Kondo behaviour in CexNd1−xCu6

IWIIII]I ELSEVIER

Physica B 223&224 (1996) 292-294

K o n d o b e h a v i o u r in C e x N d l - x Cu6 Svetlana Papian, Paul de V. Du Plessis*, Andr6 M. Strydom Department of Physics, University of the Witwatersrand, Private Bag 3, P.O. WITS 2050, Johannesburg, South Africa

Abstract

Resistivity (p) measurements on polycrystalline CexNd t -~Cu6 indicate Kondo behaviour over the concentration range x = 0.2-0.95 as evidenced from fits of p(T) = Po + b T - c In T, where b T characterizes the electron-phonon interaction.

The heavy-fermion compound C e C u 6 continues to attract attention since its initial synthesis and study of electrical, magnetic and specific heat properties by Onuki et al. [1] and Stewart et al. [2]. The material exhibits a large electronic contribution to the specific heat, 7(0) = 1530mJmo1-1K -2 [3], as well as an enhanced Pauli paramagnetism [2]. No long-range magnetic order has thus far been observed for this compound, but antiferromagnetic correlations are nevertheless observed at low temperatures and thought to play an important role in the development of the coherent state [4, 5]. The Ce-Cu-based compounds are amenable to a wide range of substitutions involving other rare-earth elements for Ce, as well as Au, Ag, A1 or Ga for Cu, without in many instances changing the crystal structure of the parent Ce-Cu compound [6]. Such substitutions may lead to drastic changes in ground-state properties, eg. crossovers from non-magnetic to magnetic behaviours. Sumiyama et al. [7] studied the electrical resistivity, magnetoresistance and magnetic susceptibility of single crystal CexLa I _xCu 6 (x = if-l). Typical Kondo In T behaviour for the resistivity p is observed for 50 K < T < 300 K for all values of x. For the concentrated Ce compounds (x = 0.73-1.0) a maximum in p is observed at low temperatures as a precursor to the develop-

* Corresponding author

ment of coherence between Kondo sites at mK temperatures. A recent study [8] of resistivity and magnetoresistivity of polycrystalline CexGdl-xCu6 alloys indicates that the Kondo interaction remains operative even for large concentrations of magnetic Gd (as high as 1 - x = 0.9). In the present experiment, Nd (with S = a2, L = 6) is substituted for Ce in the CeCu6 compound and the temperature dependence of the resistivity for the CexNdx-xCu6 series (x --- 0.2-1.0) reported. The end component NdCu6 exhibits complex antiferromagnetic order below T N = 6 K [9]. Our study should yield information on the importance of Kondo and Ruderman-Kittel mechanisms for the CexNdl-~Cu6 system. Polycrystalline Ce~Ndl-xCu6 samples have been prepared by arc-melting stoichiometric quantities of the constituents on a water-cooled copper hearth under an argon atmosphere. Starting materials of the following purity were used: Ce and Nd: 99.99wt%, Cu: 99.99 + wt %. Weight losses of less than 0.05 wt % were experienced. Metallographic investigation indicated the phase purity of specimens and scanning electron microscope elemental analysis confirmed the homogeneous stoichiometry throughout the sample volume. Resistivity measurements were performed on bar-shaped samples cut using spark erosion. Standard 4-probe DC techniques with computerised data acquisition were employed. The current direction was reversed several times at each measuring point so as to eliminate

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S. Papian et al. /Physica B 223&224 (1996) 292-294

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Temperature (K) Fig. 1. Temperature dependence of the resistivity of CexNdl-xCu6 alloys. Theoretical fits (see Eq. (1)) obtained by using in each case all the measured points, are shown as lines through a subset of the experimental points for purposes of clarity.

thermo-electric effects. Measurements were taken during both cooling and heating runs between 4 and 290 K with a rate of temperature change of 0.4 K/min. The temperature dependence of the resistivity p for different CexNdt -xCu6 alloys is shown in Fig. 1. For the end compounds, CeCu6 and NdCu6, all data points acquired are plotted. Since measurements were taken every 0.3 K the points merged to appear as lines when displayed in the figure. For the other samples only a limited subset of the measured points (approximately every 6 K apart) are plotted in order to facilitate comparison with a theoretical fit as discussed below. Samples with high Ce concentration exhibit a peak in p as is evident from Fig. 1. For all the alloys (x = 0.2-0.95) the typical increase in p with lowering in temperature expected for a Kondo system is observed. This is clearly illustrated by the solid lines in Fig. 1 which represent fits of the p ( T ) data against p ( T ) = Po + b T - cln T.

