CHARACTERIZATION OF SINGLE-CRYSTALS OF CECU2SI2 - A SOURCE OF NEW PERSPECTIVES

PHYSICAL REVIEW VOLUME 28, NUMBER JULY 1983 Characterization of single crystals of CeCu2Siz. A source of new perspectives G. R. Stewart, Z. Fisk, and J. O. Willis Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received 17 January 1983; revised manuscript received 28 March 1983) We report the first thorough characterization of single crystals of CeCu2Si2. Measurements on these flux-grown crystals, which are not superconducting above 0. 050 K, include ac susceptibility, resistivity, Hall effect, and specific heat. A review of other measurements is given, and the implica- tions of our single-crystal data are discussed. Specifically, our data are consistent with superconduc- tivity in CeCu2Siz being destroyed by having too low a Kondo temperature, although TK, „d, is not found to be inversely proportional to y as previously claimed. The entropy associated with the low- temperature specific-heat anomaly is found to be only 0. 66R ln2, in contrast to the previous result of R ln2 for polycrystalline material. The lack of superconductivity in our single crystals does not ap- pear to be due to poor stoichiometry to +5%, as proposed previously for single crystals grown by a The possibility of charge-density waves suppressing superconductivity Bridgman technique. in strain-free material is discussed, although no experimental verification is found. I. INTRODUCTION One of the more fascinating superconducting materials to be discovered in the last several years is CeCu2Si2. Steglich eI: al. ' reported that they had found a bulk specific-heat anomaly AC at about 0. 5 K in three different unannealed samples of CeCu2Si2, which polycrystalline they associated with resistive and inductive indications of This at slightly higher temperatures. superconductivity discovery aroused great interest because of the presence of an enormous y (1 J/moleK ) in these low-temperature specific heat -(LTSH) data, as well as an enormous AC, i.e. , 85. This indicated that electrons with strong AC/yT, electron-electron correlations were taking part in the su- To place this in perspective, the other perconductivity. material's system, which is today considered an example of a heavy fermion superconductor, U6Fe, has a y which, when normalized per U atom (presumably the Fe in U6Fe and the Cu and Si in CeCu2Si2 make little contri- bution to y), is only about —, '; of that for CeCu2Si2. Since Steglich et al. ' first announced their surprising ' have been result, a number of further measurements performed on CeCu2Si in order to better understand this system. Unfortunately, numerous puzzles remain, includ- ing the existence of significant sample dependence of mea- sured properties, including AC/yT„upper critical field, and even T, . ' In fact, Hull et al. observe no T, resis- tively down to 0. 060 K in a polycrystalline sample prepared similarly to those of Steglich et, al. The Meiss- ner effect has been used to characterize many of the CcCu2Si2 samples studied and varies from less than 1% in some unpowdered polycrystalline specimens to 60% in one powdered specimen, where powdering is thought to a11ow better flux penetration. In addition to the sample dependence of AC/yT„Hc2, T„and dc magnetization, y varies from approximately 1 to 1. 3 J/moleK, depending on the sample. With the exception of some resistivity as a function of pressure data on a single crystal of CeCu2Si2 taken by Aliev et al. , and T, measurements on Cu-deficient single crystals by Bredl et al. , all the characterization to date on CeCu2Si2 has been on polycrystalline samples. Since sam- ple quality plays such a crucial role in determining the properties of CeCu2Si2, it is important to closely compare materials prepared by different methods. We have grown single crystals of CeCu2Si2 from flux and have character- ized them by x-ray diffraction, x-ray fluorescence, energy ac susceptibility (0.050 4 K), dispersive spectrometry, 300 K; 0 11 T), Hall effect (2 — resistivity (1. 4 — 160 K), and specific heat (0. 3 — 33 K, 0 — 10 T). II. EXPERIMENTAL Single-crystal plates of CeCu2Si2, typically 0. 2 — 0. 3 mm thick and up to 5 mm on a side, were grown from a liquid-In flux. The particular crystals used in these mea- surements were grown by slow cooling an In:CeSi2. Cu mixture (0. 95:0.01:0. 