PHYSICAL REVIEW B VOLUME 31, NUMBER 3 1 FEBRUARY 1985

Effect of pressure on spin fluctuations and in heavy-fermion Upt3

J. O. Willis, J. D. Thompson, and Z. Fisk Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

A. de Visser, J. J. M. Franse, and A. Menovsky Natuurkundig Laboratory'um der Uni versiteit van Amsterdam, Valckenierstraat 65, 1018LE Amsterdam, The Netherlands (Received 13 November 1984)

%e have determined the effect of hydrostatic pressure on the susceptibility, on the T2 temperature dependence of the spin-fluctuation resistivity, and on superconductivity in Upt3. The spin-fluctuation tem- perature T„derived from the slope of resistivity versus T, is used within a Fermi- picture to calcu- late the susceptibility X at T=O K. The depression of this calculated X with pressure agrees with the directly measured value 8 lnx/8P = —24 Mbar i. Both the superconducting transition temperature T, and the initial slope of the upper critical field also decrease under pressure. We find that elnT, /BP= —25 Mbar i and speculate upon correlations between X and T,.

In the uranium-platinum series superconductivity oc- Hydrostatic conditions were preserved as well as possible by curs' in the compound that shows the most pronounced freezing the helium under constant pressure conditions. 6 spin-fluctuation phenomena, UPt3. The neighboring phases, The detection limit of this magnetometer is 5x10 Am . UPt2 and UPt5, exhibit weaker spin-fluctuation effects in For the UPt3 sample, the prcssure-independent diamagnetic specific-heat and resistivity measurements and do not contribution to the induction voltage amounted to 11'/o, for show, so far, any sign of a superconducting state. UPt3 can which a correction was applied. Temperatures were deter- be classified as a heavy-fermion superconductor, i.e., a sys- mined from a nearly field-insensitive carbon-glass resistance tem that behaves as a.Fermi liquid with a large effective thermometer. The field effect on the thermometer caused mass (m =200m, ), like CeCuqsi2 (Ref. 6) and UBei3. deviations in the temperature of less than 0.2 K in the tem- The unusual coexistence of spin fluctuations and supercon- perature range 4.2-40 K in a field of 5.3 T; these deviations ductivity has led Stewart, Fisk, Willis, and Smith to specu- did not affect the pressure effect on the temperature at late on p-wave superconductivity in UPt3, in analogy to He. which the maximum in X occurs. Therefore, it is an intriguing question whether spin fluctua- Both T, (midpoint) and the slope of the upper critical '2 = — tions and superconductivity are intimately connected in field near T„B, — 88,2/BTlz, , were determined resis- UPt3. tively by a standard four-terminal ac technique with the High-pressure experiments on the resistivity of UPt3 have current direction along the hexagonal c axis. These mea- been performed by De laisser, Franse, and Menovsky and surements were performed at Los Alamos on a twinned by Wire, Thompson, and Fisk at pressures up to 4.2 and 18 crystal of UPt3 that was grown in a bismuth flux and subse- kbar, respectively. De laisser et a/. pointed out that only at quently annealed at 1200'C for 40 h and 1100'C for an ad- approaching 1.4 K from higher temperatures is a T depen- ditional 20 h. Pressures up to 19 kbar were generated in a dence observed, as predicted by spin-fluctuation theories. Cu-Be self-clamping cell, modified slightly from the one The coefficient of this term and its pressure dependence are described in detail elsewhere. '0 Its principle of operation is determined- in their analysis by the slope of the p vs T identical to our earlier design. The pressure at low tempera- curve at the lowest temperatures. For current directions in tures was deduced from the inductively measured T, of a either the basal plane or along the hexagonal axis, a sub- high-purity tin manometer. Great care was taken to ensure stantial depression of this coefficient at 4.2 kbar is observed. thermal equilibration between the sample and the

