SCALING OF THE MAGNETORESISTANCE OF UBE13 UNDER PRESSURE

We report magnetoresistance measurements of the beavy electron compound UBe above the supercond~cting transitiou temperature Tr and below 4 K for pressures Pup to 19 1 kbar and for magnetlc fields Hup to 9 T. We observe strong negative magnetoresistance at ail pressures and temperatures. The resistivity p is quadratic in temperature T from T~ up to a maximum temperature of 1 Kat l bar increasing to 2 Kat 19 kbar. The slope of the T 2 term decreases with both H an~ with P. We find that o(H) = - [p(H) - p(O) j/p(O) for a given pressure scalec; as a functton of HIT and exhibits power-iaw behavior over one decade with an exponent of 1.7. In addition, 6(H) at high pressure shows this same power law over a more Jimited H /T range.

Scaling of the magnetoresistance of UBe 13 under pressure J. 0. Willis, M. W. McElfresh,a> J. D. Thompson,J. L. Smith,t>> and z. Fisk Physics Divisioll,Los Alamos National Laboratory. Los Alamos,New Mexico 87545 We report magnetoresistance measurements of the beavy electron compound UBe above the supercond~cting transitiou temperature Tr and below 4 K for pressures Pup to 19 1 kbar and for magnetlc fields Hup to 9 T. We observe strong negative magnetoresistance at ail pressures and temperatures. The resistivity p is quadratic in temperature T from T~ up to a maximum temperature of 1 Kat l bar increasing to 2 Kat 19 kbar. The slope of the T 2 term decreases with both H an~ with P. We find that o(H) = -[p(H)p(O) j/p(O) for a given pressure scalec; as a functton of HIT and exhibits power-iaw behavior over one decade with an exponent of 1.7. In addition, 6(H) at high pressure shows this same power law over a more Jimited H /T range.

INTROOUCTfON
The compound UBe 1~ ( Ref. 1) is one of a class of materia!s known as heavy fennion or heavy eiectron oompounds. 2 These systems are characterized by Curie-Weiss (!oca1 moment) susceptibility :t' at high temperatures and Pauli (itinerant) magnetic behavior at low temperature. Accompanying this change in magnetic properties is an enormous enhancement of the electronic specific heat coefficient r< n l = C( T) 111. which is proportional tc the etfective clectron mass, as the temperature approaches zero. Heavy electron compounds at low iemperatures bave been proposed tobe Kor.do lattice systems. 3 At high temperatures, each local moment is independent and beccmes partially screened by antiferromagneticaJ!y oriented conduction electrons as the temperature is decreased; this moment compensation is complete at temperatures weil below the Kondo temperature 1',:. A Kondo lattice is not just the sum of the independent Kondo sites described above, but it includes corre!ations among the sites. This results in a decrease in the resistivity p below T"' in contrast to the constant, saturated p for the isolated Kondo impurity in the same temperature regime. The resistivity of UBe 13 shows the classic Kondo resistivity at high temperatures that increases to a shouider near 20 K and a peak near 2.5 K, below which p falls rapidly with decreasing Tuntil at about 0. 9 K, the material becomes superconducting.
The magnetoresistivity of UBe 13 is large and negative with a strong temperature dependence. Below l K and for H greater than about 1 T, the data can be described by p = p 0 + AT 2 , composed ofaresiduaiscatteringtermp 0 and a T 2 contribution that suggests a Fermi liquid ground state for UBe 13 . At zero field, the p 0 value is about 100 µft cm, much larger than might be expected for nonmagnetic impurity scattcring. Indeed, p 0 decreases aJmost an order of magnitude in high fields, strongly supporting its source as Kondo (magnetic) scattering. The T 2 term also sbows an overa!l decrease with field. Pressure P has an effect similar to field on the resistivity ai Also in Matuial~ Scicnce and Tcchnology Division, Los Alamos N:ition-111 Labor111ory. Prcsent address: IBM Research Center, Yorktown Hcights, NY 10598. " 1 Ccnicr for Materials Science, Los Alamos National Laboratory.
of UBe,~. 4 ·~ The 2.5-K peak in p shifts to higher temperatures, a11d the Jow-temperature resistivity is depresscd in magnitude, as arep 0 and A. The superconducting transition temperature 7~. was found lo decrease at a rate of 16 mK/ kbar. Specific heat measurements 6 demonstrate a 30% reduction in r between 0 aud 9.3 kbar, indicating a substantial decrease in the electronic mass, or equivalently, in the renormatized electronic density of states at the Fermi level. In contrast, recent de susceptibifüy (X) measurements 7 in this same pressure rcgion show Jess than a l 0% decrease from ;r(P= 0), suggesting mi;ch smaiier change.<; in the electronic mass. Magnetoresistance data at high pressures can provide additional insight into the possible energy scales and into the properties ofthe Kondo tmpurity and Kondo iattice models ofUBeu. We report here on measurements of p as a function oftemperature (0. l 5-4 K }, magnetic field (0-9 T), and pressure (0-19 kbar).

