Phase transitions in CeCu2Si2

374

Journal of Magnetism and Magnetic Materials 90 & 91 (1990) 374-376 North-Holland

Invited paper

Phase transitions in CeCu 2Si 2 M. Hunt a, P. Meeson and W. Sun b a b

a,

P-A. Probst a, P.H.P. Reinders a.I, M. Spring ford a, W. Assmus

b

ll.ll. Wills Physics Laboratory. Unicersity of Bristol, Tyndall Al'enue, Bristol BS 8 ITL, UK Physikalisches Institut, J.IV. Goethe-Unicersitiit, Robert-Mayer-Sir. 2-4. Frankfurt am Main, Fed. Rep. Germany

We repo rt the first mea surements of the de Haa s-van Alphen effect in the heavy-fermion superconductor CeCuzSi z. In addition to pro viding information on -the -quasiparticle band structure and effective masses, the measurements reveal a complex pha se diagram in the B-T plane. By observing magnetic oscillat ions on either side of a magnetic ph ase transition, we detect in one instance a minor modification of the Fermi surface, alth ough the nature of the magnetic or other ordering is not determined. We conclude that the superconducting state in CeCuzSi z formes out of a fully developed coh erent Fermi liquid.

The recent investigation of magnetic oscillations in several heavy-fermion compounds has demonstrated rather vividly the existence in them of charged, longlived, heavy fermionic excitations. We refer here to the experimental results obtained from de Haas-van Alphen effect studies in CeCu 6 [1], UPt 3 [2], CeB6 P], CeAI 2 (4] and CeRu 2Si2 (5]. Such experiments offer many clues as to the microscopic nature of the fermion quasi particles involved, although they are still at an early stage, one is struck as much by the differences between the different compounds as by their common features. In each of the above experiments on the cerium compounds however , the magnetic measurements have revealed the pre sence of magnetic ordering transitions whose existence was already known for CeB6 , CeAI 2 and CeRu zSi2 but was unsuspected for CeCu 6 • Such transitions are consistent with the view that heavy fermion metals show a clear tendency to antiferromagnetic order, although the nature of the ordering transitions is not directly determined in magnetic oscillation experiments. In this paper we report on our measurements of the de Haas-van Alphen effect in CeCu 2Si2. It was the discovery of superconductivity in this compound by Steglich et aI. [6] which led to the intense interest in the heavy fermion group of compounds. There were two reasons for this particular attention. Firstly, the specific heat, which at temperatures below "" 10 K, is dominated by a term yT with y"" 1 J/mol K 2, suggested the existence of strongly renormalised fermion quasiparticles having a degeneracy temperature, TF == 10 K. As it was clear, from the magnitude of the discontinuity in

I

Present address: Institut fiir Festkorperphy sik, Technische Hochschule Darmstadt. Fachbereich 5, Hoch schulstrasse 8, 6100 Darmstadt. Fed. Rep. Germany.

the specific heat at 1;" that Cooper pairs were formed by the heavy quasiparticles, then it followed that Tc < TF < e D with 1;,ITF "" TFie D "" 0.05. In consequence, as Steglich et aI. [6] pointed out, CeCu 2Si2 could not be described by the conventional theory of superconductivity which assumes a typical phonon frequency kneDlh « k BTF/ h. Secondly, the experiments in CeCu 2Si2 demonstrated for the first time that Cooper pairs could form in a metal in which many-body interactions, which were probably magnetic in origin, had strongly renormalised the properties of the electrons. We have investigated magnetic oscillations in single crystals of CeCu 2Si2 grown using a cold boat technique which we ha ve described elsewhere (7]. From resistivity measurements the "as grown" crystals were superconducting with critical temperature 1;, = (0.72 ± 0.02) K. In order to examine the temperature dependence of the normal state resistivity and obtain some estimate of sample quality, the transverse rnagnetoresistance was measured in the temperature range 20-720 mK . As shown in fig. 1, above Hcz(T), a pronounced 'bump' occurs, whose origin is unclear, followed by a region of positive, approximately linear magnetoresistance. At certain orientations, as in fig. 1, the magnetoresistance curve consists of two distinct regions separated by a transition region which, as seen in the figure , is temperature dependent. As we shall discuss below, the signature of this pha se transition is also clearly evident in the magn etic mea surements. The zero field resistivity was obtained by extrapolation and found to be well represented by, P = Po + AT 2 , as depicted in fig. 2, with coefficients, Po = (4.5 ± 0.5) Iln cm and A = (2.5 ± 0.2) Iln cm/K 2 • This value of Po is the lowest value that we have seen reported for this compound. The uncertainty in the value of A is dominated by the ill-defined sample geometry and not by the fit to the experimental data which, as seen from fig. 2, yields a T 2-dependence to

