low temperature resistivity of Ce-La-Th under pressure

The low temperature resistivity ofCeo. 9 _ x Lax Tho. 1 alloys is known to vary asp 0 + aT 2. We have investigated the variation of p 0 and a with pressure for several concentrations x . An unusually strong nonlinear decrease of the residual resistivity with pressure occurs; the magnitude of the decrease is an order-of-magnitude !arger than in the isostructural nonmagnetic aJloy Lao. 8 Tho. 2 . The temperature coefficient a(P) also decreases strongly. These results are in qualitative accord with recent theories of the resistivity of disordered valence fiuctuation compounds.


INTRODUCTION
In a recent article 1 we reported the observation of a novel pressure-temperature-alloy parameter (P-T-x} phase diagram for the r-a transition in Ceo.9 -X La" Tha.1 alloys. We showed that the general features of the phase diagram follow qualitatively from a free-energy functional which incorporates in an essential way the known Fermi-liquid behavior of the 4fspin system. In particular the Fermi-liquid temperature T FL varies rapidly as the volume changes in the vicinity ofthe phase transition. In this paper, we examine the resistivity pjT,P ) at temperatures which are sufficiently low that the variation of p with temperature can be viewed as an intrinsic property of the a phase at constant T FL. In earlier work on the same alloys at ambient pressure, Grier and Parks 2 dernonstrated that the resistivity varies asp 0 + aT 2 and reported a striking variation of the residual resistivity p 0 with alloy parameter x. Here we will report the pressure variation of p 0 and a for several values of x and will discuss our results in the context of recent theories of the transport behavior of disordered valence ftuctuation compounds.

II. EXPERIMENTAL RESUL TS
Experimental techniques were reported in the earlier paper 1 ; here we report only results. We note, however, that the geometry of our samples did not allow determination of the absolute value ofthe resistivity to better than about 25%; hence, there is some minor disagreement with the absolute values reported by Grier and Parks. 2 In Fig. 1 we exhibit the low-temperature resistivity of Ceo. 8 Lao. 1 Tho. 1 at several pressures in such a way as to demonstrate that the resistivity varies as p 0 + a T 2 • W e obtained comparable data for x = 0.14 ( Fig. 2) and for x = 0.11 and 0.17 (not shown bere). In all cases the temperature interval over which the T 2 law is obeyed increases initially with pressure. For the higher-pressure data the region of T 2 behavior is followed at higher temperature by an interval where p varies linearly with ternperature; this in turn is followed by the phase transition. Another tendency (reported earlier by Grier and Parks 2 ) is that for x > 0.14 the low-pressure data ••Permanent address: Physics Dept., University of Califomia, lrvine, Califomia 92717.
varies less strongly than quadratically. This can be seen for x = 0.14 in Fig. 2 and was also found tobe true for x = 0.17.
For higher pressures in the same samples, T 2 behavior is observed. Tue deviation from T 2 behavior observed in Fig. 2 at the lowest temperatures is, we believe, an extrinsic effect, perhaps due to the presence of regions of untransformed rcerium. Inclusion of this low temperature data leads to a power Jaw Po + aT n with n > 2.
Both the residual resistivity p 0 and the temperature coefficient a decrease rapidly with pressure. For all four concentrations studied, p 0 decreases to 60% of its P = 0 value on pressurizing to 10 kbar, while a decreases by nearly a factor of 10. This is shown in Figs. 3 and 4 for x = 0.10 and 0. 17 respectively. By way of contrast, we show in Fig. 3 loy Lao.s 'fho. 2 • For this system, p 0 decreases by a much smaller factor ( 10%) between P = 0 and 10 kbar; andin contrast to the ceriwn alloys, the decrease is linear. (For Ceo.s Lao. 1 Tho.1 , between 1 and 10 kbar the residual resistivity varies as P -6 .)

