Abstract
The spin Hall effect (SHE), in which an electrical current generates a transverse spin current, plays an important role in spintronics for the generation and manipulation of spin-polarized electrons. The phenomenon originates from spin–orbit coupling. In general, stronger spin–orbit coupling favours larger SHEs but shorter spin relaxation times and diffusion lengths. However, correlated magnetic materials often do not support large SHEs. Achieving large SHEs, long-range spin transport and magnetism simultaneously in a single material is attractive for spintronics applications but has remained a challenge. Here we demonstrate a giant intrinsic SHE coexisting with ferromagnetism in AB-stacked MoTe2/WSe2 moiré bilayers by direct magneto-optical imaging. Under moderate electrical currents with density <1 A m−1, we observe spin accumulation on transverse sample edges that nearly saturates the spin density. We also demonstrate long-range spin Hall transport and efficient non-local spin accumulation that is limited only by the device size (about 10 µm). The gate dependence shows that the giant SHE occurs only near the interaction-driven Chern insulating state. At low temperatures, it emerges after the quantum anomalous Hall breakdown. Our results demonstrate moiré engineering of Berry curvature and electronic correlation for potential spintronics applications.
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Acknowledgements
This work was supported by the National Science Foundation (NSF; Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials) under cooperative agreement Nos. DMR-2039380 (sample and device fabrication) and DMR-1807810 (magneto-optical measurements), the Air Force Office of Scientific Research under award number FA9550-19-1-0390 (transport measurements) and the US Department of Energy, Office of Science, Basic Energy Sciences, under award number DE-SC0019481 (modelling). This research was also funded in part through the Cornell University Materials Research Science and Engineering Center (Grant No. DMR-1719875) and by the Gordon and Betty Moore Foundation (Grant DOI: 10.37807/GBMF11563). It was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure supported by NSF Grant NNCI-2025233. The growth of the hBN crystals was supported by the Elemental Strategy Initiative of the Ministry of Education, Culture, Sports, Science and Technology, Japan, and the Core Research for Evolutional Science and Technology programme of the Japan Science and Technology Agency (Grant No. JPMJCR15F3). We also acknowledge support from the David and Lucille Packard Fellowship (K.F.M.) and the Kavli Postdoctoral Fellowship (W.Z.).
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Z.T. and B.S. performed the optical and electrical experiments and the analysis with help from W.Z. N.C.H., Z.T. and A.H.M. performed the theoretical analysis. W.Z., B.S., Z.T., T.L., S.J., and L.L. fabricated the device. K.W. and T.T. grew the bulk hBN crystals. Z.T., K.F.M. and J.S. designed the scientific objectives and oversaw the project. All authors discussed the results and commented on the manuscript.
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Extended data
Extended Data Fig. 1 Schematic crystal structure and moiré bands in AB-stacked MoTe2/WSe2.
a, Moiré pattern (left) formed in AB-stack MoTe2/WSe2. MM, MX and XX (M = Mo, W; X = Se, Te) are the high-symmetry stacking sites (right). The Wannier orbitals of the two layers occupy the MM and XX sites, forming a honeycomb lattice. An out-of-plane electric field (E) induces the QAH effect. b, Schematic illustration of the electric-field-induced topological phase transition from a charge-transfer insulator (left) to a Chern insulator (right) at \(\nu =1\). Left: The Mo-moiré band is split into the lower and upper Hubbard bands by the on-site energy \(U\). The W-moiré band lies in the Mott gap, resulting in a charge transfer insulator. Right: When the W-moiré band is pushed up by the electric field, band inversion occurs and the Chern insulator emerges.
Extended Data Fig. 2 Basic characterization for the Chern insulator.
a, Magnetic-field dependence of \({R}_{{xx}}\) and \({R}_{{xy}}\) at 1.6 K for the Chern insulating state (\({V}_{{tg}}\) = -4.693 V, \({V}_{{bg}}\) = 3.528 V). Nearly quantized \({R}_{{xy}}\) and vanishing \({R}_{{xx}}\) are observed at magnetic fields higher than 0.2 T. b, The corresponding magnetic-field dependent MCD. A hysteresis is observed, consistent with the transport results and with the emergence of a ferromagnetic state.
Extended Data Fig. 3 Zero-bias MCD images at varying fillings and electric fields.
a, b, Zero-bias spontaneous MCD images at varying filling factors and fixed \(E=0.628\) V/nm (a) and at varying electric fields and fixed \(\nu =1\) (b). Temperature is at 1.6 K. Black dashed lines mark the sample boundaries. Strongest MCD is observed at the Chern insulating state (\(\nu =1\) and \(E=0.633\) V/nm); the MCD signal decreases with detuned \(\nu\) and \(E\). MCD inhomogeneity originating from strain and/or twist angle disorders is also observed.
