν = 3.1. c, Ferromagnetic hysteresis plots on opposite sides of the divergence of the coercive field close to ν = 2.82 (with offset). Note the change in the relative sign of ΔRyx.
a, Repeated magnetic-field hysteresis loops. b, Repeated doping hysteresis loops. Both panels taken under conditions analogous to those in Fig. 4b, described in the main text.
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Polshyn, H., Zhu, J., Kumar, M.A. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020). https://doi.org/10.1038/s41586-020-2963-8
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