Fer-Iaai Surface Instability and Symmetry Breaking in Heavy-Fermion Compound YbBiPt

on the cubic heavy-fermion compound YbBiPt at ambient and hydrostatic pressures to =6 kbar and in magnetic fields to 1 T. Resistivity anisotropy sets in below the phase-transition temperature T, = 0. 4 K. %e interpret a rise of resistivity below 0. 4 K as due to partial gapping of the Fermi surface with the weak coupling energy gap of 60/k&T, . = 1. 65 + 0. 15. Effects of hydrostatic pressure and magnetic field on the phase transition and heat capacity data are consistent with a spin density wave formation in a very heavy electron band at T = 0. 4 K.

of this material is the existence of a magnetic phase transition at 0.4 K that manifests itself as a small but rather sharp peak in specific heat. Unlike Ceor Ubased heavyfermion antiferromagnets, in which magnetic order creates an internal magnetic field that reduces y below the Neel temperature, the large y in YbBiPt persists below 0.4 K. Muon spin resonance experiments [3] have placed an upper limit on the ordered moment of 0.1p, g which is consistent with the absence of a nuclear Schottky anomaly in the very low temperature specific heat and with the absence of a strong suppression of y below 0.4 K [1]. Although smallmoment magnetism is found in heavy-fermion materials, it appears in many cases to coexist with superconductivity, e. g., in UPt3, Ui "Th"Bei3,and CeCu2Si2 [4]. This is not the case in YbBiPt, which makes it particularly interesting.
To address questions of the nature of the magnetic transition in YbBiPt and its ground state, we have studied the electrical resistivity as a function of pressure and applied magnetic fields and we argue that these results, combined with specific heat measurements, are consistent with the development of a spin density wave (SDW) below 0.4 K in a heavy-mass band of conduction electrons.
Single-crystal samples of YbBiPt were grown from an excess Bi Ilux [5]. X-ray diffraction confirms the samples to be face-centered cubic with the half-Heusler structure at room temperature. Neutron diffraction shows no evidence for a structural transition to 27 K [2]. Resistance measurements were made in standard 4-probe and Montgomery [6] configurations. Pressure was generated in a selfclamping Be-Cu cell [7] Fig. 1(a) is a sampleto-sample variation or an inherent property of YbBiPt, we performed resistivity measurements on a single-crystal square platelet in Montgomery arrangement [6]. The two pairs of the long edges of the platelet were found to be closely parallel to crystallographically equivalent (100) and (010) directions. We pass excitation current along 0031-9007/94/73 (3)/492(4)$06. 00 1994 The American Physical Society one of the edges of the sample and detect the voltage drop along the opposite edge for both pairs of edges. We can then extract resistivities in the directions along the two edges [6]. The result of such a measurement and analysis on one sample is shown in Fig. 1(b). We see that the resistivity becomes markedly anisotropic, and the cubic symmetry, apparent above T, by the coincidence of the two resistivity curves, is broken below T, = 0.4 K.
Behavior similar to that shown in Fig. 1(b) has been observed [8] in face-centered cubic Cr, which exhibits an SDW transition at 311 K. This SDW gaps part of the Fermi surface along the direction of the SDW ordering vector Q, with a corresponding increase in resistivity along the same direction. However, in the case of Cr the anisotropy must be brought out by applying magnetic field or uniaxial stress to the sample to align randomly oriented [with Q along three equivalent (100) directions] domains.
In YbBiPt, however, we see anisotropy without changing external parameters (magnetic field or stress), which is a highly unusual situation. It implies that there are very few large domains in the sample or that the domains are oriented to a high degree, perhaps by internal stress developed during material growth.
Hydrostatic pressure has been an important tool for investigating the SDW transition in Cr. The transition temperature is suppressed rapidly by pressure, at the rate of (dT~/dP)p p = 5.1 K/kbar [9]. Such a strong dependence on pressure is seen as a consequence of the delicate Fermi-surface nesting that results in an SDW transition. Figure 2 shows the effect of hydrostatic pressure on the resistivity of YbBipt. Application of a rather small pressure, between 0.78 and 1.20 kbar, suppresses any resistive signature for the low-temperature phase transition. Such high sensitivity to relatively small pressure again is consistent with the 0.4 K transition in YbBiPt being due to a Fermi-surface instability.