Extended Data Fig. 4 Temperature dependent spontaneous MCD.
Zero-bias spontaneous MCD images at varying temperatures for the Chern insulating state (\({V}_{{tg}}\) = -4.693 V, \({V}_{{bg}}\) = 3.528 V). Spontaneous MCD is observed below about 5 K. Black dashed lines mark the sample boundaries.
Extended Data Fig. 5 Dependence of the SHE on the directions of bias current and spontaneous magnetization.
a, MCD images at 1.6 K under reversed bias current compared to Fig. 2b. Positive spontaneous MCD is prepared at zero bias. The current-induced edge MCD has opposite signs compared to Fig. 2b, consistent with the bulk SHE beyond QAH breakdown. b, MCD images at 1.6 K with spontaneous MCD opposite to that in Fig. 2b. The same current-induced MCD images are observed at high bias, demonstrating that the SHE is independent of the spontaneous magnetization direction.
Extended Data Fig. 6 SHE with currents biased along the short axis.
MCD images at 6 K (a) and 1.6 K (b) under varying bias currents. The bias current is along the short axis near one end of the Hall bar. The current is confined to a small region near the tip of the electrodes. Opposite magnetizations are observed on two sides of the current and the magnitude increases with increasing bias current. The current path, identified from zero MCD, deviates from a straight line due to sample inhomogeneities. Spontaneous MCD is also observed at 1.6 K under zero bias. The spontaneous MCD is quenched beyond the QAH breakdown. The 1.6 K and 6 K MCD images are nearly identical under high bias.
Extended Data Fig. 7 Giant spin accumulation at high bias.
a, Bias current-dependent edge MCD at 1.6 K for the Chern insulating state (at P1 in Fig. 2a). A QAH breakdown is observed near 0.5 µA, where the MCD switches sign. b, The corresponding magnetic field dependent zero-bias MCD at the same sample location. We can see that the current-induced MCD at high bias (a) is as strong as the zero-bias MCD near magnetic saturation at 0.5 T (b). The results demonstrate the giant spin accumulation on sample edges due to the SHE.
Extended Data Fig. 8 Magnetic field dependent QAH breakdown.
a, b, Dependence of \({R}_{{xx}}\) (a) and \({R}_{{xy}}\) (b) on the bias current and magnetic field at 1.6 K for the Chern insulating state. QAH breakdown is marked by rapid changes in both \({R}_{{xx}}\) and \({R}_{{xy}}\) (the dashed lines). The critical current for the QAH breakdown increases with magnetic field. c, Corresponding bias current-dependent edge MCD (at P1 in Fig. 2a) at representative magnetic fields. The MCD switches sign at the QAH breakdown critical current, which increases with magnetic field, consistent with the transport results.
Extended Data Fig. 9 SHE with different bias current path.
MCD images at 1.6 K and \(\nu =1\) using different pairs of Hall probes as the source (S) and drain (D). The bias current is shown in each panel. Black dashed lines mark the sample boundaries; and arrows show the bias current direction. Due to the SHE, the sample is split into two domains of opposite MCD according to the bias current path. The current path centerline, where the MCD is zero, deviates from a straight line connecting S and D due to sample inhomogeneity.
Extended Data Fig. 10 Steady state drift-diffusion model in non-local geometry.
a, Schematic sample geometry with half-length \(L\) and width \(W\). The coordinate system is set up such that the sample center is at the origin. Current ejection/extraction points are marked by dark blue disks at \(x=0,{y}=\pm W/2\). b, c, d, Spin density \({n}_{s}\) and spin current density \({J}_{s}\) profile at \(y=0\) for representative spin diffusion lengths with sample geometry \(L=3\mu {m}\) (b), \(9\mu {m}\) (c), \(30\mu {m}\) (d) and fixed \(W=3\mu m\). A Hall angle of \(\pi /6\) is used in all cases. With increasing \(L\), the spin density becomes more localized around the current centerline and the spin current density \({J}_{s}\) shows stronger dependence on the spin diffusion length.
Supplementary information
Supplementary Video 1
Bias-dependent MCD images at 1.6 K.
Supplementary Video 2
Bias-dependent MCD difference between 1.6 and 6 K.
Source data
Source Data Fig. 1
Statistical source data for Fig. 1.
Source Data Fig. 2
Statistical source data for Fig. 2.
Source Data Fig. 3
Statistical source data for Fig. 3.
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Tao, Z., Shen, B., Zhao, W. et al. Giant spin Hall effect in AB-stacked MoTe2/WSe2 bilayers. Nat. Nanotechnol. (2023). https://doi.org/10.1038/s41565-023-01492-2
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DOI: https://doi.org/10.1038/s41565-023-01492-2
