Abstract
Heavy-fermion metals are prototype systems for observing emergent quantum phases driven by electronic interactions1,2,3,4,5,6. A long-standing aspiration is the dimensional reduction of these materials to exert control over their quantum phases7,8,9,10,11, which remains a significant challenge because traditional intermetallic heavy-fermion compounds have three-dimensional atomic and electronic structures. Here we report comprehensive thermodynamic and spectroscopic evidence of an antiferromagnetically ordered heavy-fermion ground state in CeSiI, an intermetallic comprising two-dimensional (2D) metallic sheets held together by weak interlayer van der Waals (vdW) interactions. Owing to its vdW nature, CeSiI has a quasi-2D electronic structure, and we can control its physical dimension through exfoliation. The emergence of coherent hybridization of f and conduction electrons at low temperature is supported by the temperature evolution of angle-resolved photoemission and scanning tunnelling spectra near the Fermi level and by heat capacity measurements. Electrical transport measurements on few-layer flakes reveal heavy-fermion behaviour and magnetic order down to the ultra-thin regime. Our work establishes CeSiI and related materials as a unique platform for studying dimensionally confined heavy fermions in bulk crystals and employing 2D device fabrication techniques and vdW heterostructures12 to manipulate the interplay between Kondo screening, magnetic order and proximity effects.
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The data that support the findings of this study are present in the paper and its Extended Data. Further data are available from the corresponding authors upon request.
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Acknowledgements
Research on 2D heavy-fermion materials was primarily supported by the US Department of Energy (DOE), Office of Science, Basic Energy Science, under award DE-SC0023406. ARPES measurements were performed at Beamline 21-ID-1 of the National Synchrotron Light Source II, a DOE Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory (Contract No. DE-SC0012704). We thank C. Petrovic and Z. Hu for their help with the sample mounting for ARPES. High-magnetic-field transport and tunnel diode oscillator measurements were performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation (NSF; Cooperative Agreement No. DMR-1644779) and the State of Florida. Subkelvin specific heat capacity measurements (A.F.M.) were supported by the DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. The specific heat analysis used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. The PPMS used to perform vibrating-sample magnetometry, heat capacity and electrical transport measurements was purchased with financial support from the NSF through a supplement to award DMR-1751949. STM equipment support was provided by the Air Force Office of Scientific Research via grant FA9550-21-1-037. Electrical transport measurements of low-dimensional samples were supported by the NSF (DMR-2105048). Nano-imaging experiments and theoretical modelling were supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the DOE, Office of Science, Basic Energy Sciences (Award DE-SC0019443). The theory calculations by O.E., P.T. and C.-S.O. were supported by an ERC synergy grant (FASTCORR, project 854843), the Swedish Research Council, eSSENCE, STandUPP and the Wallenberg Initiative Materials Science for Sustainability (WISE) funded by the Knut and Alice Wallenberg Foundation (KAW), the Swedish National Infrastructure for Computing, Grupos Consolidados (IT1453-22), and the German Research Foundation through the Cluster of Excellence CUI: Advanced Imaging of Matter (EXC 2056, project ID 390715994) and Project SFB-925 Light-induced Dynamics and Control of Correlated Quantum Systems (Project 170620586). V.A.P. is supported by the NSF Graduate Research Fellowship Program (NSF GRFP 2019279091). A.D. acknowledges support from the Simons Foundation Society of Fellows programme (Grant No. 855186). We acknowledge the use of facilities and instrumentation supported by the NSF through the Columbia University, Materials Research Science and Engineering Center (Grant No. DMR-2011738). The Flatiron Institute is a division of the Simons Foundation. We acknowledge support from the Max Planck–New York City Center for Non-Equilibrium Quantum Phenomena.