04 atomically) in an alumina crucible from 1400 C to 500'C at 4/h. The amount of CeCu2Si2 relative to In can be greatly increased and a somewhat lower starting temperature is possible. The crystals were leached from the In matrix with HC1. Since the Hall effect has not been performed as a func- tion of temperature on polycrystalline CeCu2Si2, we also prepared such material by arc melting high-purity starting materials in an argon arc furnace. Weight losses of up to 0. 5 wt. % were observed in these melts of 5 g typical size. The nature of this boil off was not determined. The superconducting transition temperature T, of both the single-crystal and polycrystalline material was mea- sured using ac susceptibility measurements between 0. 050 and 4.0 K. The measured single crystal shows a very slight anomaly at 0. 5 K that was within the limits of error (i.e. , less than approximately 1% of the sample was super- conducting), whereas the polycrystalline material showed a transition into the superconducting state at 0. 5 K. This result is similar to that of Bredl et al. , who re- moved a crystallite of dimension 2&&2&0. 1 mm from a 40-g boule and found no superconductivity down to 0. 020 K. Bredl et al. state that this lack of superconductivity in their single crystal is perhaps due to the 20/o Cu defi- ciency measured for their crystallite. In order to test this The American Physical Society


I. INTRODUCTION
One of the more fascinating superconducting materials to be discovered in the last several years is CeCu2Si2. Steglich eI: al. ' reported that they had found a bulk specific-heat anomaly AC at about 0.5 K in three different unannealed polycrystalline samples of CeCu2Si2, which they associated with resistive and inductive indications of superconductivity at slightly higher temperatures. This discovery aroused great interest because of the presence of an enormous y (1 J/moleK ) in these low-temperature specific heat-(LTSH) data, as well as an enormous AC, i.e. , AC/yT, -0.85. This indicated that electrons with strong electron-electron correlations were taking part in the superconductivity.
To place this in perspective, the other material's system, which is today considered an example of a "heavy fermion" superconductor, U6Fe, has a y which, when normalized per U atom (presumably the Fe in U6Fe and the Cu and Si in CeCu2Si2 make little contribution to y), is only about -, '; of that for CeCu2Si2.
Since Steglich et al. ' first announced their surprising result, a number of further measurements ' have been performed on CeCu2Si in order to better understand this system. Unfortunately, numerous puzzles remain, including the existence of significant sample dependence of measured properties, including AC/yT"upper critical field, and even T, . ' In fact, Hull et al. observe no T, resistively down to 0.060 K in a polycrystalline sample prepared similarly to those of Steglich et, al. The Meissner effect has been used to characterize many of the CcCu2Si2 samples studied and varies from less than 1% in some unpowdered polycrystalline specimens to 60% in one powdered specimen, where powdering is thought to a11ow better flux penetration. In addition to the sample dependence of AC/yT"Hc2, T"and dc magnetization, y varies from approximately 1 to 1.3 J/moleK, depending on the sample.
With the exception of some resistivity as a function of pressure data on a single crystal of CeCu2Si2 taken by Aliev et al. , and T, measurements on Cu-deficient single crystals by Bredl et al. , all the characterization to date on CeCu2Si2 has been on polycrystalline samples. Since sample quality plays such a crucial role in determining the properties of CeCu2Si2, it is important to closely compare materials prepared by different methods. We have grown single crystals of CeCu2Si2 from flux and have characterized them by x-ray diffraction, x-ray fluorescence, energy dispersive spectrometry, ac susceptibility (0.050 -4 K), resistivity (1. 4 -300 K; 0 -11 T), Hall effect (2 -160 K), and specific heat (0.3 -33 K, 0 -10 T).

II. EXPERIMENTAL
Single-crystal plates of CeCu2Si2, typically 0.2 -0.3 mm thick and up to 5 mm on a side, were grown from a liquid-In flux. The particular crystals used in these measurements were grown by slow cooling an In:CeSi2.Cu mixture (0.95:0. 01:0. 04 atomically) in an alumina crucible from 1400 C to 500'C at 4/h. The amount of CeCu2Si2 relative to In can be greatly increased and a somewhat lower starting temperature is possible. The crystals were leached from the In matrix with HC1.
Since the Hall effect has not been performed as a function of temperature on polycrystalline CeCu2Si2, we also prepared such material by arc melting high-purity starting materials in an argon arc furnace. Weight losses of up to 0.5 wt. % were observed in these melts of 5 g typical size.