EXPERIMENT
Polycrystalline UBe 13 was prepared by arc melting together stoichiometric amounts ofU and premelted Be. Measurements were performed in a self-damped Cu-Be cell 8 using a conventional four-lead, phase-sensitive ac resistance technique. The current, which was 0.07 A cm-2 or smaller to avoid Joule heating, was roughly parallel to the applied magnetic field. The pressures were determined from the Tc ofa Sn manometer. 9 Temperatures were determined with a Speer carbon radio resistor that was calibrated against a germanium resistor at zero field and was corrected '° for magnetoresistance at finite fie!ds.

RESUL TS ANO OISCUSSlON
Resistivity p vs temperature T data at 9.9 kbar are presented in Fig. 1. A !arge negative magnetoresistance is apparent in this temperature range, similar to previously reported zero pressure measurements on UBe 13 ( Refs. 11-13).
It is clear that the magnetoresistance is a complicated function of Tand H, and furthennore, it is not possible to deter-  Fig. 2. The extent of the T 2 region increases with field and alsowith pressure. At9Titextcnds up to::::: l K atP = Oand up to ::::2 Kat P = 19 kbar. For H lcss than about 3 T, the smaller range for which p has a T 2 temperature dependcnce leads to less accurate values of p 0 and A than at higher fields.
In a Fermi liquid picture, the low-temperature resistivity is proportional to (T/T* ) 2 , where T* is a characteristic temperature of the system. W e then make the identification that A is proportional to (1/T*) 2 , and therefore A " 112 is proportional to T *. Values of A ·· 11 2 havc been extracted from fitting the data in Fig. 2 and from the data at other pressures. The behavior of A · · 1 12 as a function of Hand Pis shown in Fig. 3. The initial decrease in A --112 ( a: T*) for II less than 2-3 T is not understood. 4 At highcr ficlds, A -112 increases approximately linearly with H. This rate of change (d In A -112 /dH) varies from 6.3%/Tat ! bar to 14%/Tat 19 kbar. Reroenyie: al. n were unable tofit theirdata below 5 T to ap 0 + AT 2 form. In addition, they observcd a distinct break in thep vs T 2 data near T,. (H = 0). Their A -112 values increase monotonically with field but arc a factor of 1.4 smaller (Ais a fäctor of2 targer) than seen here. This may be related to their high~field p value of 40 µH cm, twi.ce as !arge as in the present work.
In both the data of Fig. 2   at other prcssures (not shown), there appears tobe a limiting, hlgh-field, pressure-independent residual resistivity p 0 .
By extrapolating the resistivity to T = 0 K with a T 2 temperature dependcnce, p 0 values have been obtaiued and are shown in Fig. 4. Tue accuracy of these values improves with both H and P, i.e" with the length of the T 2 region and the decrcase in the length ofthe extrapolation; a typical error bar is about 2%. A ljmiting high-fieid, residuai resistivity p 0 valuc of 18 ± 1 µH cm, which is independent of pressure, is obtained from the data in Fig. 4. This value is in good agreemen t with the zero pressurep 0 of < 17 µficm reported by Rauchschwalbe,Steglich,and Rietschel,13 but is a factor of2 smaiicr than that observed by Remenyi

Willisetaf.
pounds, there is clear evidence of a change in sign of the magnetoresistance at a temperature in coincidence with a maximum in r< n and a sign change in the thermopower.  Batlogg et al. 12 and Rauchschwalbe. 16 Thelower Iimit in H /Tover which this power law is valid increases slowly with P, but the upper limit is relatively pressure independent. At high values of HIT and for all pressures studied, the normaiized magnetoresistivity saturates at 60%-70%.

CONCLUSIONS
[n summary, we fiad a large, negative magnetoresistance in UBe 13 for T less than 4 K, H 1ess than 9 T, and P !ess than 19 kbar. Tue resistivity at T = 0 K decreases rapid!y with field and pressure reaching a lower limit of 18 µfi cm.
The resistivity has an AT 2 dependence over a temperature region that increases with field and with pressure. A ·-112 , which is proportional to a characteristic temperature of the system, increases witb Hand with P. All these features are manifestations of independent Kondo scattering in the temperature region for which intersite correlations are beginning to develop, but no evidence of Kondo lattice formation was observed in the present work. The normalize magneto-

ACKNOWLEOGMENT
This work was perförmed under the auspices of the U. S. Department ofEnergy, Office ofBasic Energy Sciences.