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Light-induced ferromagnetism in moiré superlattices

Abstract

Many-body interactions between carriers lie at the heart of correlated physics. The ability to tune such interactions would allow the possibility to access and control complex electronic phase diagrams. Recently, two-dimensional moiré superlattices have emerged as a promising platform for quantum engineering such phenomena1,2,3. The power of the moiré system lies in the high tunability of its physical parameters by adjusting the layer twist angle1,2,3, electrical field4,5,6, moiré carrier filling7,8,9,10,11 and interlayer coupling12. Here we report that optical excitation can highly tune the spin–spin interactions between moiré-trapped carriers, resulting in ferromagnetic order in WS2 /WSe2 moiré superlattices. Near the filling factor of −1/3 (that is, one hole per three moiré unit cells), as the excitation power at the exciton resonance increases, a well-developed hysteresis loop emerges in the reflective magnetic circular dichroism signal as a function of magnetic field, a hallmark of ferromagnetism. The hysteresis loop persists down to charge neutrality, and its shape evolves as the moiré superlattice is gradually filled, indicating changes of magnetic ground state properties. The observed phenomenon points to a mechanism in which itinerant photoexcited excitons mediate exchange coupling between moiré-trapped holes. This exciton-mediated interaction can be of longer range than direct coupling between moiré-trapped holes9, and thus magnetic order arises even in the dilute hole regime. This discovery adds a dynamic tuning knob to the rich many-body Hamiltonian of moiré quantum matter13,14,15,16,17,18,19.

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Fig. 1: Moiré-filling-dependent magnetic circular dichroism in WS2/WSe2 heterobilayer.
Fig. 2: Observation of optically induced ferromagnetism near v = −1/3 filling.
Fig. 3: Optically induced ferromagnetism in dilute hole gas.
Fig. 4: Tuning the magnetic states using optical excitation power and filling factor.

Data availability

The data that support the plots within this paper are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

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Acknowledgements

We thank B. Spivak, T. Cao, J.-H. Chu, D. Cobden, M. Yankowitz, C. Dean and A. N. Pasupathy for helpful discussions. Research on the observation of ferromagnetism near −1/3 moiré superlattice filling is primarily supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443. Optically induced magnetism of dilute electron/hole gas is mainly supported by the DOE BES under award DE-SC0018171. Sample fabrication and piezoresponse force microscopy characterization are partially supported by the ARO MURI programme (grant no. W911NF-18-1-0431). Monte carlo simulation by D.X. was partially supported by the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA). The AFM-related measurements were performed using instrumentation supported by the US National Science Foundation through the UW Molecular Engineering Materials Center, a Materials Research Science and Engineering Center (DMR-1719797). W.Y. and C.X. acknowledge support by the Croucher Foundation (Croucher Senior Research Fellowship) and the University Grant Committee/Research Grants Council of Hong Kong SAR (AoE/P-701/20). Bulk WSe2 crystal growth and characterization by J.Y. is supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, grant number JPMXP0112101001, JSPS KAKENHI grant number JP20H00354 and CREST (JPMJCR15F3), JST. X.X. acknowledges support from the State of Washington funded Clean Energy Institute and from the Boeing Distinguished Professorship in Physics.

Author information

Authors and Affiliations

Authors

Contributions

X.X. and W.Y. conceived the project. H.P. and X.W. fabricated and characterized the samples, assisted by J.Z. X.W. performed the magneto-optical measurements, assisted by J.Z. X.W., X.X., W.Y., D.X. and D.R.G. analysed and interpreted the results. C.X. and W.Y. performed calculations of optically induced magnetic exchange interactions. C.W. and D.X. performed Monte Carlo simulations of correlated states. T.T. and K.W. synthesized the hBN crystals. J.Y. synthesized and characterized the bulk WSe2 crystals. X.X., X.W., W.Y., D.X. and D.R.G. wrote the paper with input from all authors. All authors discussed the results.

Corresponding authors

Correspondence to Wang Yao or Xiaodong Xu.