The nature of this boil off was not determined. The superconducting transition temperature T, of both the single-crystal and polycrystalline material was measured using ac susceptibility measurements between 0.050 and 4.0 K. The measured single crystal shows a very slight anomaly at 0.5 K that was within the limits of error (i.e., less than approximately 1% of the sample was superconducting), whereas the polycrystalline material showed a transition into the superconducting state at 0.5 K.
This result is similar to that of Bredl et al. , who removed a crystallite of dimension 2&&2&0. 1 mm from a 40-g boule and found no superconductivity down to 0.020 K. Bredl et al. state that this lack of superconductivity in their single crystal is perhaps due to the 20/o Cu deficiency measured for their crystallite. In order to test this 172 1983 The American Physical Society proposition for our (quite differently prepared) single crystals, we have done both x-ray fluorescence and energy dispersive spectroscopy measurements, using CeCuz as a standard. The energy dispersive spectroscopy indicated a 4.3% smaller Ce-to-Cu ratio in the standard than in the single crystal. However, the x-ray Auorescence measurement indicated a 4 -5.5% greater Ce-to-Cu ratio in the standard than in the single crystal. Therefore, within our experimental error of +5%, the Ce-to-Cu atomic ratio in our single crystals is 1:2. This still allows the possibility that the single crystals have the wrong Ce (and Cu) ratio to Si. We used a Gandolfi attachment to a Debye-Scherrer powder camera to determine the lattice parameter of a single crystal of CeCu2Si2, which occurs in the tetragonal ThCr2Si2 structure. The resultant lattice parameters (a =4. 101+0.001 A; c =9.936+0.003 A) are in good agreement with those reported" for polycrystalline CeCuqSi2 (a=4. 105A; c=9.933A) and measured by us on our polycrystalline material (a =4.099A; c =9.924A).
Therefore, we conclude that the stoichiometry in our CeCu2Si2 crystals is comparable (to +5%) to the correct 1:2:2ratio.
Additionally, since the crystals were grown in an In flux, the question of In inclusions arises. The ac susceptibility measurements indicate the presence of In in the single crystals (i.e. , an inductive anomaly at 3.4 K). Energy dispersive spectroscopy measurements place the amount of In as less than 0.5 at. %.
The resistance of a single-crystal plate was measured from 300 to 1.2 K using a standard four-probe ac technique at 220 Hz. The Hall effect on both a single crystal and a 0.4-mm slab of polycrystalline CeCu2Si2 was measured using a five-point dc method. In order to minimize contact resistance and therefore sample heating, 0.002-in.
Pt leads were spot welded onto the samples. At temperatures below 10 K, a current of 5 mA was used. Above 10 K, 50 mA could be used without excessive sample heating, Hall voltage, V~, was zeroed at zero field for both current directions at each temperature, and then fields of 5.5 and 11. 0 T were applied. Within measurement error (10%), V~went linearly with H and was independent in magnitude (but not sign) of current and field direction. Magnetoresistance measurements were made on both the single crystal and polycrystalline samples at the same time as the Hall-effect measurements.
The calorimeter used for measurements from 1.2 to 33 K and H =0 and 10 T has been described elsewhere. ' A new sample platform of similar design but using an unencapsulated Cr 250 Ge thermometer from Cryocal, Inc. was used from 4 to 0.3 K, giving the specific heat of a vacuum-annealed 350-mg piece of 99.9999% pure Cu to within +3%%uo of the known' values.
Three single crystals of CeCu2Si2 with a total weight of 4.21 mg were then measured on this platform from 0.3 to 1.2 K in zero field and on our usual higher-temperature platform from 1.2 to 11 K in 0and 10-T applied fields.
Since the addenda correction to the total measured specific heat, which was~0.5% for T~1.2 K, grew to be too large a percentage (50%) by 7 K, a third measurement was made on a collection of ten single crystals (different from the first three measured), with a total weight of 15.56 mg, from 1.2 to 33 K in zero field. The addenda correction for this third measurement remained below SO%%uo f' or all temperatures of measurement. The accuracy of all these specific-heat measurements is +3%, except for the second run on 4.21 mg of material above 7 K, where the accuracy is only + 5%.

