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Unusual high-field metal in a Kondo insulator

Nature Physics volume 17, pages 788–793 (2021)Cite this article

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Abstract

Strong electronic interactions in condensed-matter systems often lead to unusual quantum phases. One such phase occurs in the Kondo insulator YbB12, the insulating state of which exhibits phenomena that are characteristic of metals, such as magnetic quantum oscillations1, a gapless fermionic contribution to heat capacity2,3 and itinerant-fermion thermal transport3. To understand these phenomena, it is informative to study their evolution as the energy gap of the Kondo insulator state is closed by a large magnetic field. Here we show that clear quantum oscillations are observed in the resulting high-field metallic state in YbB12; this is despite it possessing relatively high resistivity, large effective masses and huge Kadowaki–Woods ratio, a combination that normally precludes quantum oscillations. Both quantum oscillation frequency and cyclotron mass display a strong field dependence. By tracking the Fermi surface area, we conclude that the same quasiparticle band gives rise to quantum oscillations in both insulating and metallic states. These data are understood most simply by using a two-fluid picture in which neutral quasiparticles—contributing little or nothing to charge transport—coexist with charged fermions. Our observations of the complex field-dependent behaviour of the fermion ensemble inhabiting YbB12 provide strong constraints for existing theoretical models.

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Fig. 1: The SdH effect in YbB12.
Fig. 2: Field-dependent FS in the metallic state.
Fig. 3: Temperature dependence of resistivity in the metallic state.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank L. Jiao, L. Fu, S. Todadri, T. Lancaster, P. Goddard, H. Kontani, H. Shishido and R. Peters for discussions. This work is supported by the National Science Foundation under Award No. DMR-1707620 and No. DMR-2004288 (transport measurements), by the Department of Energy under Award No. DE-SC0020184 (magnetization measurements), by the Office of Naval Research through DURIP Award No. N00014-17-1-2357 (instrumentation) and by Grants-in-Aid for Scientific Research (KAKENHI) (Nos. JP15H02106, JP18H01177, JP18H01178, JP18H01180, JP18H05227, JP19H00649, JP20H02600 and JP20H05159) and on Innovative Areas ‘Quantum Liquid Crystals’ (No. JP19H05824) from the Japan Society for the Promotion of Science (JSPS) and JST CREST (JPMJCR19T5). A major portion of this work was performed at the National High Magnetic Field Laboratory (NHMFL), which is supported by National Science Foundation Cooperative Agreement No. DMR-1644779 and the Department of Energy (DOE). J.S. and M.J. thank the DOE for support from the BES program ‘Science in 100 T’. Development of the 75 T duplex magnet at the NHMFL Pulsed Field Facility at Los Alamos National Laboratory was supported by the National Science Foundation through the NHMFL. The experiment in NHMFL is funded in part by a QuantEmX grant from ICAM and the Gordon and Betty Moore Foundation through Grant GBMF5305 to Z.X., T.A., L.C., C.T. and L.L. We are grateful for the assistance of Y. Lai, D. Nguyen, X. Ding, V. Zapf, L. Winter, R. McDonald and J. Betts of the NHMFL.

Author information

Authors and Affiliations

  1. Department of Physics, University of Michigan, Ann Arbor, MI, USA

    Ziji Xiang, Lu Chen, Kuan-Wen Chen, Colin Tinsman, Tomoya Asaba & Lu Li

  2. Department of Physics, Kyoto University, Kyoto, Japan

    Yuki Sato, Yuichi Kasahara & Yuji Matsuda

  3. MPA-Q, Los Alamos National Laboratory, Los Alamos, NM, USA

    Tomoya Asaba

  4. National High Magnetic Field Laboratory (NHMFL), Los Alamos National Laboratory, Los Alamos, NM, USA

    Helen Lu, Marcelo Jaime, Fedor Balakirev & John Singleton

  5. Institute of Quantum Beam Science, Graduate School of Science and Engineering, Ibaraki University, Mito, Japan

    Fumitoshi Iga

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Contributions

F.I. grew the high-quality single-crystalline samples. Z.X., L.C., K.-W.C., C.T., Y.S., T.A., H.L., F.B., J.S. and L.L. performed the pulsed-field PDO and resistivity measurements. Z.X., T.A. and J.S. performed the pulsed-field magnetometry measurements. L.C., C.T. and M.J. performed the pulsed-field magnetostriction measurements. Z.X., K.-W.C., Y.K., Y.M., J.S. and L.L. analysed the data. Z.X., Y.M., J.S. and L.L. prepared the manuscript.

