LOW-TEMPERATURE PROPERTIES OF THE HEAVY-FERMION SYSTEM UCD11

PHYSICAL REVIEW B Low-temperature VOLUME 30, NUMBER 11 properties of the heavy-fermion Z. Fisk, G. R. Stewart, and system DECEMBER 1984 Ucd» J. O. Willis Materials Science and Technology Division, Los Alamos Rational Laboratory, Los Alamos, New Mexico 87545 H. R. Ott and Laboratorium fur Festkorperphysik, F. Hulliger Eidgenossische Technische Hochschule (Received 7 June 1984) H— onggerberg, 8093 Zurich, Stoitzerland specific-heat, and thermal-expansion magnetic-susceptibility, We present electrical-resistivity, data for UCd 1 &. The low-temperature specific heat indicates that the electronic subsystem has a highly enhanced specific heat which is partially removed by a phase transition at 5.0 K. Recent work on various U intermetallic compounds has demonstrated that the low-temperature properties of these materials are dominated by a very unusual behavior of the Most probably, it originates electronic subsystem. ' from very strong electron-electron interactions, and, as the most obvious result, extremely large electronic specific The electronic heats are observed at low temperatures. nature of these specific heats has most convincingly been in demonstrated by the observation of superconductivity UBe~3 and the corresponding anomaly of the specific heat at the phase transition. ' UPt3 is another, more recent ex- is formed out of an elec- ample where superconductivity tronic state with a large density of states at EF, similar to what was first observed in CeCu2Si&. In all these com- pounds the strong enhancement of the electronic specific heat occurs only below about 10 K, giving rise to a strongly-temperature-dependent C, /T ratio below this A somewhat different behavior is observed temperature. A very large specific heat varying linearly in U2Zn&7. with temperature is already observed at 15 K. Here, the C, /T ratio is temperature independent with decreasing temperature. The temperature dependence of Cz through phase transition is and below the antiferromagnetic governed by a sharp positive discontinuity at T„, a finite and still rather large contribution to C& varying linearly with temperature and, in addition, a considerable nonlat- tice T contribution at the lowest temperatures. The data or- were interpreted as being due to an antiferromagnetic dering within the strongly interacting electron system. These facts stimulated the search for other examples of low-temperature phase transitions in similar -materials. UCd» crystallizes in the cubic BaHg» structure with a lattice constant of 9. 29 A. ' The nearest U-U neighbor distance is large (6.56 A with 5. 13 A for UBe» and 4. 39 A for U2zn~7). Therefore direct overlap of the 5f electron wave functions should be negligible. By simple analogy, we expected similar low-temperature features of the physical properties of UCd» as were observed before in UBe&3 and UzZn&7. on UCd» have measurements Magnetic-susceptibility been made before. Cafasso and co-workers measured the magnetic susceptibility X. between 2 and 300 K. From six data points a Curie-% eiss behavior at high temperatures 3. 79p~ and a with an effective magnetic moment p, ff — 41. 5 K, as well as a paramagnetic Curie temperature of — temperature-independent X of 39. 6X 10 emu/mol below 4. 2 K, were reported. Later, Misiuk and co-workers re- over an extended temperature peated the measurements range between 4. 2 and 900 K. They more or less con- firmed the results of Cafasso and co-workers, although value of with a somewhat larger low-temperature X =45 )& 10 emu/mol. The temperature-independent X at low temperatures was, in both cases, interpreted as be- ing due to a singlet ground state of the crystal-field-split J=4 Hund's-rule ground state of a Sf configuration of the U ions. Our experimental data shown below demon- strate convincingly that UCd» undergoes a phase transi- tion at about 5 K. Our experiments were performed variously on small single-crystalline cubes grown from excess molten Cd, as material. The latter was ob- well as on polycrystalline tained by reacting uranium tubings with cadmium vapor for 4 d at 320'C in closed silica tubes and subsequent an- nealing of the pressed powder in a quartz tube at 440'C for 10 d. A Guinier photograph confirmed the correct BaHg»-type structure. An x-ray analysis of our single crystals revealed a lattice constant ao of 9. 283(8) A, close to what has been reported before. ' Samples with good chemical composition could also be identified by the ab- sence of superconducting transitions around 0. 5 K which indicate precipitated excess Cd. In Fig. 1 we show the temperature dependence of the inverse magnetic suscepti- bility 7 ' between 1. 5 and 300 K, measured on a poly- crystalline sample with a sample-moving magnetometer. The high-temperature Curie-%'eiss — type behavior may be 3. 45pz and characterized by an effective moment of p, ff — — 20 K. Below a paramagnetic Curie temperature about 80 K, deviations from this behavior are discernible, and around 5 K there is an abrupt change of slope, the susceptibility below this temperature being nearly con- stant, with a value of 38. 4& 10 emu/mol at 1. 5 K, close to what has been reported by Cafasso and co-workers. These results give no conclusive clue to the 5f-electron configuration of the U ions. In view of the occurring phase transition, as will be shown below, the previously suggested Van Vleck — type behavior at low temperature, indicative of a 5f configuration of the U ions, can no longer be considered valid. The American Physical Society

electronic subsystem. ' Most probably, it originates from very strong electron-electron interactions, and, as the most obvious result, extremely large electronic specific heats are observed at low temperatures.
