Neutron inelastic scattering study of CePb3

Physica B 156 & 157 (1989) 815-817 North-Holland, Amsterdam

NEUTRON INELASTIC SCATTERING STUDY OF CePb, G. BALAKRISHNAN,

D.McK. PAUL and N.R. BERNHOEFT’

Department of Physics, University of Warwick, Coventry CV4 7AL, ‘Department of Physics, University of Durham, Durham DHl 3LE,

UK UK

The dynamical response of the heavy fermion system CePb, consists of two parts, a narrow quasielastic line and a broad crystal field excitation, the width of each component is strongly temperature dependent. The linewidth of the quasielastic line (r) is well represented by the expression r/2 = 0.17 + 0.12T”‘.

CePb, is often classified as a “heavy fermion” antiferromagnetic compound. The experimental trade mark of heavy fermion systems is a greatly enhanced contribution to the linear term in the specific heat at low temperatures, compared to similar normal materials, e.g. YPb, or LaPb,, presumably due to the presence of a large, localised density of f-electron states at the Fermi energy. CePb, is of particular importance in attempting to understand the origin of the unusual magnetic properties of such materials for the following reasons. CePb, is the only known cubic example of a Ce-based heavy fermion system and adopts an ordered antiferromagnetic ground state at temperatures less than 1.16 K. Further this material is thought to be one of the few examples of a magnetic field induced superconductor [l]. The properties of CePb, are very sensitive to alloying on the Pb site and considerable modifications in magnetic properties may be brought about without radically altering the Ce sublattice. CePb, would appear to be a system in which the various interactions are delicately balanced. It is therefore important to have available high quality experimental data on the magnetic properties of the pure compound if it is intended to understand the origins of the heavy fermion behaviour and explain the sensitivity of the physical properties to altering the balance of the various interactions. Previous investigations of the properties of CePb, using neutron scattering techniques have been made by Vettier et al. [2] and by Renker et al. [3]. Vettier et al. studied the magnetic order-

ing in a single crystal sample of this compound at low temperatures and found that below the critical temperature for long range antiferromagnetic ordering, TN = 1.16 K, the magnetic structure was of a complicated, modulated and incommensurate type. This is an additional example of the sensitivity of this material to the types and magnitudes of the various interactions present. Additionally they measured a heavily broadened crystal field excitation of half-width-half-maximum (HWHM) 1.2 meV at very low temperatures, but found no evidence for any quasielastic scattering. The dynamics of this material were examined by Renker et al., using a polycrystalline sample, at a temperature of 4.2 K and for a momentum transfer of 0.9 A-‘. These authors interpret their data as consisting of two Lorentzian components, a quasielastic signal of HWHM 1 meV and an inelastic crystal field excitation at an energy of 5.8meV with a HWHM of 1.9meV. In the study of the dynamics of CePb,, which is the subject of this paper, a large polycrystalline sample of -30 g was examined using the time-focussed time-of-flight spectrometer IN6 at the Institut Laue-Langevin, Grenoble, France. Typical experimental data is presented in fig. 1. Measurements were also made on a similar sample of LaPb, and used to estimate and subtract the nuclear contribution to the data obtained for CePb,. Under the conditions of the experiment high energy resolution was obtained. Two configurations were used corresponding to incident energies of 2.27 meV and 3.04 meV with energy resolution about the elastic channel of 56 PeV

0921-4526 / 89 / $03.50 0 Elsevier Science Publishers B .V. (North-Holland Physics Publishing Division)

G. Balakrishnan e( al. I Neutron inelastic scattering study of CePh,

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Fig. 1. Inelastic magnetic spectrum of CePb, quasielastic and an inelastic contribution.