III. DISCUSSION
The strong nonlinear decrease of the residual resistivity with pressure is quite unusual for an alloy. The Iarge magnitude of the effect (relative to the case of isostructural but nonmagnetic lanthanum alloys) suggests that the residual scattering is not simply due to the nonmagnetic solutes but involves the cerium 4f electrons in an essential way.
There is general agreement that the ground state of valence fiuctuation metals can be described as a Fermi liquid where the conduction electrons scatter from renormalized/ resonances whose energy scale is then T FL. In a perfect lattice the resonant potential is uniform from site to site and the resistivity vanishes at T = 0. Finite resistivity arises from fiuctuations in the resonant potential. 3 · 4 These can exist already at T = 0 due to alloy disorder and can result in a very large resistivity for two reasons. 3 .s. 6 First, each solute atom can cause deviations in the resonant potential at many surrounding sites: at the very least, each near neighbor is affected, and more distant neighbors can be affected if the impurity gives rise to long range strain fields. Secondly, the SCattering cross section depends on the 4/ spectral density at the Fermi Ievel, which is !arge due to the resonance.  Lawrence et at.
Ramakrishnan 6 hypothesizes that ifthe resulting disorder is sufficiently great, the conduction electrons will then scatter from a set of decoupled resonances. Utilizing the Friede} sum rule he argues that the residual resistivity will saturate to a maximum value which varies quadratically with the 4/ occupation number n 1 . Mihalisin and co-workers7 have attempted to extract valences (4n 1 ) in this way from residual resistivities, demonstrating strong correlations between diverse experimental quantities (lattice constants, susceptibilities, specific heat, and resistivities) consistent with such an analysis; however, the valences so obtained do not appear to agree with those obtained from x-ray absorption measurements. 8 For temperatures greater than T FL the conduction occurs in states away from the resonance. For strongly disordered systems the resistivity should then decrease with increasing temperature. 3 In the opposite limit of perfect order the resistivity vanishes at T = 0 and increases initially with temperature. Tue increase is due to fluctuations in the resonant potential which either can be directly excited 4 · 9 or,ifthe local resonance is coupled to lattice strain fields, can be created by thermal excitation of phonons. 6 • 1° For T > T FL the resistivity begins to decrease for the reason cited above. This combination of events can lead to a resistivity maximum in pure systems, as observed in many Ce and Yb compounds. lt also silggests that the initial increase of p(T) should scale with some inverse power of T FL.
The results exhibited here for CeLa Th alloys can be understood qualitatively in these terms. The large residual resistivity arises from disordering of the 4/ resonance created by the La and Th impurities. The rapid decrease of p 0 with pressure indicates a decreasing 4/ spectral density at the Fermi level, consistent with the expected decrease in n 1 with pressure. The disorder is not total, however, as indicated by the positive temperature coeffi.cients. The large decrease in a 3133 J. Appl. Phys., Vol. 57. No. 1, 15 April 1985 reflects the expected broadening of the resonance (i.e., increase in T FL) with pressure, 1 with a varying as some inverse power of T FL .
Based on lattice constants, neutron linewidths 11 and xray absorption 12 , we expect n 1 ::::.:: 1 at P = 0 for all four concentrations, and n 1 ::::.::0.8 at 10 kbar. For x = 0.10 atP = 0 it isknown 11 that T FL ==200K; at IOkbarweexpect T FL ==800 K. 8 These numbers are consistent with the observed decrease inp0 f p 0 (10 kbar)::::'.0.6p 0 (P = O)] ifp 0 ex: n}. Given the sixfold decrease in a , they are consistent with a variation a ex: l/T~ with 1 < n < 2. (lt would be interesting to directly observe the variations in n 1 and T FL by studies of the x-ray absorption and neutron linewidths at high pressure.) As for theobserved increaseinp 0 withx atP = Oobserved byGrier and Parks, 2 in our view this reflects increasing disorder, as opposed to changes in the valence.