III. RESULTS AND DISCUSSION
A. Do charge-density waves exist in CeCu2Si&?
In addition to the unusual polycrystalline sampledependent properties discussed in the Introduction, Aliev et al. discovered that as pressure was applied up to 2.5 kbar, their single crystal (preparation method unstated), which had T, &0.05 K at zero pressure, had its T, increase monotonically to 0.5 K. Another system that immediately comes to mind' which has similar sampledependent superconducting properties [T, -0.2 K for single crystals, ' 1 K (not bulk) for some polycrystals, ' and 2 K at 10 kbar (Ref. 19)] is U. U has long been known to have an anomaly at 43 K in the specific heat, as well in other properties.
Recently, this anomaly has been shown ' to be due to a charge-density wave. The existence of this charge-density wave (CDW) in U, which suppresses the superconductivity, is severely dependent on pressure as noted above, with only 10 kbar completely suppressing the CDW and allowing bulk superconductivity as measured by specific heat.
The polycrystalline material, on the other hand, has no bulk superconductivity down to 0.1 K at zero pressure but has small regions that superconduct as high as 1 K due to a local suppression of the chargedensity wave.
Is there a superconductivity-destroying charge-density wave at some temperature in single-crystal CeCu2Si2 which is suppressed by small applied pressures'7 Is this charge-density wave partially suppressed depending on details of sample preparation in polycrystalline samples, where a large anisotropic thermal expansion is expected"' to produce internal stresses ' In order to investigate whether a charge-density wave exists in single-crystal CeCu2Si2, we have measured the Hall effect in both single-crystal and polycrystalline material. The changes in Fermi-surface topology associated with the formation of a charge-density wave cause a sign change [in both U (Ref. 23) and the layered transitionmetal dichalcogenide compounds~] in the Hall coefficient R~, RII --VII t /BI, where T is the thickness, 8 is the field transverse to the direction of the current I, and V~is the voltage transverse to the direction of both the current and the field. It should be pointed out that the lack of a sign reversal in R~does not rule out a charge-density wave in a given material, since the way in which the charge-density wave affects R~will depend upon the details of the Fermi-surface topology.
The Hall voltage at 11 T and normalized to 50 mA of current is shown in Fig. 1 for a single crystal of CeCu2Si2, t=0. 14 -0. 19 mm, and a polycrystalline sample, t=0.4 mm. There is no sign reversal for either sample out to the highest temperature of measurement. The ratio of VII for the two samples is, within the limits of error, simply the inverse of the respective thicknesses, Eq. (1). Thus our measurement of the Hall effect in CeCu2Si2 shows no sign of a charge-density wave in this material up to 160 K. The Hall coefficient R~corresponds to an electron carrier density n (using the simple formula RH --4&10 V cm/GA=1/ne, where e is the electric charge) for both samples of 1.4)&10 ' cm at 4.2 K. Aliev et al. ' state n at 4.2 K for their polycrystalline CeCu2Si2 to be 2&10 ' cm. . The Hall coefficient R~found here is large compared to that of a simple metal (RH --0.8 & 10 Vcm/GA for Cu) and is comparable to values found for the anomalous Hall effect in rare-earth metals. age fell below 2 p V, not only was the dc current reversed, but also the direction of the field was reversed to assure that a sign reversal of VH was not obscured by noise.

B. Resistivity~Ĩ
Our resistivity data on single-crystal and polycrystalline CeCu2Si2 is shown in Fig. 2. There has been a large range of resistivity behavior reported for CeCu2Si2. It means, however, that T, is an extremely critical function of the exact value of Tp o for 6.3 K & T o &7 K.
The other approach to connecting TK»do and T"via specific-heat data, will be discussed for our single-crystal results below.
Resistivity data for both samples in an applied field of 11. 0 T (not shown in Fig. 2) showed a negative magnetoresistance effect (characteristic of dense Kondo systems) of about 4.5% at 2 K. This change in resistance with field went to zero by 30 K for the polycrystalline sample but remained nonzero until 90 K for the single crystal (e.g. , 2.1% decrease at 30 K and 11 T). Aliev et al. ' found a negative magnetoresistance for polycrystalline CeCu2Si2 of 1.5% in a 4-T field below 40 K, which is inconsistent with our result both in magnitude and temperature dependence.

C. Specific heat
The data are shown in Fig. 3 plotted as C vs lnT, along with the data from Steglich et al. ' lt should be stressed that their data, which extend only to 7 K, and our data coincide, as best as we can determine from their published graph, to +3% below 2 K until their polycrystalline sample goes superconducting at -0.5 K.
