Elastic constants of CeCu6−xAux at the magnetic instability

ELSEVIER

PhysicaB 223&224 (1996) 329-332

Elastic constants of CeCu6-xAux at the magnetic instability D. Finsterbusch a' *, H. Willig ~, B. Wolf a, M. Amara a, G. Bruls a, B. LiJthi a, M. Waffenschmidt b, O. Stockert b, H.V. LShneysen b a Physikalisches Institut der Johann Wolfgang Goethe, Universitiit Frankfurt, Robert-Mayer-Str. 2-4, D-60054 Frankfurt, Germany b Physikalisches Institut, Universitiit Karlsruhe, D-76128 Karlsruhe, Germany

Abstract

The elastic constant c22 of CeCu6_xAu x with x = 0 and x = 0.1 has been measured in the temperature range of 0.1-60 K. The signature of the non-Fermi-liquid behaviour for x = 0.1, right at the onset of antiferromagnetic order, is weak as might be expected from the overall small change of the internal energy U ( T ) with respect to U ( T ) of pure CeCu 6. For x = 1 the features in the elastic constant c33 in field and temperature sweeps are used to confirm the previously obtained complex B - T phase diagram of this anti-ferromagnetically ordered compound.

1. Introduction

Non-Fermi-liquid (NFL) behaviour has recently been observed in strongly correlated electron systems such as Uo.zY0.aPd 3, CeCus.9Auo. x and other systems. It manifests itself through a logarithmic temperature dependence of the specific heat, C / T oc In(T/To), and unusual temperature dependences of other physical properties like the magnetic susceptibility and the electrical resistivity. The microscopic origin of N F L behaviour, although in some way related to the strong coupling between conduction electrons and 4f or 5f magnetic moments via the Kondo effect, might be quite different. One possible reason is an unconventional moment compensation process (overscreening) as might be present in the multichannel Kondo effect. This is essentially a single-ion effect. Another possibility is a T = 0 quantum phase transition between magnetically ordered and disordered states which is driven by critical quantum fluctuations. Reviews on these systems can be found in Refs. [1, 21. In addition,

* Corresponding author.

marginal Fermi-liquid behaviour has been suggested to occur in high-To superconductors. It is of considerable interest to investigate the electron-phonon coupling in these unusually strongly correlated electron systems, In the transition region from the high-temperature regime with noninteracting (or weakly interacting) stable U 4 ÷ or Ce 3 + ions to the compensated moment regime, sound waves can couple effectively to these ions with concomitant anomalous temperature dependences of the elastic constants [3]. In the case of Uo.2Yo.sPd3, N F L behaviour is thought to arise either from a multichannel Kondo effect (involving the overscreening of the quadrupolar degrees of freedom, hence quadrupolar Kondo effect [4] ) or, alternatively, from incipient (spin-glass like) magnetic order [5]. In the temperature range from 1.5-100 K we found no evidence for an anomalous temperature dependence associated with the quadrupolar Kondo effect [6], thus eliminating this possibility for this particular system. A detailed analysis of the environment around the quasi-cubic sites of the U4+-ions in U P d 3 and Uo.zYo.sPd 3 showed that the magnetoelastic coupling constant should be of similar strength in both alloys [6]. However, while considerable elastic softening is observed

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D. Finsterbusch et al. /Physica B 223&224 (1996) 329-332

in UPd3 which was interpreted in terms of the usual cooperative Jahn-Teller mechanism [-3], no indication of softening was observed in Uo.zYo.8Pd3 1,6]. In this paper we present the elastic constant c22 as a function of temperature for C e C u s . 9 A u 0 . 1 , another thoroughly investigated N F L alloy I-7]. This alloy is at the verge of antiferromagnetic ordering with the N6el temperature T N rising linearly from T N = 0 for x = 0.1 to 2.3 K for x = 1 [8]. Therefore, in order to fully characterize the elastic behaviour of this alloy we compare it with that of the antiferromagnetically ordered stoichiometric compound CeCusAu and of the Fermi-liquid (FL) compound C e f u 6 [9].

2. Experimental results and discussion For the present study, single crystals grown by the Czochralski technique were used I-7, 8]. Fig. 1 shows the temperature dependence of the c zz-mode for C e C u 6 [-10] and CeCus.9Auo.1, respectively. This mode is the one with the most pronounced temperature dependence of all longitudinal modes. It is seen that the modes of both systems are rather similar. One can distinguish various temperature regions. For T > 10 K crystal field effects are seen for both substances. They are quantitatively interpreted for C e C u 6 in Ref. [9]. It is known [11] that the crystal field splittings in C e C u 6 and C e C u 6 xAux are

very similar, with a smooth evolution towards betterdefined crystal field levels upon increasing x, due to the decrease of the K o n d o temperature. The crystal field effect would give a plateau of Czz(T) for lower temperatures. Griineisen parameter coupling of the developing heavy fermion state gives, however, an additional pronounced softening for T < 1 K. For T < 1 K the temperature dependence of the modes is shown in the inset of Fig. 1. It is seen that the two substances exhibit a slightly different behaviour, a linear temperature dependence for CeCus.9Au0.1 above 180 m K and a more quadratic temperature dependence for C e C u 6. For both substances this behaviour is suppressed in magnetic fields larger than 3 T applied along the c-axis, where the elastic constant becomes nearly independent of temperature (not shown). The slight difference in this low temperature behaviour of the c22-elastic constant can be understood in the following way. For Ce compounds we know I-3, 12] that the adiabatic longitudinal elastic constant follows the simple law c L = cOL-}- O2U(T), where 0 is the corresponding uniaxial Grfineisen parameter [-3] and U(T) is the internal energy of the electron system. With the measured specific of CeCu 6 and C e C u s . 9 A u 0 A we can determine U(T) as shown in Fig. 2. It is seen that both curves look rather similar but below 1 K U(T) increases more strongly for CeCus.9Auo.1 than