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V.A.P., S.T., A.N.P. and X.R. conceptualized the project. V.A.P., D.G.C. and E.M. were responsible for synthesis and methodology. V.A.P. and M.E.Z. were responsible for magnetometry. V.A.P., A.S. and A.F.M. were responsible for heat capacity measurements. S.T. and M.T. were responsible for scanning tunnelling microscopy. V.A.P. was responsible for bulk electrical transport. D.R.N. and X.-Y.Z. were responsible for spectroscopy. V.A.P., A.D., C.R.D. and D.G. were responsible for high-magnetic-field electrical transport measurements. V.A.P., M.E.Z. and D.G. were responsible for tunnel diode oscillator pressure experiments. M.R., X.C. and P.K. were responsible for 2D electrical transport. R.A.V., R.J., S.X. and D.N.B. were responsible for atomic force microscopy. V.A.P, A.J., M.R., M.L.F. and X.C. were responsible for exfoliation. C.S.O., P.T., O.E., A.J.M. and A.R. conducted the first-principles calculations. A.K.K., T.V., T.Y. and E.V. were responsible for ARPES. V.A.P., S.T., M.R., A.D., A.K.K., C.S.O., A.J.M., M.E.Z., A.N.P. and X.R wrote the paper. A.N.P. and X.R. supervised.
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Extended data figures and tables
Extended Data Fig. 1 Magnetism and electrical transport of LaSiI.
a, Temperature dependence of the magnetic susceptibility measured with an applied magnetic field of 1 T. The magnetic susceptibility of LaSiI is essentially temperature independent over the whole temperature range with no magnetic transition, and ca. one order of magnitude smaller than that of CeSiI. This is consistent with a non-magnetic system with a small amount of a ferromagnetic impurity, presumably iron or iron oxide. Inset: the field dependence of the magnetization at T = 2 K, showing a clear ferromagnetic response, verifies the presence of a ferromagnetic impurity. Assuming the impurity is Fe, we can estimate the amount in the sample to be ~1.83 µg (~0.01 wt%). b, Temperature dependence of the resistivity of LaSiI at zero magnetic field. c, Magnetoresistance of LaSiI at T = 2 and 30 K.
Extended Data Fig. 2 Magnetic heat capacity, entropy, and dilution refrigerator heat capacity.
a, Heat capacity of multiple samples of CeSiI and LaSiI. Inset: C/T vs T2 fit for the LaSiI samples. b, Temperature dependence of the heat capacity of CeSiI and LaSiI. The magnetic heat capacity of CeSiI is estimated by subtracting CLaSiI from CCeSiI (Cmag = CCeSiI – CLaSiI). c, Temperature dependence of the magnetic heat capacity and a fitted Schottky anomaly corresponding to a low-lying crystal field level. d, Temperature dependence of the magnetic heat capacity at different magnetic fields with the Schottky contribution subtracted. e, Temperature dependence of the entropy calculated from the heat capacity data with the zero-field Schottky contribution subtracted. The entropy associated with the magnetic transition is close to the expected value Rln(2) for a doublet ground state. f, Low temperature dependence of C/T measured at different magnetic fields.
Extended Data Fig. 3 Heat Capacity Fits for Sommerfeld Coefficient of CeSiI.
C/T of CeSiI (red) and fitted model (black/grey) for 15 < T < 100 K. The Bethe Ansatz Sommerfeld and CEF contributions to the total model are shown by blue and green dashed curves, respectively. Grey lines are fits with \({\chi }^{2}\) > 0.01, and thick black lines are fits with \({\chi }^{2}\) < 0.01.
Extended Data Fig. 4 Temperature dependence of STS and ARPES, and comparison to LaSiI.
a, Scanning tunneling spectra of CeSiI and LaSiI measured at T = 8 K, 300 mV, and 200 pA. The Fano fit for CeSiI is shown in red. b, The temperature dependence of the spectra of CeSiI with the smaller data set shown in Fig. 1e. c, Magnified ARPES spectrum from the red box in Fig. 2a along the \(\bar{\Gamma }-\bar{{\rm{M}}}\) path showing the hybridization between the itinerant states and the f bands. (Conditions: T = 10 K, photon energy of 135 eV). ARPES spectra of CeSiI at d, 35 K, e, 60 K, and f, 122 K taken at a photon energy of 121 eV.
Extended Data Fig. 5 Orientation dependent magnetism of CeSiI.