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and 90 FeV respectively. These resolutions should be compared to those obtained by Renker et al. who used a triple-axis spectrometer with an incident energy of 13.8 meV where the elastic energy resolution was 640 ueV. The following conclusions were drawn from the experimental data. The magnetic scattering from CePb, contains two components, one quasielastic the other inelastic, which may both be well described by Lorentzian functions, although the relatively large width of the inelastic portion may make such a separation dubious in the present case. The temperature dependence of the intensity of the quasielastic and inelastic contributions and the relative weights of the two components strongly suggest that the crystal field scheme for Ce in CePb, has a r, level as ground state and a r, as the excited level. This is in agreement with the conclusions of Renker et al. No evidence could be found for any wavevector dependence of the magnetic scattering, over the range 0.22.4 A’ at any temperature between 2 and 128 K except for the intensity reduction due to the magnetic form factor. No additional component could be detected at low temperature which might relate to the incipient antiferromagnetic ordering at 1.16 K. The measurement of the inelastic feature, which we can only observe in energy gain mode and hence at high temperatures, agrees with the previous studies as to the position and width of the excitation from the

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ground state to the r, level. The measured HWHM for the inelastic feature is 2.1 ? 0.4 meV at 12 K and 3.5 -C 0.1 meV at 128 K demonstrating that the lifetime in the excited state is a marked function of temperature. The width of the quasielastic component to the scattering is very small at low temperatures, although the resolution of the experiment is sufficient to separate the background elastic intensity from the required signal. At 4.2 K where we can compare our results with the previous study we estimate a HWHM of 0.41 meV as compared to 1 meV. The differences between the two measurements is thought to be due to the difficulties in estimating the width of a Lorentzian component of less than the width of the experimental resolution in the presence of a strong tail from an inelastic feature. The temperature dependence of the quasielastic HWHM is presented in fig. 2 and may be well represented by a functional of the type r/2 = a + bT”’ with a = 0.17 IT 0.03 meV and b = 0.12 ? 0.01 meV K-l”. This form for the temperature dependence is that used to describe the quasielastic scattering from Kondo systems. Specific heat studies of the linear term in the specific heat (y) of CePb, suggest that y is only 200 mJ/f-mol K’ based on a high temperature extrapolation. This is a large value relative to the non-magnetic isomorph LaPb, (Y= 10 mJ/f-mol K’), but small compared to that of a “strong” heavy fermion material such as a

G. Balakrishnan

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paramagnet CeAl,, which has a y value of magnitude 1620 mJ/f-mol K*. There are considerable difficulties in accurately estimating the y magnitude at low temperatures in CePb, due to the problem of extracting the linear term from the contribution of the specific heat anomaly due to the antiferromagnetic ordering. Experiments in a large magnetic field of 11 tesla, which is sufficient to suppress the antiferromagnetic ordering, estimate that y( T = 0) is of the order of 1 J/f-mol K2 but the influence of the applied field may have some effect on the heavy fermion behaviour and the crystal field excitations and hence restrict the significance of this derived quantity. The experimental data discussed in this paper would however agree with the contention that y(O) for CePb, should be considerably greater than that derived from the high temperature extrapolation. The magnitude of the quasielastic linewidth at T = 0 should be approximately inversely proportional to the linear coefficient of the specific heat and the fact that the value for r/2 at low

temperatures is similar to that derived for CeAl, [4] and CeCu, [5] suggests that y(0) should also be of the same magnitude. Further experiments of interest on this material would involve the examination of the magnetic field and alloying dependence of the quasielastic width. It would also be of interest to examine the wave vector dependence of the quasielastic line in the 9 = 0 limit to check for any correlation effects due to the presence of a lattice of cerium atoms. References C.L. Lin, J. Teter, J. Crow, T. Mihalsin, J. Brooks, A.I. Abou-Aly and G.R. Stewert, Phys. Rev. Lett. 54 (1985) 2541. 121C. Vettier, P. Morin and J. Flouquet, Phys. Rev. Lett. 56 (1986) 1980. [31B. Renker, E. Gering, F. Gompf, H. Schmidt and H. Rietschel, J. Magn. Magn. Mat. 63-64 (1987) 31. I41A.P. Murani, K. Knorr and K.H.J. Buschow, Solid State Commun. 36 (1980) 523. PI U. Walter, D. Wohlleben and Z. Fisk, Z. Phys. B 62 (1986) 325.

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