Superconductivity under pressure in (U1-xThx)Be13: Evidence for two superconducting states.

The inAuence of pressure P on the superconducting transition temperature T, has been deter- mined for the {Ui „Th„)Bei3 system. The magnitude of dT, /dP increases by a factor of 3 for x ) 1. 7'/o where an increase of T, is observed at ambient pressure. The phase diagram of T, {x) for I' = 10 kbar shows two distinct regions of superconductivity.

The compound UBei3 belongs to a small class of heavy-electron superconductors which are characterized by enormous normal-state electronic specific-heat coefficients y of = 1 J/mole-K2, relatively low superconducting transition temperatures T, (1 K, and extraordinarily large values for the initial slope of the upper critical magnetic field H, 2. '~T he unusual superconducting properties of these materials include power-law dependences in T for T&& T, found in measurements of the spin-lattice relaxation rate, ultrasonic attenuation coefficien, s and thermal conductivity. 9 These results have generated a great deal of excitement since they may be indicative of an unusual superconducting state in which the superconducting energy gap vanishes at points or lines on the Fermi surface.~9 The substitution of Th for U in UBei3 produces complex and unexpected behavior such as a nonmonotonic depedence of T, on composition'o and the observation of two features in the specific heat for some compositions. " The specific-heat feature at higher temperature is associated with the development of the superconducting state, while the one at lower temperature corresponds to another phase transition that occurs without destroying superconductivity.
On the basis of an analogy with superfluid 3He, it has been proposed that two superconducting states with different order parameters are revealed in these specificheat data. " Another interpretation involving the characteristics of the ultrasonic attenuation is that an itinerant-electron antiferromagnetic state which coexists with superconductivity develops at the second transition.
We have investigated the influence of pressure P to 12 kbar on the superconducting transition temperature of various compositions in the (Ui "Th")Bei3system.
The results presented in this paper reveal a suppres-sion of T, by pressure that is greater by a factor of 3 for x & 1.7/0 than for x=0. (We use x to represent the atomic percentage of Th that is substituted for U).
We have constructed T, (x) phase diagrams for pressures to 12 kbar to show how the nonmonotonic behavior observed at ambient pressure evolves when pressure is applied. Two distinct regions of superconductivity are present for P & 9 kbar which are separated by a range of x where no superconductivity is observed. This suggests that two different superconducting states occur in (Ui "Th")Bei3 which are affected very differently by the application of pressure.
The arc-melted polycrystalline samples used in this study were prepared in a manner described previously.
'o Nearly hydrostatic pressures to 12 kbar determined by use of a Sn manometer were applied at room temperature in Be-Cu clamped piston and cylinder devices. Other experimental details are given elsewhere '3 The temperature dependence of the ac magnetic susceptibility X"(T) was determined at various pressures and the background from the empty clamp was subtracted from the data. Sharp superconducting transitions were observed at ambient pressure in good agreement with previous measurements. '0 Application of pressure typically broadens the transitions somewhat, although for x =2.31'/o and 2.60'/0, substantially broader transitions are observed at all pressures with X"continuing to decrease even at the lowest temperatures. No hysteresis with either temperature (within 3 mK) or pressure (within 0.5 kbar) is observed for any value of x, We define T, as the temperature where X" decreases by 10'/0 of the total change observed at each prt:ssurc.
The variation of T, with P determined in this way is shown in Fig. 1  where a much stronger initial decrease = 0.05 K/kbar is observed. At a higher pressure which increases as x increases, an abrupt reduction in the slope dT,/dP is observed. As x changes from 3.00'/0 to 3.78%, the magnitude of dT, /dP when P = 0 decreases with strong curvature of T, (P) at higher pressure with no abrupt variations in dT,/dP. Finally, for x=6.03'/0, T, initially decreases at a rate 0.013 K/kbar, and there is a distinct rise in T, for P = 3.8 kbar. Further decreases are observed in T, as the pressure increases, with stronger suppression at the highest pressures investigated.   For sufficiently high pressure, the distinct break in slope of T, (P) and substantially smaller sensitivity of T, to pressure indicates that type-B superconductivity has been suppressed by pressure and replaced by type A. When x = 3.00%, the initial decrease of T, with P is smaller than for x=2.60'lo, even though type-B superconductivity is expected for this x and P. This can be understood since application of pressure is moving the maximum in T, (x) to higher x, an effect that would to some extent compenstate the sensitivity of type-B superconductivity to pressure observed for 1.90'/o~x~2.60%.