Temperature dependence of the magnetic susceptibility with an applied magnetic field of 1 T with the field parallel and perpendicular to the c-axis. The inset shows an optical microscope image of a CeSiI crystal with a scale bar of 100 μm. b, Curie-Weiss curve with a field of 1 T parallel to the crystallographic c-axis and the grey dashed line representing the Curie-Weiss fit with C = 0.771 emu K mol−1 (μeff = 2.48) and θ = −3 K. The expected value of C for Ce3+ is 0.804 emu K mol−1 (μeff = 2.54).
Extended Data Fig. 6 Pressure dependence of magnetism and the metamagnetic transitions in tunnel diode oscillator devices.
a, The inverse frequency of the tunnel diode oscillator (TDO) as a function of temperature at different pressures. The fits to extract the broad antiferromagnetic peak are shown as dotted blue lines. b, Pressure dependence of TN obtained from the fits in panel (a). c, Magnetic field dependence of the inverse TDO frequency at T = 1.8 K. The blue dotted lines denote the fit for the first metamagnetic transition and the inset displays the derivative to extract the field for the second metamagnetic transition. d, Pressure dependence of the field for the first (open grey square) and second (closed grey square) metamagnetic transitions (HMM). The first metamagnetic transition shows a slightly greater pressure dependence than the second.
Extended Data Fig. 7 STM analysis of LaSiI and nesting vector.
a, STM topographic image of LaSiI, displaying the hexagonal lattice of iodine atoms and surface defects. Scale bar: 8 nm. Conditions: T = 8 K, 100 mV, 50 pA. Inset: Fourier transform of the STM topography, showing the same peak at qAFM ~ 0.28 r.l.u. (dark blue arrow, r.l.u. = reciprocal lattice units) as CeSiI (Fig. 3c), which results from a nesting wavevector. Scale bar: 0.25 r.l.u. b, Line cut of the Fourier transform along kx showing a peak in intensity at qAFM (blue arrows) for LaSiI and CeSiI and in the DFT calculated spectrum of LaSiI. c, Contour plot of the calculated DFT band of LaSiI. The blue arrow indicates the qAFM nesting wavevector between two critical points in the Brillouin zone. d, Simulation of the LaSiI STM Fourier space displaying a peak in intensity at the qAFM nesting wavevector.
Extended Data Fig. 8 Analysis of the CeSiI SdH oscillations.
a, High field magnetoresistance of CeSiI at different temperatures. b, Amplitude of the Fast Fourier transform (AFFT) versus the frequency (F) at different temperatures. c, Oscillatory component (ΔRxx) obtained by subtracting a polynomial background from the magnetoresistance. d, Temperature dependence of the SdH oscillation amplitudes (A) with the effective mass for each frequency peak displayed with respect to the mass of a bare electron (m0). The dashed lines are the fits used to calculate the effective electron masses. e, Filtered oscillations compared to the raw data.
Extended Data Fig. 9 Atomic force microscopy image and additional electrical characterization for the 15 L device.
a, Atomic force microscopy image of a 15 L device. b, 2D plot of the longitudinal resistance (Rxx) as a function of the temperature and applied magnetic field. c, 2D plot of the Hall resistivity (Rxy) as a function of the temperature and applied magnetic field.
Extended Data Fig. 10 Optical microscope image and additional electrical characterization for the 4 L device.
a, Optical microscope image of the 4 L device. b, Temperature dependence of the resistivity. The overall behavior is qualitatively similar to that of the bulk crystal, with a broad transition around 50 K and a sharp kink at 7.5 K resulting from the AFM ordering. Inset: R versus T2. The linear fit (red line) denotes a Fermi liquid state. c, Field dependence of the magnetoresistance at different temperatures with H || c-axis. d, Field dependence of the magnetoresistance of the 4 L and 15 L flakes.
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Posey, V.A., Turkel, S., Rezaee, M. et al. Two-dimensional heavy fermions in the van der Waals metal CeSiI. Nature 625, 483–488 (2024). https://doi.org/10.1038/s41586-023-06868-x
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DOI: https://doi.org/10.1038/s41586-023-06868-x
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