Magnetic quantum oscillations in Ce-based heavy-fermion compounds

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Physica B 230-232 (1997) 114-116

Magnetic quantum oscillations in Ce-based heavy-fermion compounds R.W. Hill, C. H a w o r t h , T.J.B.M. J a n s s e n , P.J. M e e s o n * , M. S p r i n g f o r d , A . L . W a s s e r m a n H.H. WillsPhysics Laboratory, University of Bristol, Royal Fort, Tyndall Avenue, Bristol BS8 1TL, UK Abstract

We report on quantum oscillation studies in Ce-based heavy-fermioncompounds, in particular on the magnetic field dependence of the quasiparticle effectivemass in CeB6 at the lowest possible fields.We make use of a new SQUID-based de Haas van Alphen (dHvA) spectrometer, which was developed for use in very high magnetic fields (upto 19 T) and at ultralow temperatures (< 3 mK) for the study of heavy-fermionmaterials. As a result of the unprecedentedsensitivity,the dHvA measurements have been extended to much lower magnetic field regimes and temperatures than previously possible. Keywords: Q u a n t u m oscillations; CeB6

The study of Landau quantum oscillation effects in metals has long been one of the most direct and productive techniques for inspection of the detailed ground-state properties of metals and has been used for many years to study electron correlation effects [1]. A major experimental long-term objective in the field has been to increase signal amplitudes, generally by the use of lower temperatures, very high magnetic fields, and high-purity singlecrystal samples. In the study of heavy-fermion compounds where the sample quality is generally not ideal for these purposes, and the very high effective quasiparticle mass at the Fermi surface necessitates temperatures of the order 1 mK, the signal amplitude is usually far from maximised. Temperatures this low are also incompatible with conventional de Haas-van Alphen (dHvA) detection techniques [2] which involve an AC magnetic field, typically of order 0.1 Yrms at a few Hertz, thus causing eddy current heating in the metallic samples. By developing a SQUID-based detection system for dHvA oscillations we have been able to overcome these * Corresponding author.

problems and at the same time have considerably improved the sensitivity. Although this SQUID detection system is currently being used upto 19 T and with sample temperatures below 3 mK for the study of very heavy fermions, we report here on an investigation of dHvA in CeB6 to the lowest fields possible making use of the high sensitivity of this technique. CeB6 is cubic, it has an electronic specific heat coefficient of approximately 250 mJ/(mol K 2) at zero field, and it is available (at least for purposes other than dHvA) as good-quality single crystals. These factors, amongst others, have made this a very well studied material [3-6]. Despite this extensive effort CeB6 remains an incompletely understood compound. In particular, the dHvA studies are not yet complete, the bandstructure calculations do not agree in detail with what is observed, and the relationship of the heavy electron fluid to the low magnetic field phase transitions, which seem to play a major part in determining the strength of the heavy-fermion interaction, is uncertain. In passing we observe that these problems are not restricted to CeB6, it seems that dHvA data in most heavy fermions is likely to be incomplete,

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Frequency [T] Fig. 1. An example of a Fourier transform in lIB space of the de Haas-van Alphen signal from CeB6. The crystal is oriented 20 ° from (1 1 0) towards (1 00). The presence of the multiple peaks in the region (1.0-1.7) kT is incompatible with a model of the Fermi surface topology based on LAB6.

especially so in the heaviest compounds where for experimental reasons studies have so far generally been limited to temperatures above 20 mK, conventional sensitivities then restrict observable sheets of Fermi surface to those with an effective quasiparticle mass of, at most, a few hundred electron masses, severely limiting our knowledge in some cases. Further, it seems generally true that band structure calculations are unable to accurately predict the Fermi surface topology in detail, nor do they approach an estimate of the Fermi surface density of states. Fig. 1 shows a representative Fourier transform in inverse magnetic field space of the dHvA signal from CeB6 at a direction 20 ° from (1 1 0) towards ( 1 0 0 ) . The signal is derived from a conventional modulated field spectrometer at 2 0 m K and 13 T. X-ray studies indicate that the crystal is not twinned. The presence of several frequencies in the range (1.0-1.7)kT, which do not occur in the f-electron free "reference compound" LAB6, should be noted. Furthermore, whilst similar frequencies occur in both LaB 6 and CeB6 at approximately 8 kT the angular behaviour is different. For some 20 ° about (1 1 1) in CeB6 this 8.7 kT signal disappears, whilst in LaB6 the signal continues up to and through (1 1 1). These results imply that the heretofore common identification of the Fermi surface topology of f e B 6 with that of LaB 6 is not correct. Inversion of the dHvA data to obtain a correct