From both experiments one must conclude that a strong temperature-sensing thermometer, located . outside the depression of the spin-fluctuation contribution to the resis- high-pressure volume. tivity takes place at low temperature. Magnetization curves of polycrystalline UPt3 at 4.2 K are To examine in greater detail the interplay of spin fluctua- shown in Fig. 1 for two different pressures: 1 bar and 4.5 tions and superconductivity in UPt3 and its Fermi-liquid na- kbar. The value for the relative pressure derivative of the ture, we have performed high-pressure studies on the sus- susceptibility, |ilnX/8P, as derived from the data of Fig. 1, ceptibility, on the superconducting transition temperature is —24 Mbar . The zero-pressure susceptibility derived T„and on the upper critical field near T,. from these data is 104x 10 9 m3/(mole formula units) and The magnetization studies (performed in Amsterdam) is larger than the value expected for a polycrystalline sample made use of an induction method. A polycrystalline UPt3 with random orientation of the crystallites, pointing to pref- sample (cylinder, qh=6 mm, 1=8 mm), prepared by arc erential orientation in this sample. [The susceptibility in the melting and casting of the material into a water-cooled cru- hexagonal plane is 110x 10 s m3/(mole formula units) at cible, was placed in a diamagnetic Cu-Be cell and moved 4.2 K (Ref. 4).] between the centers of two oppositely wound pickup coils. The temperature dependence of the magnetic moment of helium served as the pressure transmitting medium. UPt3, in a field of 5.3 T, has been measured between 4.2

31 1654 1985 The American Physical Society EFFECT OF PRESSURE ON SPIN FLUCTUATIONS AND. . . 1655

0.5 17.6 K

UPt 3 1) 5.3 T 0.4— 4.2 K / (D / / ~ ~ 115— / / I C3 C3 l 19.6 K I 0.3— I E I «b&r I / Q ~r '/ t / l 1 bar 105- 0 I t 0.2— 4.5 kbar ( CV / ~ -4.5 kbar / I I 0.1 95— (

1 I I 0 0 10 20 30 40 50

FIG. 2. dc susceptibility as a function of temperature at different pressures for polycrystalline The arrows indicate the tem- FIG. 1. Magnetization curves for polycrystalline UPt3 at 4.2 K at UPt3. T~ the pressures indicated. perature for which the susceptibility maximum occurs. and 40 K, at zero pressure and at 4.5 kbar. From these data calculate T,(P) from the data. The results are shown in the temperature dependence of the susceptibility has been Fig. 4. The relative pressure change of T„BlnT, /BP, is 25 Mbar '. At low temperatures, a Fermi liquid, such as determined and, in particular, the temperature T where the = maximum in the susceptibility occurs and its pressure UPt3, is expected to obey the relation x(T=O) C/T„ dependence BT /BP (see Fig. 2). The temperature T where C is an appropriate Curie constant. This implies that BlnX/BP= —BlnT, /BP, so that the effect of pressure on shifts towards higher temperatures with a rate of 2 K over — 4.5 kbar, resulting in a relative pressure dependence the spin-fluctuation resistivity of UPt3 is Bl nX /BP= 25 '. mea- B ln T /BP of 25 Mbar ', which is almost equal to the value Mbar This agrees very satisfactorily with the direct surement of the susceptibility at 1 bar and 4.5 kbar on po- for BlnX/BP. Therefore, the product XT may be con- = — sidered as pressure independent. lycrystalline UPt3 (B lnX/B P 24 Mbar ') discussed The resistivity versus temperature data for Upt3 up to 2 above. Wire et al. report similarly good agreement K, plotted on a log-log scale, yield a slope of 2.0+0.1 for each of the applied pressures. Therefore, we display the resistivity versus T in Fig. 3. Clear deviations from T behavior were apparent for temperatures above about 1.5 K, with the resistivity increasing less rapidly than T . The (ex- trapolated) residual resistivity is independent of pressure at the 1% level. The residual resistance ratio, p(300 K)/p(0 K), is approximately 280 at 1 bar, the highest value report- ed to date for Upt3. We estimate the residual resistivity of this sample to be about 0.5x10 0 m based on a 300-K c-axis resistivity value of 130& 10 Qm. Figure 3 also shows the systematic decrease of the slope + + + Bp/BT with pressure. In the spin-fluctuation model of + Ig+ + ++ + Kaiser and Doniach, the resistivity for T && T„ the spin- + + fluctuation temperature, is proportional to (T/T, )~. The +-- determination of T, is not clear cut for UPt, as discussed by Wire etal. However, in our analysis, it is only neces- 0 I I l sary to determine relative changes in T, and not absolute 0 0$ - l0 l.5 2.0 values. We choose the peak in susceptibility (Fig. 2) as T (K) representative of T„ i.e., T, (P = 1 bar) = 17.6 K. There- FIG. 3. Resistance vs temperature squared for single-crystal fore, employing p = pq+ A ( T/ T, )~, we calculate A at 1 bar, UPt3. Pressures were applied in the order: 1 bar, 10.2 kbar, 19.1 and assuming that A is not a function of pressure, we then kbar, and 4.1 kbar. The straight lines are a guide to the eye. 1656 J. O. WILLIS et aI.