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Nature thanks David Ruiz-Tijerina, Tomasz Smolenski and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Determination of filling factors.

a, Gate dependent photoluminescence (PL) spectra obtained at 7 K. The excitation wavelength is 740 nm with 50 nW power. Charge neutrality is assigned with the voltage corresponding to the brightest PL with symmetric spectra on the electron and hole sides. b, Gate-dependent differential reflectance spectra (ΔR/R) near the WSe2 exciton resonance, measured at base temperature 1.6 K. The power used for reflectance spectroscopy is 15 nW. c, Gate-dependent differential reflectance spectra differentiated with respect to photon energy (the same data as in Fig. 1c). All three figures share the same y-axis. Gate voltages are labelled at the left axis of panel (a). Assigned filling factors are labelled at the right axis of panel (c). The optical doping effect is negligible. The data of panels (a)–(c) are taken at a different spot of the same sample. d, Monte Carlo simulation of correlated insulating states at fractional moiré miniband fillings. The transition temperature of charge ordered states in the vertical axis is determined as the temperature where the specific heat is maximum in Monte Carlo simulations.

Extended Data Fig. 2 Excitation Energy dependent RMCD at selected filling factors.

a, Excitation Energy dependent RMCD signal at v = −1. b, Excitation Energy dependent RMCD at v = Harding Text1/7. Maximized RMCD signals are observed when the excitation energy is between 1.676-1.678 eV (739-740 nm) as indicated by the dash lines.

Extended Data Fig. 3 RMCD signal near v = −1 and its dependence on optical excitation power.

a, RMCD signal with a few selected filling factors near ν = −1 at T = 1.6 K. The excitation wavelength is 739.2 nm. Laser power is 24 nW. b, Power dependence of RMCD signal at the condition ν = −1. The RMCD signals barely changes by varying the excitation power. c, RMCD amplitude, i.e., saturation RMCD signal difference on the positive and negative sides of magnetic field, as a function of optical excitation power. The saturation amplitude of RMCD signal reduces slightly as optical excitation power increases.

Extended Data Fig. 4 Hysteresis loop width as a function of filling factors and temperature.

a, Extracted hysteresis loop width vs filling factor of the sample in the main text. b, Temperature dependent hysteresis loop width of RMCD signal at filling factor v = −1/7, showing similar instrument determined offset at high temperature. The loop width is determined by the difference between the magnetic fields at which the RMCD signal crosses zero as µoH is swept back and forth. The error bar is the standard deviation obtained by averaging over 5 data points. The set of data in a were taken at different thermal cycles. This causes a slight offset of loop width in (a) compared with those at the same filling factors in (b) and Fig. 2d in the main text.

Extended Data Fig. 5 RMCD signal near ν = −1/3 and its dependence on the magnetic field scanning rate.

a. RMCD signal vs µoH in a narrow doping regime near v = −1/3, showing typical ferromagnetic behavior. Data are extracted from Fig. 1d. b. Magnetic field sweeping rate dependent RMCD hysteresis loops at v = −1/3 with 76 nW excitation.

Extended Data Fig. 6 Data from an additional device at near zero twist angle on sapphire substrate.

It resembles the main results observed in the device presented in the maintext. a, RMCD signal as a function of filling factor v and magnetic field μoH. Temperature: 1.6K. Optical excitation power: 590 nW. b, RMCD signal vs µ0H measured sweeping back and forth at selected filling factors. c, Power dependent RMCD at v = −1/3. d, Temperature dependent RMCD at v = −1/3 and optical excitation power of 590 nW. The data in (c) and (d) are offset for clarity.

Extended Data Fig. 7 Calculated Exciton mediated exchange interaction J.

a–c, shows the J amplitude plot as a function of the separation r between moiré trapped holes and exciton density with exciton temperature of (a) 10 K, (b) 20 K and (c) 50 K.

Extended Data Fig. 8 Excitation power dependent RMCD at v = −1/7.

a, Line cuts of Fig. 4b in the main text at three different optical excitation power (indicated in the panels). b–c, RMCD signal vs temperature at optical excitation power of (b) 253 nW and (c) 26 nW.

Extended Data Fig. 9 RMCD signal as a function of filling factor and magnetic field at select temperatures.

The excitation power is 200 nW at a wavelength of 739.2 nm.

Extended Data Fig. 10 Extracted RMCD signal amplitude as a function of temperature and filling factor.

a, The same plot of Fig. 4d in the main-text. b, replot of panel (a) with the RMCD signal normalized to its maximum at each fixed filling factor. The enhanced magnetic response at v = −1/3 becomes visible.

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Wang, X., Xiao, C., Park, H. et al. Light-induced ferromagnetism in moiré superlattices. Nature 604, 468–473 (2022). https://doi.org/10.1038/s41586-022-04472-z

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