The temperature of the peak, T,",in our specific-heat data can be compared to TK,"d" if we assume T&ondo 2 Tp, o -3 5 K, then Tmax /T&ondo 0.6, much different from the value of -, ' quoted for the data of Steglich et al. , ' which was comparable to the dilute Kondo case. The peak in our specific-hest data is lower in temperature than that for the Steglich eI; al. ' data, and therefore TKQndp(single crystal) & TKpndp(polycrystalline) is again consistent with the argument ' that TK,nd, must be above a certain temperature so that uncompensated Ce + 4f spins do not prevent superconductivity.
Two other comparisons of our specific-heat data to those of Steglich et al. are informative. In order to facilitate these comparisons, our data are replotted in Fig. 4, with just the low-temperature data, as C/T vs T, and in Fig. 5 a similar plot is shown for all the data up to 33 K. In Fig. 4, if we describe C/T as equal to an electronic term y and a lattice term PT, where the lattice term is & 1% of the electronic term, we see that y increases 10% with just a 1 K temperature decrease. Such a rapid change of an electronic term, if such it is, with temperature is unusual. Such a negative slope of y has also been noted above T, in polycrystalline CeCu2Si2 by Lieke et al. Although this behavior in y vs T is at present unexplained, the value of y(T=0) =1.05 J/mole K casts doubt on one of the important systematic behaviors reported by Steglich et al. and by Bredl et al. , i.e. , their claim that T, =const)&y ' based on four samples. Our value of y=1.05 I/mole K for y is comparable with that obtained ' for their highest T, (0.6 K) material (as is the entire specific-heat behavior from 0.5 to 2 K, Fig. 3 Fig. 3) and subtracted from the measured lowtemperature specific heat. An entropy integral from 0 to 19 K of (C/T)d T is then performed, giving S = 3.8 J/mole K, which is 0.66 of the expected amount of entropy due to completely lifting the degeneracy of the lowlying doublet, i.e. , R ln2 or 5.76 J/mole K. This is not in disagreement with work in dilute systems, where in at least one system only one-half of the expected entropy was measured.
However, Lieke et al. , presumably referring to the data of Steglich et ah. ' shown in Fig. 3, claim that the anomaly in polycrystalline CeCuzSiz has "an entropy connected with it of about kbln2 per Ce ion" or R ln2 per Ce mole. Since, as discussed above in the experimental section, we are confident to + 5 ' of having the correct stoichiometry (and therefore Ce content) in our samples, we find this difference confusing. Partly, Lieke et ah. appear to have underestimated y for "normal" CeCuzSiz by using y for LaCuzSiz (stated to be 4.4 mJ/moleK ). Also, since the data of Steglich et Fig. 3 (a straight line through the three highesttemperature points shown in Fig. 3 and joining our data at 11 K), we find the entropy associated with the anomaly in polycrystalline CeCuzSiz to be only 4.8 J/moleKstill well short of R ln2. It is interesting to note that Bloomfield and Hamann predict the entropy under a spin--, Kondo anomaly to be 0.45k& per impurity in the dilute case, or just 0 65 of kz ln2to be compared to the 0.66R ln2 for a dense Kondo system reported here.

IV. CONCLUSIONS
We have seen one confirmation of previous work by our single-crystal characterization. Both our resistivity and specific-heat data on nonsuperconducting single-crystal CeCuzSiz point to a low TK "d, for this material, which is consistent with the earlier work ' which found that TK "d, had to be above a certain minimum value for superconductivity to occur.
We have measured the Hall effect of both single-crystal and polycrystalline material to investigate the possibility that there exist charge-density waves in CeCuzSiz which might explain some of the unusual properties in this system, in analogy to U. No evidence for such a phenomenon was found, either in the temperature dependence of the Hall effect or in a room-temperature electron-diffraction experiment performed here by Rohr.
We have discovered three cases where propositions in the literature appear to be fa1se: (1) TK,"d, and therefore T"is not proportional to the apparent y ', (2) the entropy under the anomaly of both polycrystalline and singlecrystal material appears to be significantly less than R ln2 per mole of CeCu2Si2, (3) the lack of a superconducting transition in our single crystals of CeCuzSiz is not due to a Cu deficiency to +5~o. An order-parameter determination for our single crystals would be necessary to completely answer the question of whether lattice perfection in CeCuzSiz is essential for superconductivity.