40 calculate the Fermi-surface area and also make the assump- tion that it is pressure independent, then we may calculate y as a function of pressure. We find, using either the full or hC I- 6 30 the clean limit formula, that y is essentially constant to 10 «C4 O kbar and drops less than 10% at 19 kbar, even though T, CD and 8,2 have changed by 50%. If our above stated assump- tions and the use of these equations are justified, then we 2P (h find that superconductivity in UPt3 is not as strongly corre- C) lated with y as is the case for high-T, 315 superconduc- T tors. '3 [We note that, given our assumptions in calculating — Bc2 10 y(P), by 19 kbar X/y has decreased by about 40% or the ~ T Fermi-surface area has decreased by the same amount for X/y independent of pressure. ] I I 0 We note finally that 12 16 20 P (kbai) [) lnX/[1P =—t) lnT /"t)P( = [1ln8,'2 /QP) =——25 Mbar FIG. 4. The spin-fluctuation temperature T„ the superconducting This is suggestive of a correlation between the large suscep- transition temperature T„and the initial slope of the upper critical tibility (spin-fluctuation phenomenon) and superconductivi- field 8,'2 =——88,2/8 T[& vs pressure for single-crystal UPt3. C ty in UPt3. Although a decrease in T, with pressure is not unusual, Tachiki, Maekawa, and Takahashi' suggest that a depression of T, should occur if the superconductivity is not of the conventional BCS (S=O) type, but rather is of a between X derived from T, and X measured directly for the type enhanced by spin fluctuations. We suggest that this spin-fluctuation system UA12 under pressure. These same may be the case for UPt3. We note that for other heavy- authors report a somewhat larger value for [)InX/[)P of —30 fermion systems T, has been observed to increase with Mbar ' for UPt3 from e-axis resistivity down to 1 K. We pressure in CeCu2Si2 (Ref. 15) and to decrease with pres- believe that the present value of —(24 to 25) Mbar sure in UBei3, ' Furthermore, Valls and TeRanovic'7 represents a more accurate result than was previously attain- within a Fermi-liquid model in the limit of large ef- able. predict, fective electronic mass, that T, should be proportional to We now discuss the effects of pressure on superconduc- T„ or inversely proportional to X, which is the opposite of what tivity in UPt3. Figure 3 shows the depression of T, with we find here for UPt3. We can only comment that the dif- pressure; the results are replotted in Fig. 4. The relative ferent pressure dependences observed experimentally for depression of T, with pressure [) InT, /[1P is —26 Mbar these three heavy-fermion systems are as perplexing as are The initial slope of the upper critical field '2 is also B, the different theoretical predictions. depressed with pressure at a relative rate of —28 Mbar In summary, we have performed resistivity and suscepti- Based on our data to 19 kbar, both T, and 8,'2 extrapolate to bility measurements on single-crystal and polycrysta11ine zero at 37J1 kbar, corresponding to a volume change UPt3 under pressures up to 19 kbar. Superconductivity and 5 V/ Va of —0.018." spin fluctuations are both found to be strongly depressed We have analyzed the effect of pressure on the electronic by pressure with specific-heat coefficient y using our measured values of T„ B,2, and p and the equations derived from the Bardeen- [llnT /[ip=ti[nX/[)P= —25 Mbar Cooper-Schrieffer (BCS) theory found in Orlando, NcNiff, Foner, and Beasley. '2 Assuming the dirty limit (mean free The correlations between T, and X(0) are highly suggestive path I much shorter than the superconducting coherence of a non-BCS-type pairing mechanism. length go) and using the measured 7 value (=1.06x10~ J/m' K2)', a value for 8,'2 of 0.34 T is obtained which is The work performed in Amsterdam was part of the only about 5% of the measured value. Clearly, our UPt3 is research program of the Stichting FOM (The Dutch Foun- not in the dirty limit. A knowledge of the Fermi-surface dation for Fundamental Research of Matter). The research area is required for use of the clean limit or the full expres- at Los Alamos National Laboratory was performed under sion relating y to T„B,'2, and po. If we use 1-bar data to the auspices of the U.S. Department of Energy.