0304-8853/90/$03.50
375

M. Hunt et al. / Phase transitions in CeCu 2 S i 2

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B (tesla) Fig.!. Magnetoresistance and dHvA effect in CeCu2Si2' The magnetoresistance is shown measured at the four temperatures, 22, 262, 437 and 508 mK, with the current directed along the c-axis tranverse to the field which is directed along the a-axis. The approximately linear magnetoresistance above l/c2(T) is extrapolated to H = 0 in order to determine the zero field resistivity at temperature T. Shown also are dHvA effect oscillations at 20 mK and at the same crystal orientation, recorded both above and below the phase transition region.

better than 1 %. The value that we obtain for A is however considerably different from the larger values reported by Rauchschwalbe [8] and Onuki et al. [9] of 10.0 and 11. 71l Q cm/K 2, respectively. The reason for this is unclear, but it may relate to the exact stoichiometry. Shown also in fig. 1 is an example of de Haas-van Alphen effect oscillations in CeCu 2Si2 measured at 20 mK, seen both above and below the phase transition region. They have been investigated in detail in the c-a

plane (CeCu2Si2 has the body-centred tetragonal ThCr2Si2 structure) to yield information on the quasiparticle band structure and effective masses, and the angle resolved measurements have shown a group of frequencies in the range 130-550 T, having effective masses of 4.5-6 me' Whilst these values are not large by heavy fermion standards, they are nevertheless comparable with our measurements in CeCu 6 for a similarly small sheet of the quasiparticle Fermi surface. We conclude that they are strongly renormalised quasiparticles and that the superconducting state is formed out of a fully developed coherent Fermi liquid. A full description will be published elesewhere [10]. The magnetic measurements reveal the presence of double phase transition, which has the form shown in fig. 1 because of the second derivative experimental technique employed. This feature would seem to be an intrinsic property of CeCu 2Si2 as we find no evidence in the angle resolved dHvA measurements of a loss of symmetry such as would occur with a hi-crystal say. For a given crystal orientation we may then construct a portion of the phase diagram in the B-T plane as in fig. 3. The superconducting phase region is consistent with that found by others, bearing in mind its known sensitivity to the precise metallurgy [11]. To our knowledge, however, the phase boundaries in the region of 7 T are a new feature. It is clear from the evolution of the magnetoresistance with temperature in fig. 1 that this feature is no longer present at temperatures above 0.47 K. We find no evidence of the phase boundaries inferred from NMR measurements by Nakamura et al. [12] shown as

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Fig. 2. Temperature dependence of the resistivity of CeCu2Si2 showing excellent agreement with expression, P = Po + AT 2 ; Po= (4.5 ± 0.5) 1-'0 ern and A = (2.5 ± 0.2) 1-'0 cmy'K2

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Fig. 3. Phase diagram for CeCu2Si2 constructed in the B-T plane (B parallel to a) from the measurements illustrated in fig. 1 (solid circles). The open circles are inferred from NMR measurements in polycrystalline material by Nakamura et al. (12).

M. Hunt et al. I Phase transitions in CeCu lSi 1

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change in the many-body renormalisation which determines the effective mass and g-factor. That such changes should accompany a change in magnetic order is not surprising, and indicates that magnetic quantum oscillations offer a sensitive probe for the investigation of the complex phase diagrams of heavy fermion compounds.

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The financial support of this work by the SERe is gratefully acknowledged, and one of us, P-A.P, acknowledges partial support from Swiss National Funds.

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References

a

Fig. 4. Anisotropy of part of the phase diagram of CeCu2Si2 measured for magnetic field directions in the e-:a plane.

open circles in fig. 3. However, their measurements were made in polycrystalline material and, as we illustrate in fig. 4, the position of the phase boundaries as deduced from magnetic measurements is appreciably anisotropic. On the basis of the observation of a large distribution of hyperfine fields at the Cu sites in CeCu 2Si z, Nakamura et al, [12] concluded that the magnetic structure they observed above Tc was of SDW type. From the present experiments we show that the phase diagram in the B-T plane is considerably more complicated than a single ordered magnetic phase with some phases, as is clear from figs. 3 and 4, having only a small region of existence. As discussed by us elsewhere (10], at some orientations the magnetic oscillations show a small change of both frequency and effective mass in passing through the phase transition region at "" 7 T. Thi s is accompanied by a modification of the amplitude and harmonic content of the oscillations as is clearly visible in fig. 1. Such changes are consistent with a minor reconstruction of the quasiparticle Fermi surface, together with a

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