Thermodynamics. and magnetism in U 1 _ xThxBe 13 _yBy

We report specific heat and µ.SR measurements on Th (x = 0.019) and/or B (y = 0.03) substituted UBe 13• The specific heat data show that either Thor B substitution reduces the Kondo temperature T K and increases the entropy at the superconducting transition by almost 20%, indicating an enhanced density of states. However, wbereas µ.SR shows clear evidence for magnetic corre1ations for Th substitutions (0.019<X<0.043), no magnetism is observed for B substitutions. The enhanced specific heat jump in the B-substituted material is associated with a change in the superconducting properties as Tf< iS reduced.


INTRODUCTION
T he ground state properties of heavy electron (HE) compounds are often very sensitive to doping with small quantities of impurity atoms.Perhaps the most unusual case is that of U 1 __ xThxBe 13 , where Th substitution pro-duces1 both a nonmonotonic depression of the superconducting transition temperature Tc ~nd a second phase transition below Tc for 0.019.;;;x<0.043.Recent muon spin rotation (µSR) experiments 2 have demonstrated that this lower phase possesses small magnetic momehts, of order 10-3 -10-2 µ 8 /U-atom.Thus the magnetism and superconductivity are closely coupled in this system.Recently it was reported 3 that substitution of B for Be in UBe 12 .97 B 0 .03 drastically increases the specific heatjump at Tc>.and it was surmized that magnetic correlations were also produ.c,-:ed in UBei 2 .97Bo.03 , as in {U,Th)Be 13 • In this paper we report µSR and specific heat measurements in U 1 -xThxBe13 _)3y for x = 0.019 and y = 0.03, to further investigate these phenomena.
The µ.SR experiments were carried out in zero applied field between temperatures 0.05 and 1.7 K at the lowtemperature facility (LTF) of the Paul Scherrer Institute.T he samples for µSR were arc-melted polycrystalline ingots about 1 mm thick with 2 cm 2 cross-sectional area. 2 The :specific heat data were collected between T -0.3 K and 20 K using a small~mass calorimeter. 4.SPECIFIC HEAT DATA Figure l shows the temperature dependence of the specific heat for pure UBe 13 , UBe 12 .97 B 0 ,03(UBeB), and Uo.9s1Tho.0 1 9Be12,9 7 Bom (UThBeB) between 0.3-20 ~-The UBe 13 data show the characteristic features of a rise in C/T below about 6 K associated with the Kondo resonance, followed by a superconducting specific heat anomaly with an onset temperature Tc ::::;0.91K. (The midpoint of the rise in C!T occurs at about 0.82 K.) The UBeB data, although qualitativeJ.ysimilar, are quantitatively different in several important ways.First, the gentle rise below 6 K .• in C/T reflecting the Kondo.anomaly_is pushed to lower temperatures in UBeB.Second, C/T at Tc is somewhat larger in UBeB than in UBe 13 ; and finally, the jump in .
specific heat ilC at Tc is much larger in UBeB than in UBe 13 • The Tc from either the onset or midpoint of the jump in CIT is unchanged and x-ray analysis does not show a distinguishable difference • between UBe 13 .and U BeB. T he resistivity maximum at about 2.5 K in U Be 13 is shifted to a slightly lower temperature in UBeB, however.
When Th is added to UBeB Tc is reduced to about 0.6 K and two specific heat transitions are clearly visible below 0.6 K.The latter is similar to specific heat data reported previously for unborated U 1 -xThxBe 13 (0.019<x< 0.043).

III. µSR DATA
The µSR time differential spectra were analyzed 2 using the Standard zero-field Kubo-Toyabe relaxation function, which gives very good fits to the data.The µSR relaxation rate a(µ.s -1 ) in pure UBe 13 is due to inhomogeneous broadening from the 9 Be nuclear-dipole-field distribution at the µ + site.No change in relaxation rate a for T < 8 K •has been observed 2 in UBe 13 • Figure 2 shows u as a function of temperature for l.TBeB, UThBeB, and UThBe.As in UBe 13 , UBeB shows no change in a between 0.05.and 1.7 K .When Th is added to the system, however, the µ.SR rate rises dramatically below about 0.4 K, as reported previ-ously2 for (U,Th)Be 13 .This rise in a is due to the onset of magnetic correlations associated with the lowertemperature phase in (U,Th)Be 13 , as mentioned in the in~ troduction.

IV. ANALYSIS AND CONCLUSIONS
Although the substitution of a few percent B for Be or T h for U in UBe 13 produces a significant increase in tl.C at Tc compared to pure UBe 13 , only Th produces an onset of magnetic correlations, at least for the boron concentration studied here.This may be due to the fact that, unlike B, Th is substituted at thef-electron site.We confine the remainder of this discussion to a comparison of UBe 13 and UBeB,  .
/\_ ..... where no magnetism is present, and the interpretation of the specific heat data is therefore less complicated.
The entropy S removed by the supercorrducting transition is given bys (1) .
One must have S(Tc) = rTc to conserve entropy, where at low temperatures in a free electron picture the . .Sommerfeld constant r is independent of temperature.Table I gives S( Tc), y( Tc), and Teo showing that iti our UBe 13 sample entropy is not quite conserved with the assumption of a temperature-independent y.The entropy conservation is somewhat worse in UBeB.This indicates that the beavyelectron state is still fonning when the si.iperconducting transition occurs [i.e" y(T) l.s increasing as T decreases]~ • If we assurne for simplicity that y increases linearly below Tc, tben we arrive at a value y( T ,,12) necessary to conserve entropy in the superconducting transition [i.e" S(Tc) =rTcl• One obtains y(T/2) = 1.17 and 1.35 J/mol K 2 for UBe 13 and UBeB, respectively (Table l).Thus adding ~ to UBe 13 in.creases the low-temperature density of states, which is proportiönal to y.This could happen if the Fermi energy is changed as electrons are added to the conduction band with B doping, or through a shift in the Kondo temperature T K• • or both.As noted above, however, the shape of the C!T data between about 1 and 6 K indicates that T K has been lowered in UBeB.We note that the total entropy S(20 K) released up to 20 K is the same within 5% for the two systems (Table I ).The specific heat jump AC is given by 5 the difference in the rate of change of entropy with temperature above and below Tc: (2) In BCS theory a = 1.4.3 for the assumption of weak S-wave coupling.Taking r = y( T /2) in Eq. (Z) one has a = 1.5 and 2.5 in UBej 3 and UBeB, respectively.Thus the large 6.C in UBeB is not simply a consequence of an increased density of states (!arger r)' bu.t reflects a significant change in the properties of the supercondu_cting state.This is evident from a plot of S(D (not shown).The slope cas;aT)sjust below Tc is Seen tobe significantly !arger in  1.17 1.5

1 .
Temperature dependence of specilic heat per Kelvin C!T.

TABLE I ,
Specific heat data for {/Be 13 _ ,.ß 7 Symbols are defined in the