Upper critical magnetic field of the superconducting heavy fermion system

Measurements of the ac electrical resistance as a function of temperature and applied magnetic field R ( T Jf) were made for various compositions x $ 0.03 in the mixed binary system (U 1 _ x Th„ )Be 13• All samples within this range of x exhibit heavy Fermion superconductivity with a superconducting transition temperature Tc that is rapidly suppressed by the substitution of Th for U. The shape ofthe upper critical field curve Hci (T) detennined from the R (T ,H) data is similar for all compositions with a very !arge initial slope ( - dHc 2 I dT Ir,.

Measurements of the ac electrical resistance as a function of temperature and applied magnetic field R ( T Jf) were made for various compositions x $ 0.03 in the mixed binary system (U 1 _ x Th" )Be 13 • All samples within this range of x exhibit heavy Fermion superconductivity with a superconducting transition temperature Tc that is rapidly suppressed by the substitution of Th for U.The shape ofthe upper critical field curve Hci (T) detennined from the R (T ,H) data is similar for all compositions with a very !arge initial slope ( -dHc 2 I dT Ir,.

INTROOUCTION
There has been considerable interest recently in a small class of"heavy Fermion" compounds in which the effective mass of the conduction electrons is enonnous, -100 times the free electron mass.Superconductivity has been observed in this class of compounds for CeCu 2 Si 2 , 1 UBe 13 , 2 UPt 3 , 3 and U 2 PtC 2 , 4 characterized by superconducting transition temperatures Tc $ 1 K and very !arge electronic heat capacities.Studies of alloy systems revealed that Tc is rapidly suppressed by the substitution of any other element for U in UBe 13 • s Measurements of the heat capacity C ( T) of samples in the (U 1 _ x Thx )Be 13 system 6 showed the )arge discontinuities at Tc characteristic of heavy Fermion systems.Of Special interest in these data was the observation of two distinct transitions in C(T) for x-0.03, possibly indicating another condensation ofthe superconducting electrons at a temperature Iower than the observed Tc . 6We present here the temperature dependence of the upper critical magnetic field Hc 2 (T) determined from measurements of the ac electrical resistance R for several compositions in the (U 1 _ x Tux )Be13 mixed binary system.

EXPERIMENTAL OETAILS
Tue polycrystalline samples used in this study were prepared at Los Alamos National Laboratory (LANL) by arc melting stoichiometric quantities of the elements on a watercooled copper hearth.Bar-shaped specimens were spark cut from the arc-melted ingots and leads of copper wire were attached using silver epoxy.Measurements of the ac electrical resistance at 16 Hz were perfonned in a He 3 -He 4 dilution refrigerator at the University of Califomia, San Diego (UCSD) for T~ 0.07 Kin magnetic fields Hup to 6 T applied with a superconducting solenoid.A Speer l 00-fJ resistor calibrated in zero field against the susceptibility of cerium magnesium nitrate (CMN) was used to determine the temperature.The magnetoresistance of this thermometer could be estimated to yield a maximum error of 12 mK for measurements in this range of Tand H from data for other resistors. 7Measurements were made as a function of temperature in fixed magnetic fields.Tue Tc was defined as the temperature at which R decreased to 50% of the value extrapolated from the normal state, while the transition width was determined from a similar extrapolation of the 10 and 90% points.Resistance measurements at the Francis Bitter National Magnet Laboratory, (FBNML), Massachusetts Institute ofTechnology, were performed at 40 Hz in the mixing chamber of a dilution refrigerator at fixed temperature by sweeping the magnetic field produced by a Bitter solenoid up to 17.5 T. 8 Two carbon thermometers within the mixing chamber were used to detennine the temperature and a correction for magnetoresistance was made in a manner described elsewhere. 8For a given temperature, H a was defined from the 50% point of the transition while the width in applied field was defined from the 10 and 90% points.

RESULTS
Figure 1 shows a plot ofR { T) in various applied magnetic fields for (U 1 _" Th" )Be 13 with x = 0.The normal-state resistance decreases as the temperature is lowered in all applied magnetic fields.In addition, strong negative magnetoresistance is evident.Rather sharp transitions into the superconducting state are found with transition widths that increase from 30 to 60 mK as H increases from 0 to 6 T.
Similar data are observed for x = 0.0260 and 0.0331.For x = 0.0175, very broad superconducting transitions are observed, possibly indicating a sample oflesser quality.Shown in Fig. 2 are Hc 2 ( T) data for the four samples investigated in this study with transition widths, indicated by horizontal and vertical lines, defined as described above.The solid lines are guides to the eye, and in the case of x = 0.0175 indicate the results of more detailed low field measurements.In agreement with previous work, 5 Tc decreases rather rapidly as Th is substituted for U.However, the overall shapeof Hc 2 {T) remains nearly the same.In each case, a rapid increase of Hc 2 is observed for low H with strong curvature at intermediate fields.In higher fields, Hc 2 (T) varies nearly linearly with Twith a slope -9 T/K.For x = 0, one point at T -90 mK and H -12 T lies significantly above a linear extrapolation of the lower field data.A more extensive set of measurements on this sample are cur-TABLE 1.The superconducting transition temperature T, in zero applied magnetic field and thc initial slope ofthe H,2 \T) curve 1-dH,,ldJ')r, for four comp<>sitionsx in thc mixed binary systern (U1 rently in progress.lt is notewortby that the shape of the Hc 2 (T) curves is the same for x = 0.0331 as it is for lower x .
As noted above, two transitions have been observed in heat capacity measurements of samples with x-0.03. 6These data sbow that the Iower temperature transition at T-0.47 K for this composition has no effect on Hc 2 (T) determined from resistance measurements.
In addition to the data presented in Fig. 2, more detailed low field measurements were made at UCSD to investigate theinitial slope oftheHc 2 curve, ( -dHc 2 !dT)T<For measurements over such a small range oftemperature (-20 mK) in magnetic fields up to 1 T, tbe magnetoresistance of the carbon thermometer becomes a very important factor.The low field magnetoresistance of our thennometer was estimated by comparing Hc 2 (T) data measured at UCSD on a single crystal ofUBe 13 in the He 3 -He 4 dilution refregerator with that determined in a He 3 cryostat where the temperature was inferred from the vapor pressure ofHe 3 • 9 Following the work of others, 7 we assumed a linear variation of H to determine the magnetoresistance for various temperatures.The initial slope of Hc 2 (T) resulting from this analysis is given in Table I, where for x = 0.0175 the steepest part of theH ... 2 (T) curve has been measured.lt is difficult to estimate the uncertainty in these values since our extrapolation of the magnetoresistance could be incorrect.Nevertheless, it is clear that very large values of the initial slope are found for all compositions.Also listed in Table I is Tc(H = 0).

CONCLUSIONS
We have determined the upper critical magnetic field H c 2 ( T) from measurements of the ac electrical resistance for four compositions in the (U 1 _ " Thx )Be 13 mixed binary system.Despite the strong suppression of the superconducting transition temperature Tc when Th is substituted for U, the shape of Hcz (T) remains nearJy the same.This indicates that the nature of superconductivity of the system of heavy Fermions remains unchanged despite a decrease by -30% of Tc (H = 0).The data are characterized by very large values of theinitial slope ( -dHc 2 ldT)Tc and strong negative magnetoresistance in the normaJ state.

FIG. 1 .FIG. 2 .
FIG.1.ac electrical resistance vs temperature in various applied m.agnetic fields in T for a polycrystalline sample of UBe".