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Magnetic Field-Tuned Fermi Liquid in a Kondo Insulator

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Magnetic Field-Tuned Fermi Liquid in a Kondo Insulator ARTICLE https://doi.org/10.1038/s41467-019-13421-w OPEN Magnetic field-tuned Fermi liquid in a Kondo insulator Satya K. Kushwaha 1,2, Mun K. Chan 1, Joonbum Park1, S.M. Thomas 2, Eric D. Bauer 2, J.D. Thompson2, F. Ronning2, Priscila F.S. Rosa2 & Neil Harrison1* Kondo insulators are expected to transform into metals under a sufficiently strong magnetic field. The closure of the insulating gap stems from the coupling of a magnetic field to the 1234567890():,; electron spin, yet the required strength of the magnetic field–typically of order 100 T–means that very little is known about this insulator-metal transition. Here we show that Ce3Bi4Pd3, owing to its fortuitously small gap, provides an ideal Kondo insulator for this investigation. A fi metallic Fermi liquid state is established above a critical magnetic eld of only Bc 11 T. A peak in the strength of electronic correlations near Bc, which is evident in transport and susceptibility measurements, suggests that Ce3Bi4Pd3 may exhibit quantum criticality ana- logous to that reported in Kondo insulators under pressure. Metamagnetism and the breakdown of the Kondo coupling are also discussed. 1 MPA-MAGLAB, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. 2 MPA-CMMS, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. *email: [email protected] NATURE COMMUNICATIONS | (2019) 10:5487 | https://doi.org/10.1038/s41467-019-13421-w | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-13421-w ondo insulators are a class of quantum materials in which 2.0 the coupling between conduction electrons and nearly K 40 localized f -electrons may lead to properties that are dis- tinct from those of conventional band insulators1–3. Remarkable 1.5 ) properties of current interest include topologically protected –2 surface states that are predicted4–6 and reportedly confirmed by – 1.0 experiments7 12, and reports of magnetic quantum oscillations .cm K Ω – 30 originating from the insulating bulk13 16. The very same mag- ( fi A netic eld that produces quantum oscillations also couples to the 0.5 f -electron magnetic moments, driving the Kondo insulator inexorably towards a metallic state17,18. The required magnetic fi 17,19 elds in excess of 100 T have, however, proven to be prohi- (K) 20 0.0 T ∂ ∂ ∂ /∂ T > 0 bitive for a complete characterization of the metallic ground state. xx/ T < 0 xx Thermodynamic experiments have thus far provided evidence for the presence of electronic correlations in Kondo insulators at high-magnetic fields. Quantum oscillation experiments, for TFL example, have found moderately heavy masses within the insu- 10 lating phase in strong magnetic fields15. Furthermore, heat capacity experiments have shown that the electronic contribution TM FL undergoes an abrupt increase with increasing magnetic field20,21: in one case20 the increase occurs within the insulating phase, 22 0 suggesting the presence of in-gap states , whereas in another, it 0204060B 21 c coincides with the onset of an upturn in the magnetic B (T) susceptibility18,19 and reports of metallic behavior7,18.An Fig. 1 Magnetic field versus temperature phase diagram of Ce Bi Pd . T unambiguous signature of metallic behavior, such as electrical 3 4 3 M χ χ resistivity that increases with increasing temperature at accessible indicates the peak in the susceptibility ( ) obtained from versus T (triangles) and B (stars) from Fig. 6. Here, B ¼ BðT ! 0Þ is indicated by magnetic fields, has yet to be reported. c M a green circle. Also shown is the temperature T (circles) above which the We show here that insulating Ce Bi Pd , once polished to FL 3 4 3 resistivity departs from ρ ¼ ρ þ AT2 (i.e., Fermi liquid) behavior. Shaded remove surface contamination, exhibits properties consistent with xx 0 it being a reduced gap variant of its sister Kondo insulator regions and lines are drawn as guides to the eye. The gray dashed line ∂ρ =∂ ¼ 22,23 shows where the derivative xx T 0 (plus symbols from sample A in Ce3Bi4Pt3 , which is also a topological Kondo insulator 4,24,25 fi static fields, ´ symbols from sample A in pulsed fields and asterisk candidate . The atypically small magnetic eld of Bc 11 T symbols from sample B in static fields; see Methods). To the left of this line required to overcome the Kondo gap of insulating Ce3Bi4Pd3 (see 26 ∂ρ =∂ Fig. 1), makes this material ideal for investigating the metalli- xx T < 0, indicative of insulating behavior, while to the right of this line ∂ρ =∂ zation of a