The electronic nature of these specific heats has most convincingly been demonstrated by the observation of superconductivity in UBe~3 and the corresponding anomaly of the specific heat at the phase transition. ' UPt3 is another, more recent example where superconductivity is formed out of an electronic state with a large density of states at EF, similar to what was first observed in CeCu2Si&. In all these compounds the strong enhancement of the electronic specific heat occurs only below about 10 K, giving rise to a strongly-temperature-dependent C, /T ratio below this temperature.
A somewhat different behavior is observed in U2Zn&7.
A very large specific heat varying linearly with temperature is already observed at 15 K. Here, the C, /T ratio is temperature independent with decreasing temperature. The temperature dependence of Cz through and below the antiferromagnetic phase transition is governed by a sharp positive discontinuity at T", a finite and still rather large contribution to C& varying linearly with temperature and, in addition, a considerable nonlattice T contribution at the lowest temperatures. The data were interpreted as being due to an antiferromagnetic ordering within the strongly interacting electron system. X at low temperatures was, in both cases, interpreted as being due to a singlet ground state of the crystal-field-split J=4 Hund's-rule ground state of a Sf configuration of the U ions. Our experimental data shown below demonstrate convincingly that UCd» undergoes a phase transition at about 5 K.
Our experiments were performed variously on small single-crystalline cubes grown from excess molten Cd, as well as on polycrystalline material. The latter was obtained by reacting uranium tubings with cadmium vapor for 4 d at 320'C in closed silica tubes and subsequent annealing of the pressed powder in a quartz tube at 440'C for 10 d. A Guinier photograph confirmed the correct BaHg»-type structure. An x-ray analysis of our single crystals revealed a lattice constant ao of 9.283(8) A, close to what has been reported before. ' Samples with good chemical composition could also be identified by the absence of superconducting transitions around 0.5 K which indicate precipitated excess Cd. In Fig. 1 we show the temperature dependence of the inverse magnetic susceptibility 7 ' between 1.5 and 300 K, measured on a polycrystalline sample with a sample-moving magnetometer.
The high-temperature Curie-%'eisstype behavior may be characterized by an effective moment of p,ff -3. 45pz and a paramagnetic Curie temperature 0= -20 K. Below about 80 K, deviations from this behavior are discernible, and around 5 K there is an abrupt change of slope, the susceptibility below this temperature being nearly constant, with a value of 38.4& 10 emu/mol at 1.5 K, close to what has been reported by Cafasso and co-workers. These results give no conclusive clue to the 5f-electron configuration of the U ions. In view of the occurring phase transition, as will be shown below, the previously suggested Van Vlecktype behavior at low temperature, indicative of a 5f configuration of the U ions, can no longer be considered valid. The temperature dependence of the electrical resistivity p between 1.3 and 300 K is shown in Fig. 2. The single crystal measured was not suitable for an accurate determination of the geometry factors and, hence, the absolute value of p. We estimate an approximate roomtemperature value for p of about 100 pAcm. The observed temperature dependence of p is similar to that reported for USn3, except for a distinct break in the p(T) curve (see inset of Fig. 2) near 5 K, corresponding to the temperature dependence of 7 and therefore suggestive of some kind of phase transition.
