Low-Energy Excitations and the Electronic Specific Heat of YbBiPt

Neutron scattering data from the cubic heavy-fermion compound YbBiPt are presented, along with an interpretation in terms of strongly broadened crystal-field levels. To first order, the ground state is sixfold degenerate, consisting of a doublet (17) and quartet (I' s). Integration over these levels reproduces the observed linear specific-heat coefficient y of 8 Jmol ' K to within ~20%. At the lowest temperatures, an extra symmetry-forbidden splitting is observed.

lowest temperatures, an extra symmetry-forbidden splitting is observed. The discovery of a huge linear-temperature coefficient of specific heat y = 8 Jmol ' K in YbBiPt [1,2] has generated considerable excitement. This value is an order of magnitude more than in typical heavy-fermion materials [3] and three orders of magnitude greater than in normal metals. The origin of this huge specific-heat contribution is of central interest to the understanding of the electronic properties of heavy-fermion systems, and we have been carrying out inelastic neutron scattering experiments to probe the low-energy dynamics of this material directly. We find that the I's quartet and I'7 doublet crystal-field levels lie at low energies and are broadened strongly relative to their splitting by intersite exchange interactions. The calculated specific heat, based on these broadened magnetic excitations, accounts semiquantitatively for the enormous experimentally observed specific heat of this material.  study [4], we have shown that the Pt ion is on the unique site, in contrast to what had been reported previousl [2].
The e Yb ion therefore has only Pt ions as nearest neighbors. In a study of the whole RBiPt series [1], where R symbolizes the rare-earth element, the lattice parameter of YbBiPt showed no deviation from the general trend, and this is good evidence that Yb is in the Yb3+ state.
In all heavy fermions, the correlated state can be thought of as developing from a crystal-field eigenstate (a doublet in Ce-based heavy fermions). The subsequent many-body interactions with the conduction electrons broaden this underlying crystal-field state, giving a large continuous density of excited states down to zero energ .
In YbBiPt, the cubic crystal field splits the eightfold ro energy. degenerate 1 = 7/2 state of Yb + into two doublets, I 6 and I 7 and a quartet, I s. Assuming a simple pointcharge model, one arrives at a crystal-field scheme such as that shown in Fig. 1(a), where the levels are I 7, 1 s, and 6 in that order, and the total splitting is of order 12 meV.
However, in order to interpret their original susceptibility data, Fisk et al. [2] invoked a crystal-field level at roughl roug y 1 meV and proposed the level scheme given in Fig. 1(b). Their specific-heat results gave an integrated entropy of R&nln2 by 1 K, indicating an electronic degeneracy of 2 below 0.1 meV, and Rln5 by 20 K.
We have conducted inelastic neutron scattering experiments using the LAM-40 spectrometer [5] at the Japanese National Laboratory for High-Energy Physics (KEK), the QENS spectrometer [6] at Argonne National Laboratory, and the Cold-Neutron Fermi-Chopper Spectrometer [7] at the National Institute of Standards and Technolog ( ST). LAM-40 and QENS are time-of-fiight crystal-NI ec no ogy analyzer spectrometers with quasielastic resolutions of 0.35 and 0.07 meV FWHM, respectively. The NIST experiments were performed in a He cryostat using incident energies F; of 4.5 and 2.7 meV, giving resolutions of 0.28 and 0.11 meV, respectively. The work on LAM-40, a preliminary account of which has been published previously [8], showed a clear crystal-field level just below 6 meV, with a more complicated response at low energies as shown in Fig. 2(a). Other than some weak magnetic scattering at around 8 meV, no further excitations were seen up to 20 meV. Although we show only the lowest temperature data at 3.3 K in Fig. 2(a), data were also collected at various temperatures up to 77 K. The temperature dependence of the intensity of the 6 meV level can be used to extract its degeneracy, g1, relative to that of a hypothetical sharp ground-state level, go. The intensity of the 6 meV line is shown in Fig. 3(a), while the energies and widths obtained from the fits are shown in Figs. 3(b) and 3(c), respectively. The temperature dependence of th t e intensity can be fit assuming it to be proportional to the total ground-state occupancy no given bỹ = 11 + (g /g. ) -'-"")-'.
We obtain gi/go = 0.56~0.10, which is clear evidence that the 6 meV level is a doublet and not a quartet. The level also softens slightly with increasing temperature, as shown in Fig. 3(b).
The entire spectrum can be fit fairly well assuming that the imaginary part of the dynamic susceptibility consists of three Gaussian components, two of which are PHYS ICAL REVIEW LETTERS picture is inappropriate and that intersite correlations must be important. One quasielastic component is narrow and has a width of roughly 0.2 meV, which corresponds to a correlation temperature of 2 K, and the second quasielastic component is broader. Given these observations, the fact that the scattering below 2 meV must contain both the I 8 quartet and one of the doublets and the fact that the specific heat only gives an entropy of Rln2 by 1 K, we proposed [8] the level scheme given in Fig. 1(c). In this scheme, the sharp quasielastic response would belong to the I 7 doublet, while the broad quasielastic response would belong to the quartet. To a first approximation the ground state contains both, but they are hybridized with the conduction electrons in different ways. It is well known that the quartet is very sensitive to perturbations [9], and it is plausible that it is hybridizated more strongly. The temperatures dependences of the widths, which can be thought of as correlation or Kondo temperatures, are shown in Fig. 3(c).
However, the fits are not perfect, and there is clearly some structure within the "broad quasielastic" response, especially at low temperature. This is even clearer in the data shown in Fig. 2(d), some of which were taken at 350 mK and some at 450 mK. The intent was to look for differences above and below the 400 mK phase transition [1,10]. No differences were found and to improve statistics, the two data sets have been added. There are clearly two separate levels at roughly 1 and 2 meV, respectively. specific heat as a function of temperature can be reproduced, but the quantitative agreement is still not perfect. In summary, we have identified the excitations responsible for the huge "electronic" specific heat in this extraordinary compound, and we propose a very simple explanation in terms of broadened crystal-field levels.
YbBiPt is in many ways a prototypical heavy-fermion compound to study, because the hybridization is not so strong as to wash out the crystal-field levels completely, in contrast to many uranium-based heavy fermions, but yet it is still hybridized more than the cerium-based heavy fermions which show clearly separated levels. The remaining questions for the future concern the cause of the "forbidden" splitting shown in Figs. 2(c) and 2(d), and the exact nature of the 400 mK transition. In addition, it is remarkable that this huge amount of entropy is expressed at such low temperatures, without the compound developing conventional long-range magnetic order. But clearly, crystal-field degrees of freedom are active on the same energy scale as the correlation energy and any exchange energy. Finally, we note that excitation spectra fairly similar to ours have been observed by Marshall [13]  The inset shows the corresponding density of excited states. In (b) the solid line is the full calculation, and the points are the experimental specific-heat data from Ref. [2].
10 J mol ' K is in remarkable agreement with the measured value of 8 J mol ' K ' [2], and roughly half of this comes from the broadened "sharp" doublet and may be considered "normal" heavy-fermion behavior. This is in very good agreement with the independent estimate of 5 J mol ' K for this component from an analysis of the resistivity associated with the 400 mK transition, assuming a spin-density wave model [10]. The other half originates from the crystal-field degeneracy at low energies.
This model gives an entropy of Rln2 by 0.9 K and Rln5 by 9.2 K, in fairly good agreement with values derived from the bulk specific heat [2]. If one goes further and includes the split levels as separate Kramers doublets, the qualitative structure of the bumps at 0.5 and 6 K in the [I) P. C. Canfield et a/. , J. Appl. Phys. 70, 5800 (1991).