(1)

In Eq. (1) the term b T is used for the conduction electron-phonon interaction. It was verified that using a Bloch-Grfineisen description for the electron-phonon interaction rather than the b T term does not appreciably change the fit in Fig. 1 or the value obtained for p,~ (see Eq. (2)). Since the variation of the Debye temperature

293

across the alloy series is unknown, the approximate b T description was used. The term - c in T represents the well-known temperature dependence of p expected from the Kondo spin-flip scattering of conduction electrons from an isolated magnetic impurity. The residual resistivity po is mainly comprised of a Nordheim-like contribution [7, 10] reflecting the occurrence of two kinds of rare-earth atoms (Ce, Nd) in the Cefu6 lattice. The contribution of lattice defects (dislocations, grain boundaries, etc.) is expected to be considerably smaller than the preceding contribution for our samples as is evident from a value of po = 2 x 10 -8 f~m observed by us on a LaCu6 sample and of p at 4 K observed for N d f u 6 (see Fig. 1). The determination of po which enables inter alia the determination of the unitarity limit of resistivity when x ~ 0, requires measurements to temperatures below 0.1 K for the (Ce, La)Cu6 system [7]. In our investigation, po, which takes values ranging from 70 to 140 × 10-8 f2 m, is considered only as a fitting parameter in the analysis. In the least-squares iteration fits in Fig. 1 all measured data points were employed although considerably fewer points were plotted. The usual approach taken in analysing resistivity data for (Ce, La)Cu6 [6, 7-1 or other similar systems [63 is to subtract the resistivity of an isostructural non-magnetic compound like LaCu6 from the resistivities of the alloy samples to yield the magnetic contribution Pm which may then be compared with theoretical expectations. It is noted that p ( T ) for NdCu 6 almost matches p ( T ) for LaCu6 which makes it tempting to follow such a procedure also in the present case. However, the values of b obtained from our fits decrease from 0.15x 10-8 f~mK -1 for x = 0 . 2 to 0.044x 1 0 - 8 O m K -~ for the x = 0.95 sample. This seems to indicate that the electron-phonon contribution to the resistivity changes significantly across the series. As an alternative approach we consider the quantity p m = p ( T ) - b T = po - cln T.

(2)

Values of p , thus obtained are plotted per mol Ce in Fig. 2 for the various CexNd 1-xCu6 alloys. A satisfactory agreement with the expected - in T dependence is observed for all compositions and with the temperature region of validity of Kondo behaviour extending to lower temperatures for the dilute alloys. Sumiyama et al. [7] indicated a value for the unitarity limit of 320 + 30 x 1 0 - S f ] m / m o l Ce from their study of (Ce, La)Cu6. Our measurements obviously need to be extended to lower temperatures in order to determine this quantity. A crude extrapolation of the x = 0.2 curve in Fig. 2 seems nevertheless to be compatible with the value for the unitary limit given by Sumiyama et al. We also intend to perform measurements of p above the room temperature in order to ascertain the validity of

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S. Papian et al./Physica B 223&224 (1996) 292-294 . . . . . . .

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The Foundation for Research Development is thanked for financial support.

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References

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Temperature(K) Fig. 2. Ce-molar concentration dependence of Pm of Ce~Ndl -x Cuo versus In T (see Eq. (2)). associating the observed slopes in Fig. 1 with the electron p h o n o n contribution.

[1] Y. Onuki, Y. Shimizu and T. Komatsubara, J. Phys. Soc. Japan 53 (1984) 1210. [2] G.R. Stewart, Z. Fisk and M.S. Wire, Phys. Rev. B 30 (1984) 482. [3] H.R. Ott, H. Rudigier, Z. Fisk, J.O. Willis and G.R. Stewart, Solid State Commun. 53 (1985) 235. [4] J. Rossat-Mignod, L.P. Regnault, J.L. Jacoud, C. Vettier, P. Lejay, J. Flouquet, E. Walker, D. Jaccard and A. Amato, J. Magn. Magn. Mater. 76-77 (1988) 376. [5] A broad peak at ~ 3 mK and a second peak at ~ 0.5 mK have recently been observed in AC susceptibility measurements on CeCu6 single crystals by C. Jin et al., Physica B 194-196 (1994) 207, thus possibly indicating ordering in its electronic system. [6] E. Bauer, Adv. Phys. 40 (1991) 417. [7] A. Sumiyama, Y. Oda, H. Nagano, Y. Onuki, K. Shibutani and T. Komatsubara, J. Phys. Soc. Japan 55 (1986) 1294. [8] E. Bauer, E. Gratz, M. Maikis, H. Kirchmayr, S. B. Roy and B. R. Coles, Physica B 186-188 (1993) 586. [9] S. Takayanagi, E. Furukawa, N. Wada, Y. Onuki and T. Komatsubara, Physica B 163 (1990) 574. [10] C. Chen and Z.-Z. Li, J. Phys.: Condens. Matter 6 (1994) 2957.