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T (Kelvin) Fig. 1. Relative sound velocities (for the c22-mode) as a function of temperature for CeCu6 and CeCus.9Auo. 1- Inset shows results for T < 1 K. Absolute sound velocities are 3933 m/s (CeCu6) and 3700 m/s (CeCus.9Auo,1) at T = 4.2 K.

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2

3

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Fig. 2. Internal energy U versus temperature for CeCus.9AuoA. Inset gives curves for T < 1 K.

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D. Finsterbusch et al. /Physica B 223&224 (1996) 329-332 I "2

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Fig. 3. Relative sound velocities (for the c33-mode) as a function of increasing (upper curve) and decreasing (lower curve) magnetic field (B//c) for CeCusAu at 520 mK.

Fig. 4. B - T phase diagram for CeCusAu (B//c) as measured by magnetization (open circles), specific heat (triangles), magnetocaloric effect (squares), elastic constants (full circles). Lines are guides to the eyes.

for CeCu 6 (see inset of Fig. 2). This behaviour is reflected in the elastic constant change for the two substances illustrated in the inset of Fig. 1. A more quantitative fit of U ( T ) to the elastic constant is not possible for the moment. We would have to know exactly a possible temperature dependence of the Griineisen parameter f2. In addition, the one-band picture for these substances on which the above formula is based is questionable. Typical values for the uniaxial Grfineisen parameter f2(c22) determined from Figs. 1 and 2 are Q(c22)~ 55 for CeCu 6 in good agreement with previous results [9] and ~2(c22) ~ 60 for CeCus.9Auo.1. In summary, we have shown the similar global behaviour for both substances, but below 1 K we can clearly distinguish a different temperature dependence for the c22-mode of N F L and F L substances both of which do not exhibit long-range magnetic order. In order to establish for the CeCu6_xAu x system the signature of long-range antiferromagnetism in the elastic constants, we also investigated the antiferromagnetic stoichiometric compound CeCusAu. This compound is known to possess a complex magnetic phase diagram with several different magnetic phases. Fig. 3 shows two characteristic field sweeps of the c33-mode of CeCusAu at 520 mK, taken for increasing and decreasing magnetic field, respectively. A small hysteresis of the minimum at about 3 T is observed. The phase transition at 0.6 T is only seen in the field-up curve. Ultrasonic measurements are taken to complete our earlier determination of the B - T phase diagram from

measurements of the magnetization, specific heat and magnetocaloric effect [-8]. All data are collected in Fig. 4 where the complete phase diagram is shown. The initial fast decrease of c33(B) below 0.1 T observed at low temperatures does not have a corresponding feature in the magnetization or the magnetocaloric effect. Another open question concerns the weak feature observed in the ultrasound data around 2 T of Fig. 3. In fact, a similar feature was observed in the magnetization data [8] but was not included in the phase diagram [8-1 because this feature could not be confirmed on a second CeCusAu crystal. For a more detailed discussion of the phase diagram, including the possibility of a spin-flop phase and of a tetracritical point, the reader is referred to Ref. [8]. The nature of the different phases has yet to be determined by elastic neutron scattering. These measurements are presently in progress.

Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft through SFB 252 and grant No. Lo 250/9-1.

References [1] H.v. L6hneysen, Physica B 206&207 (1995) 101. [2] M.B. Maple et al., J. Low Temp. Phys. 99 (1995) 223.

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I-3] P. Thalmeier, B. Liithi, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 14, eds. K.A. Gschneider, Jr. and L. Eyring, (North-Holland, Amsterdam, 1991) Chap. 96. [4] D.L. Cox, Phys. Rev. Lett. 59 (1987) 1240; C.L. Seaman et al., Phys. Rev. Lett. 67 (1991) 2882. [5] B. Andraka, A.M. Tsvelik, Phys. Rev. Lett. 67 (1991) 2886. [6] M. Amara et al., Phys. Rev. B 51 (1995) 16407.

[7] H.v. L6hneysen et al., Phys. Rev. Lett. 72 (1994) 3262. 1,8] C. Paschke et al., J. Low Temp. Phys. 97 (1994) 229. 191 D. Weber et al., Europhys. Lett. 3 (1987) 827; T. Suzuki et al., J. Phys. Soc. Japan 54 (1985) 2367. [10] Note that in Ref. [9] the a- and b-axes are interchanged from the notation used here. [11] B. Stroka et al., Z. Phys. B 90 (1993) 155. 1,-12"1 B. Liithi et al., J. Low Temp. Phys. 95 (1994) 257.