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model of the Fermi surface geometry will require further angle-resolved data to be obtained. Band-structure calculations I-7] in which the felectrons are alternately treated as core electrons or band electrons suggest that more frequencies in the 1 kT region, and hence better agreement, are available in the f-band case. This is perhaps a further indication that the LaB 6 model is inappropriate. These calculations do not take account of the antiferro-quadrupolar phase within which the dHvA measurements are performed. Whilst broad features of the Fermi surface are reflected in the calculations, they do not agree in detail with the measurements, and again a confident statement of the Fermi surface topology is unavailable. In CeB6 the linear term in the electronic specific heat coefficient rises with magnetic field from its value of about 250 mJ/(mol K 2) at zero field, passes through a peak at about 2 T and then falls continuously as the field rises [8, 9]. The peak is presumably associated with the magnetic phase transition from a low-field antiferromagnet to an antiferroquadrupolar phase. The magnetic phase transitions further complicate our understanding of CeB6 but the intimate way in which the phase transition seems to affect the electronic heat capacity, and hence the heavy-fermion interaction, is intriguing. To study this further we performed measurements as a function of magnetic field of the quasiparticle effective mass of the 8.7 kT orbit in the ( 1 0 0 ~ orientation. Another reason to study this involves the debate over the presence of neutral quasiparticles [10] in heavy-fermion compounds. This has involved, in part, the question of whether experiments are performed in a 'low magnetic field regime'. This is particularly true for de Haas-van Alphen effect studies which by the nature of the effect are often performed at the highest available fields, the signal amplitude generally rising exponentially with the intensity of the magnetic field. The question of definition of the low-field regime is left somewhat open, however, dHvA studies provide one of the few ways in which direct information about the nature of the heavy quasiparticles at the Fermi surface, through a measurement of quasiparticle mass, can be related to the measured heat capacity [3] and hence determine unambiguously the presence of neutral quasiparticles.

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Magnetic Field [B] Fig. 2. The measured effective quasiparticle mass of the 8.7 kT orbit in the ( 1 0 0 ) direction of CeB6. Present data is shown in black diamonds with work from other authors as described in the legend. The field dependence of the mass mimics the measured specific heat capacity of Muller et al. [8] to within an overall scale factor.

However, the absence of band structure predictions which agree with the known parts of the Fermi surface, and the uncertainty from dHvA measurements of the full Fermi surface topology, cause difficulties in integrating the dHvA data to obtain the total density of states for comparison with the measured heat capacity. The newly discovered sheets of Fermi surface shown in Fig. 1 invalidate the Fermi surface topology used in Ref. [3]. Even so, the newly observed sheets of Fermi surface in CeB6 tend to weaken the neutral quasiparticle argument as more of the density of states can be accounted for. Fig. 2 shows the measured dHvA mass of the 8.7kT orbit in the [100] direction of CeB6 as a function of magnetic field taken using the SQUID detection technique. The present data has extended the field range down to approximately 5 T where the signal amplitude is less than one hundredth of its value at 10 T, the previous detection limit for these measurements. The full line is the heavy-fermion dHvA theory of Wasserman et al. [11] which is based on the periodic Anderson Hamiltonian and seems to give a reasonable fit to the data with fitting parameters ~1 = 95 _+ 5 and ~2 = 0.08 + 0.005 [3]. The form of the effective mass plot with field accurately mimics the specific heat data [8] to within an overall scale factor. This correlation, if

repeated at other orbits and orientations, will presumably allow the thermodynamic electron mass from heat capacity measurements to be accounted for throughout the magnetic field range. One can only speculate at present whether the quasiparticle mass will fall again, as the heat capacity falls, on lowering the magnetic field into the antiferromagnetic phase. Clearly, the presence of the magnetic phase transition has a controlling effect on the electronic mass renormalisation, at least in the antiferro-quadrupolar state. In summary, we have built a SQUID based dHvA spectrometer, the very high sensitivity of this technique has allowed us to improve our knowledge of the quasiparticle effective mass in CeB6 to much lower magnetic fields than previously possible. The correlation of this with specific heat data and the discovery of new sheets of Fermi surface cast further doubt on the validity of the neutral quasiparticle model, and open the question of the correct Fermi surface topology for CeB6. We are grateful to the EPSRC, The Royal Society and the European Union for financial support and wish to thank Professor Gehring and Dr. Suvasini for sharing their unpublished results with us.

References [1] A. Wasserman and M. Springford. Adv. Phys. 45 (6) (1996). [2] D. Shoenberg, Magnetic Oscillations in Metals (Cambridge University Press, Cambridge, 1984). [3] N. Harrison, P. Meeson, P.-A. Probst and M. Springford, J. Phys.: Condens. Matter 5 (1993) 7435. [4] Y. Onuki, T. Komatsubara, P.H.P. Reinders and M. Springford, J. Phys. Soc. Japan 58 (1989) 3698. 15] W. Joss, J.M. van Ruitenbeek, G.W. Crabtree, J.L. Tholence, A.P.J. van Deursen and Z. Fisk, Phys. Rev. Lett. 59 (1987) 1609. [6] A.P.J. van Deursen, R.E. Pols, A.R. de Vroomen and Z. Fisk., J. Less-Common Met. 111 (1985) 331. 1.7] M.B. Suvasini, G.Y. Guo, W.M. Temmerman, G.A. Gehring, Physica B 206-207 (1995) 37 and private communication. [8] T. Muller, W. Joss, J.M. van Ruitenbeek, U. Welp, P. Wyder and Z. Fisk, J. Magn. Magn. Mater. 76-77 (1988) 35. [-9] C.D. Bredl, J. Magn. Magn. Mater. 63-64 (1987) 355. [I0] Y. Kagan, K.A. Kikoin and N.V. Prokof'ev. Physica B 182 (1992) 201; and JETP Letts. 56 (1992) 219. [11] A. Wasserman, M. Springford and A.C. Hewson, J. Phys.: Condens. Matter 1 (1989) 2669.