Kondo-lattice — mixed-valence resistance scaling in heavy-fermion CeCu6 under pressure

From measurements of the electrical resistance of heavy-fermion CeCu6 subjected to hydrostatic pressures, we infer a continuous pressure-induced transition from Kondo-lattice to more strongly mixed-valence behavior. The resistance is found to scale over an appreciable temperature interval with a pressure-dependent characteristic temperature that reflects this transition. Similarities in the resistive behaviors of CeCu6 and CeA13 are discussed.

Los Alamos Rational Laboratory, Los Alamos, Xew Mexico 87545 (Received 14 August 1984) From measurements of the electrical resistance of heavy-fermion CeCu6 subjected to hydrostatic pressures, we infer a continuous pressure-induced transition from Kondo-lattice to more strongly mixed-valence behavior. The resistance is found to scale over an appreciable temperature interval with a pressure-dependent characteristic temperature that reflects this transition. Similarities in the resistive behaviors of CeCu6 and CeA13 are discussed.
There now appears to be a distinct class of materials characterized by huge electronic specific heats (y's) and correspondingly large effective electronic masses. ' Each of the known representatives of this class of heavyfermion materials contain either 4f or 5f elements.
Whether the large-y enhancements are a result of the intrinsic electronic band structure or many-body effects remains an open question. What is clear, however, from thermal variations in properties such as specific heat, magnetic susceptibility, and resistivity is that electronic excitations from the heavy-mass ground state develop on a characteristic temperature scale that is small, typically much lower than phonon energies. Such observations suggest that sufficient energy could be supplied by routine high-pressure techniques to perturb noticeably the electronic spectrum of these materials. Four-probe ac resistance measurements were made on a single crystal of CeCu6 grown by slow cooling from a melt. The direction of current flow with respect to crys- shows an expanded view of the low-temperature resistance.
Curve 5 is not shown for clarity only.
tallographic axes was not determined.

X-ray analysis
showed only lines characteristic of the CeCu6 orthorhombic structure. The resistance was determined over the temperature interval 1 -300 K and at hydrostatic pressures up to 18 kbar, generated by a self-clamping pressure cell whose operation has been described in detail elsewhere. ' We show in Fig. 1  where I is the cerium 4f angular momentum, c is the concentration of cerium atoms, kF is the Fermi momentum, and v is the number of electrons per atom. Assuming a free-electron value for kF (as done by Andres et al. for CeA13) and approximating the CeCu6 unit cell as cubic, we arrive at an expression for the rate of change of p " with pressure: (2) where 8 is the bulk modulus taken' to be 500 kbar.
Equating p, "with the maximum value of the measured resistance R,",we find v=vo+0. 005P (kbar). Therefore, we estimate the valency change induced by our highest pressure to be less than 0.09 electron. Bemuse we have ignored coherency effects that are present even at R ", this crude approximation undoubtedly overestimates the valency change. However, our results for R,"(P) do indicate that, already at 17.4 kbar, BR,"/BP appears to be decreasing, which would imply an approach to saturation in the maximum valency change. Such an observation is consistent with many experiments on cerium-based compounds that show evidence for a maximum cerium valency of about 3.2. " We emphasize, though, that arguments given here have completely neglected crystalline-electricfield (CEF) effects which might be important. ' As indicated, a maximum in the resistance near 15 K (at P=0) signals the onset of coherency ainong the ceriurn atoms such that they no longer act as independent scatterers. We show in Fig. 2 the resistance normalized to its peak value (i.e. , normalized to constant valency) as a function of reduced temperature T!T~, "(P), where T~,"(P) is the temperature at which the maximum resis- FIG. 2. Resistance normalized to its maximum value as a function of reduced temperature T/T, ", where T," is the temperature at which the resistance peak occurs. The inset is an expanded view of the scaled resistance for temperatures near Tmax ' tance occurs. [T,"(P)changes by over a factor of 3, increasing approximately linearly from -15 K at I' =0 to -51 K at 17.4 kbar. ] The normalized resistance scales as T/T, "(P) to temperatures in excess of T,"(P). We attach no particular significance to the choice of T,"as the scaling parameter except to note that it must be proportional to some temperature that characterizes the underlying physics. We also have found that the normalized resistance of CeCu6 scales over an appreciable temperature interval as a function of reduced temperature. To our knowledge, this is the first example of resistance scaling in such a system.
That the scaling persists with pressure for T « T "may be attributed to the fact that at -low temperatures both the Kondo-lattice and mixed-valence states may be described as Fermi liquids and that one evolves continuously into the other as the 4f level approaches the Fermi energy.
The pressure dependence of T,",then, reflects this evolution. However, an important aspect of this work, namely, that scaling continues to hold even for T) T,", remains theoretically unexplained.
Note added. Recently, our attention was brought to the work of Onuki  We would like to thank P. S. Riseborough, R. D. Parks, and G. R. Stewart for helpful discussions. This work was performed under the auspices of the U.S. Department of Energy.