Clear evidence for such a phase transition is obtained from our results of specific-heat and thermal-expansion measurements as shown in Figs. 3 and 4, respectively. In Fig. 3 we show the ratio Cz/T as a function of T for temperatures between 0.4 and 13 K, measured on a collection of single-crystalline specimens weighing a total of 20 mg. The specific-heat anomaly associated with the phase transition peaks at 5.0 K. Above 8 K our data are consistent with a temperature dependence of Cz given by C~= yT+PT where y = 840 m J/mol K and 13=5.75 m J/mol K, result-ing in a Debye temperature OD --152 K. Also shown in Fig. 3 are some data points taken in an external magnetic field of 11 T. Similar to U2Zn~7, UCd& & has an anomalously large electronic specific heat in the paramagnetic state just above the phase transition, but this y value is again drastically reduced below the phase transition to about 250 mJ/molK, as may be evaluated from our experirnental data below 1 K. Of course, this value is still considerably higher than those found in normal metals or transition-metal compounds. An external magnetic field of 11 T depresses the transition temperature to below 4 K.
Similar to Cz(T), the linear thermal-expansion coefficient a, measured on a suitably shaped polycrystalline sample, also displays a rather broad anomaly with a hightemperature tail ranging from 5 to about 8 K. The absolute magnitude of the o. peak value is comparable to that observed in U2Zn&7, and, again, is rather small when com- ous as to how it should be interpreted. The temperature dependence of g around the transition, while not definitive, may be taken as an indication of antiferromagnetic ordering. This interpretation is also supported by the substantial loss of Fermi surface through the transition, as evidenced by the large reduction of y, as mentioned above.
Although these facts suggest an antiferromagnetic ordering among itinerant electrons with a large effective mass, we note that with decreasing temperature a net entropy loss is associated with the phase transition. The estimate of the entropy balance is again obscured by the large high-temperature tail of the specific heat, but an integration up to 8 K, where C/T reaches a constant value, reveals AS=0.28R ln2, where AS is the difference betweeñT =8 K (C/T)dT and 8y. This, of course, raises the 0 question of whether additional degrees of freedom from localized electrons may, at least partly, be involved.
Since the 5f-electron configuration of the U ions is not really known, one should not rule out a Jahn-Tellertype structural transition, which is most likely to occur if the U ions adopt a Sf configuration, and which is often observed in Pr compounds where the rare-earth ions adopt a 4f configuration. ' However, the magnitude of the anomaly of the linear thermal-expansion coefficient is, as mentioned above, rather small, and therefore gives little support for such an interpretation.
Although both the specific-heat and the thermalexpansion results indicate a considerable high-temperature tail of the phase transition, a possible explanation for part of this behavior is suggested by a comparison with the low-temperature properties of UBet3, " UPt3, CeA13, " and CeCuzSiz. In these compounds the ratio C, /T increases rapidly with decreasing temperature below a certain temperature (-7 K for UPts). Such a behavior, if it occurs below about 8 K in UCd&&, could easily be hidden in the observed tail in C~a bove 5 K for UCd». The T=O K value for y would then be larger than 840 mJ/mol K, and the net entropy valence of the transition might be zero or even negative, as in U2Zn&7. Similarly, both in UBe&3' and CeA13, ' increasing o. values with decreasing temperatures have been observed in the same temperature range. Thus, at least part of the hightemperature tail in C of UCd~& might be accounted for by a behavior as just described, and is observed in compounds that are in many ways very similar to UCd& &.
Since both positive and negative changes of C& of 5 -10% in magnetic fields of 11 T have been observed before in UBet3 (Ref. 14) and UPt3 (Ref. 15), the field data for UCd» cannot conclusively decide for or against a possible variation of C, /T with T below 8 K that would significantly alter AS. The amount of temperature dependence required to make AS=0 would give C, /T (extrapolated to T=O) of 1.3 J/mol K, or only a 50%%uo increase in y from 8 K, whereas y changes by over a factor of 7 in the same temperature range in UBe&3. It should be noted that the field data for UCd~& do rule out, down to 5 K, the same sort of rapid variation in C, /T observed in UBe&3, CeCu2Siz, and CeA13, where C, /T increases by -50% between 8 and 5 K.
In conclusion, UCd&& is another compound whose electronic subsystem has a highly enhanced specific heat at low temperatures. Part of this specific heat is removed by a phase transition at 5.0 K whose origin and character remains to be clarified.