Similar arguments hold for x = 3.40'/0 and 3.78'/o. The data for x = 6.03% strongly suggest that the increase of T, observed for P = 3.8 kbar occurs when pressure has moved the maximum in T, characteristic of type-B superconductivity to sufficiently high concentration to be observed for x=6.03'lo. Further measurements are planned for 40/0~x~6'/0 to clarify the influence of pressure on T, for this range of compositions. It is interesting to speculate about the behavior that might occur for higher concentrations of Th in (Ui "Th")Bei3. Extrapolation of the present data indicates that for x = 10%, no superconductivity would be observed at ambient pressure. However, application of pressure = 10 kbar might induce type-8 superconductivity at a temperature sufficiently high to be detected.
One important question concerning these results is whether pressure has substantially altered the heavyelectron superconducting state. Preliminary measurements of a sample with x = 3.78'/0 at a pressure of 8.4 kbar show that the critical magnetic field retains the enormous slope found at ambient pressure for the same composition. '4 This is a clear indication that the superconductivity found at high pressure in what we call the B phase has its origins in the heavy-electron ststc.
The data that we have presented can be interpreted as evidence for two different superconducting states in the (Ui "Th")Bei3system. It may be that more than two states occur which are not revealed in our measurements.
For example, three different superconducting states have been proposed by Joynt, Rice, and Ueda'5 to explain the behavior observed in this system at ambient pressure. Our results have some implications concerning the phase diagram at ambient pressure which are illustrated in Fig. 2(b). The data for 1.90'/o~x~2.600/o clearly show that at sufficiently high pressure, the behavior of T, (P) is very similar to that for lower Th concentrations. This strongly implies that the lower-temperature feature observed in the heat-capacity data for this range of compositions signals a transition to the same superconducting state (type A) observed for 0~x «1.72%. No such state-ments can be made for higher Th concentrations since the isobars of T, (x) displayed in Fig. 2(a) show that type-A superconductivity will be suppressed by pressure more quickly than type B for x & 3%, and so would not be detected by our &" measurements. It will be interesting to measure the heat capacity under pressure for x = 3% to see if the second transition shows the pressure dependence expected for type-A superconductivity from the data for x & 1.8%, and such an experiment is included in our future plans. In this context, it is interesting to compare the variation of T, (x) for (Ui "M")Bei3 for M=La, Th, and Lu as illustrated in Fig. 2(b). ' Also plotted in this figure is the temperature for the onset of the lowertemperature feature observed in the heat-capacity data. " Curvature of T, (x) is observed'for M=La and Th, and the expansion of the lattice with x is nearly the same in these two cases. '0 The similarity of T, (x) when x & 3% for M= La and Th lends support to our suggestion that the lower-temperature transitions observed in the heat-capacity data are a continuation of the phase boundaries observed for x ( 1.7'/0.
Other mechanisms must also be important, however, since transitions at higher temperatures are observed for M = Th when x & 3%.
Finally, for P=10 kbar, the linear variation of T, (x) for M = Th is similar to that for M = Lu at zero pressure. This suggested to us that for a given impurity concentration x, T, might be determined by the change in lattice parameter associated with both chemical substitution and pressure. The rate dT, /da(P) at which T, changes with lattice parameter a because of the application of pressure can be estimated using the bulk modulus B = -V dP/dV which can be calculated from the formula B=(Cii+2Ci2)/3 and values for the elastic constants Cii and Ci2 determined at 10 K from neutron-scattering experiments by Robinson et al. '6 The value B = 1.03X10" N/m2 obtained is very close to the value (1.00X 10"N/m2) for pure Be. The rate at which T, (x) varies with lattice parameter because of the different radii r~o f the M = La, Lu, or Th impurity atoms, dT, /da(r~), can be determined from x-ray diffraction data. ' For (Ui "M")Bei3 samples with x~1.9%, we find for a given value of x that dT,/da(P) for M = Th is about a factor of 10 smaller than dT/da(r~) for M=La and Lu. We plan to measure dT,/dP for La and Lu impurities in UBei3 to investigate these ideas further. Another possibility that should be considered is that the minimum in the T, (x) curve which occurs at x = 1.7'/0 at zero pressure reflects the onset of a profound change in the electronic structure as tetravalent Th is substituted for U in UBei3, rather than a boundary between two distinct types of superconductivity.