'Also in Division. 5A. de Visser, J. J. M. Franse, and A. Menovsky, J. Magn. Magn. G. R. Stewart, Z. Fisk, J. O. Willis, and J. L. Smith, Phys. Rev. Mater. 43, 43 (1984). Lett. 52, 679 (1984). 6F. Steglich, J. Aarts, C. D. Bredl, W. Lieke, D. Meschede, W. A. de Visser, J. J. M. Franse, A. Menovsky, and T. T. M. Palstra, Franz, and H. Schhfer, Phys. Rev. I.ett. 43, 1892 (1979). Proceedings of the Fourth General Coqference of the Condensed 7H. R. Ott, H. Rudigier, Z. Fisk, and J. L. Smith, Phys. Rev. Lett. Matter Division of'the European Physical Society, The Hague, 1984 50, 1595 (1983). [Physica B (in press)]; J. Phys. F 14, L191 (1984). SM. S. Wire, J. D. Thompson, and Z. Fisk, Phys. Rev. 8 30, 5591 T. T, M. Palstra, P. H. Kes, J. A. Mydosh, A. de Visser, J. J. M. (1984). Franse, and A. Menovsky, Phys. Rev. B 30, 2986 (1984). 9A. B. Kaiser and S. Doniach, Int. J. Magn. 1, 11 (1970). 4P. H. Frings, J. J. M. Franse, F. R. de Boer, and A. Menovsky, J. iOJ. D. Thompson, Rev. Sci. Instrum. 55, 231 (1984). Magn. Magn. Mater. 31-34, 240 (1983); P. H. Frings, thesis, iiBased on the room-temperature, isothermal compressibility i University of Amsterdam, 1984. tc 0.48 Mbar of UPt3 [A. de Visser, J. J. M. Franse, and A. 31 EFFECT OF PRESSURE ON SPIN FLUCTUATIONS AND. . . 1657

Menovsky, J. Phys. P (to be published)). Phys. Rev. B 30, 1182 (1984). 2T. P. Orlando, E. J. NcNiff, Jr., S. Foner, and M. R. Beasley, ~~J. %'. Chen, S. E. Lambert, M. 8. Maple, Z. Fisk, 3. L. Smith, and Phys. Rev. B 19, 4545 (1979). H. R. Ott, in Proceedings of the 17th International Cottference on t&K. C. Lim and J. D. Thompson, Phys. Rev. B 25, 6053 (1982); K. Lo~ Temperature Physics, edited by U. Eckern, A. Schmid, W. C. Lim, J. D. Thompson, and G. W. Webb, ibid 27, 2781 (1983). Weber, and H. Wtthl (North-Holland, Amsterdam, 19&4), p. 325. M. Tachiki, S. Maekawa, and S. Takahashi, Phys. Rev. B 31, 228 ~70. T. Valls and Zlatko Tesanovic, Phys. Rev. Lett. 53, 1497 (1984). (1984). ~58. Bellarbi, A, Benoit, D. Jaccard, J. M. Mignot, and H. F. Braun,