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Correspondence to Ziji Xiang, John Singleton or Lu Li.

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Extended data

Extended Data Fig. 1 The magnetostriction and magnetization of YbB12.

a, The experimental arrangements for magnetostriction measurements. An optical fiber containing fiber Bragg gratings serves as the strain gauge. The single-crystal sample of YbB12 with dimensions 2.3 × 1.0 × 0.2 mm3 is glued to the fiber Bragg grating section of the fiber. A 60 T pulsed magnetic field is applied along the direction of the optical fiber. The longest edge of the single crystal is parallel to the crystallographic a axis, therefore in this arrangement the parallel strain ΔL∣∣H∣∣[100] is measured. b, Field dependence of the linear magnetostriction ΔL/L along the a axis at different temperatures ranging from 10 K to 40 K. The inset shows the high-temperature magnetostriction curves in a logarithmic scale. The dashed line is a power-law field dependence with an exponent n = 3.5. c, The linear magnetostriction measured at temperatures below 5 K. d, Magnetization of the same YbB12 single crystal measured at T = 0.64 K using a compensated-coil susceptometer (see Methods). Field was applied along the [100] direction. The gray dashed line indicates the consistency of the step-like decrease in the linear magnetostriction in c and the abrupt increase of magnetization in d at the field-induced I-M transition, μ0HI−M = 46.3 T.

Extended Data Fig. 2 The angle, temperature and field dependence of the SdH effect.

a, Oscillatory component of the PDO frequency, Δf, obtained after a 4th-order polynomial background subtraction from raw data at different tilt angles. The SdH effect is weaker in the field downsweeps (short-dashed lines) than in the upsweeps (solid lines), probably due to sample heating. b, Δf taken at θ = 10. 9∘ at different temperatures. The field-dependent cyclotron energies shown in Fig. 1d are obtained by fitting the frequency difference between adjacent peaks and valleys to the LK formula. Horizontal bars denote the peaks and valleys used for the fits in Fig. 1d. The inset displays the interval between spin-up and spin-down SdH peaks in inverse magnetic field, as a function of μ0H. If the effective mass and the g-factor are field independent, this value is expected be a constant (see Methods). c, PDO frequency measured up to 75 T in the Duplex Magnet; only the lowest pair of Landau levels, that is, N = 2±, are shown. The inset shows the small amplitude differences of N = 2± levels between T = 0.57 K and 1.51 K, suggesting a nondiverging quasiparticle mass up to at least 72 T. d, MR measured by the pulsed current technique (see Methods) in the Duplex magnet. A downward kink is observed at 68 T and coincides with the N = 2− sublevel. This slope change may imply a crossover to an unknown high-field state in YbB12.

Extended Data Fig. 3 The pulsed current technique.

a, A schematic diagram of the pulsed current technique used for measuring the MR of YbB12 samples in the KM state (see Methods). The current pulse is triggered with a precisely controlled time delay after the start of the magnetic field pulse. In the measurements we adjust the value of Rs to maintain the excitation amplitude 2-3 mA at different temperatures. b, The longitudinal MR of YbB12 in the KM state below 10 K, measured with both field and current applied along the crystallographic [100] direction. The data taken at 1.44 K, 2.00 K and 3.09 K are measured with the sample in 4He liquid, whereas other curves are measured in 3He liquid or vapour. The vertical dashed line marks the 55 T field at which we extract resistivity values from the upsweeps for the temperature dependence analysis (see Methods).

Extended Data Fig. 4 X-Ray diffraction.

X-ray diffraction pattern of the YbB12 single crystal measured with Cu Kα radiation. Only the (00l) series Bragg peaks are observed. The lattice parameter is calculated to be a = 7.47Å.

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Supplementary discussion, Figs. 1 and 2 and Table 1.

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Xiang, Z., Chen, L., Chen, KW. et al. Unusual high-field metal in a Kondo insulator. Nat. Phys. 17, 788–793 (2021). https://doi.org/10.1038/s41567-021-01216-0

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