Kondo insulator in strong magnetic fields. We find a xx T > 0, indicative of metallic behavior. The right-hand-axis indicates magnetic field-induced metallic state exhibiting an electrical the magnetic field-dependence of the A coefficient (squares), with the resistivity that varies as T2 at low temperatures (where T is the values for B ≲ 20 T corresponding to the average of samples A and B in temperature), thereby revealing a Fermi liquid ground state in the Fig. 5. Error bars represent the standard error. high-magnetic field metallic phase. We also identify a magnetic fi eld-tuned collapse of the Fermi liquid temperature scale TFL fi near Bc, indicating that Ce3Bi4Pd3 may exhibit a magnetic eld- Kondo insulators have Kondo gaps of several millielectronvolts, tuned quantum critical point analogous to that observed in SmB6 accompanied by inverse residual resistivity ratios in the range 27–31 2 À1 5 as a function of pressure . The origin of the collapsing Fermi 10 <RRRR < 10 and maxima in the magnetic susceptibility and 20,36 ≲ liquid temperature scale in Ce3Bi4Pd3 is revealed by susceptibility heat capacity in the range of temperatures 10 K TM fi fi fi measurements, which nd a peak as a function of magnetic eld 100 K. Ce3Bi4Pd3, however, appears to have a signi cantly smaller at Bc that can be traced back to a broad maximum in the sus- Kondo gap, accompanied by an inverse residual resistivity ratio of À ceptibility as a function of temperature at TM in weak magnetic only R 1 5 (see Fig. 2a) and maxima in the susceptibility (see fi RRR elds. This maximum implies the formation of Kondo singlets at Fig. 2b) and heat capacity (see Fig. 3)atT 5 K. A possible ¼ 20 M a temperature TK cTM (where 3 <c<4) , yielding 15 <TK < explanation for the smaller Kondo gap in Ce Bi Pd compared to 20 K. A gradual evolution of the susceptibility from a crossover 3 4 3 its sister compound Ce3Bi4Pt3 is the reduction in the strength of along the temperature axis to a sharper peak along the magnetic fi 37 fi the hybridization identi ed in electronic structure calculations . eld axis at Bc is therefore unveiled. The small size of the Kondo gap in Ce3Bi4Pd3 in Fig. 2a gives rise to a shallow slope of the resistivity Arrhenius plot in Fig. 2a Results (see Supplementary Fig. 2 for the magnetic field B-dependence), Evidence for a small gap Kondo insulator. Typical signatures of which therefore has a strong likelihood of being affected by the a Kondo insulating state include an electrical resistivity that exhi- presence of in-gap states and changes in the transport scattering ∂ρ =∂ bits a thermally activated insulating xx T<0 behavior (where rate with temperature. To obtain an estimate of the Kondo gap ρ that is less dependent on the scattering rate, we turn to the xx is the electrical resistivity) over a wide range of temperatures and a Curie–Weiss behavior in the magnetic susceptibility at high approximately activated behavior observed in Hall effect temperatures that crosses over via a maximum in the susceptibility measurements38 (see Fig. 4a), whereupon we obtain Δ ¼ 1.8 ± into a Kondo gapped state at low temperatures1,3,22,32–35. Zero 0.5 meV ( 21 K). This value is quantitatively consistent with magnetic field electrical resistivity and magnetic susceptibility estimates obtained from modeling the heat capacity and measurements reveal Ce Bi Pd to exhibit such signatures (see susceptibility (see below). An important factor in being able to 3 4 3 ρ Figs. 1 and 2 and Supplementary Fig. 1), but with a Kondo tem- extract the carrier density is that xy (shown in Fig. 4a) is linear fi fi Δ perature scale that is signi cantly reduced relative to those found in in B at low B. We therefore nd that kBTK, which is the archetypal Kondo insulators SmB6 and Ce3Bi4Pt3.Typical quantitatively consistent with the hybridized many-body band 2 NATURE COMMUNICATIONS | (2019) 10:5487 | https://doi.org/10.1038/s41467-019-13421-w | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-13421-w ARTICLE 5.0 a 6 10 1/T (K–1) Ce Pd 0.20 0.15 0.10 0.05 Sample A Bi Δ ∼ 4 meV 4.5 0 T ) 4 105 10 –2 4 K 7 –1 .cm) Ω .cm) 9 Ce Ω ( xx ( –1 xx 3 Δ ∼ 0.4 meV 4.0 10 104 Spin up 10(J mol 0 Spin down T B = 0T 5 10 20 300 / C T (K) (meV) 3.5 E –2 Ce3Bi4Pd3 Sample A 3 10 Ce Bi Pd Sample B 3 4 3 0369 Ce3Bi4Pt3 Sample D B (T) 3.0 246810 0 50 100 150 200 250 300 T (K) b Fig. 3 Specific heat data. Low-temperature heat capacity divided by T M 450 temperature, C=T, plotted versus logarithmically scaled T (symbols). Solid 2.5 Ce Bi Pd 3 4 3 lines represent fits in which the Kondo gap is modeled using the 360 Schotte–Schotte model (see Methods).
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