Extending the analogy with Cr, we have analyzed the resistivity curve shown by open circles in Fig. 1 Here the subscripts g and p refer to the ease when the region 2 of the Fermi surface is gapped or made paramagnetic, respectively, by application of pressure. In using Eq. (1), we assume that neither relaxation times nor (T( are affected by the ordering [10], and that R~, the paramagnetic background that has to be subtracted, is given by the p = 1.2 kbar curve of Fig. 2. The ratio (T2g/(T2~is given by [11]  To further investigate this transition we performed a series of resistance measurements in a magnetic field. The two samples used were of a "Montgomery type" thin square platelets, each oriented to have one pair of long edges along the magnetic field. Figure 4 displays the resulting magnetic-fieldtemperature phase diagram for the low-temperature phase of YbBiPt. For both the temperature and magnetic field sweeps the phase transition was marked by a kink in the V/I traces [13). Within an SDW picture of the 0.4 K phase transition in YbBiPt, it is now possible to make a rough estimate of the heavy-fermion contribution to the low-temperature specific heat, which as mentioned is one of the central issues raised by YbBiPt. Figure 5 shows C~v s T near T" which is similar to the data reported previously [1]. An equal-area construction, shown by the dashed line, gives the ideal change in heat capacity at T, of AC = 0.470 .1 J/mole K. The resistivity analyses above indicate that YbBiPt follows weak-coupling BCS theory, and consequently b C/yT, should be equal to 1.43. To proceed further we need an estimate of the percentage of the Fermi surface that is gapped. This estimation is complicated by the formation of large domains that are responsible for anisotropic resistance below T, . In polydomain samples (like Cr) the resistivity is averaged with respect to the direction of the SDW wave vector, and it can serve as a good estimate of the gapped fraction of the Fermi surface. We obtain an "effective polydomain" estimate by averaging relative resistivity changes at T = 0, similar to that shown in Fig. 3, for all available data YbBiPt is not the first heavy-fermion system where the existence of an SDW phase has been suggested. The first and only other candidate so far has been the Tp = 17.5 K phase transition in URu 2Siz [15],where a rise in resistivity at the transition terrqx", rature and an exponentially decreasing heat capacity below To have been interpreted within SDW hypothesis. Analysis of the heat capacity data gave a value of the energy gap as Ap = 7.2kaTO, with about 40% of the Fermi surface removed by the formation of the SDW state [15]. In spite of extensive experimental and theoretical work on the nature of the 17.5 K phase transition in URu2Si& since original investigation, the pre-494 cise picture of the magnetic order below To = 17.5 K "remains an enigma" [16]. Consensus, however, is shifting towards a complicated ordering of local moments. Given that YbBiPt may be the first clear case of a heavy-fermion system where antiferromagnetism is of itinerant character, with Fermi surface nesting occurring in the very heavily renormalized bands. In summary, below T, = 0.4 K the resistivity of YbBiPt becomes highly anisotropic, indicating that the cubic symmetry is broken below T, . The rise in resistivity along some directions of the lattice is consistent with partial gapping of the Fermi surface. From an analysis of the temperature dependence of the resistivity increase below T"we conclude that the gap is described by a weak-coupling energy gap h(T) = kpf ac(sT/T, ) with b p/kttT, = 1.65~0. 15. The H Tphas-e diagram is that of a classic weak-coupling transition, with the phase boundary closely following BCS theory. We suggest that these observations are consistent with a spin-density wave transition in YbBiPt at 0.4 K that gaps a part of the Fermi surface. This identification is supported further by the extreme pressure dependence of the transition temperature. Analysis of the specific heat near T, in view of this interpretation indicates that the SDW occurs within a strongly renormalized band of heavy fermions that accounts for much of the low temperature Somraerfeld coefficient y = 8 J/mole K . We want to thank Dr. Giinter Spam for help with constructing apparatus and Dohn Arms for writing some of the software. We also acknowledge Dr. S.A. Trugman