J. Phys. Chem. B 2001, 105, 4867-4871
4867
Superconducting Transition Temperature of 2H-TaS2 Intercalation Compounds Determined by the Phonon Spectrum A. Schlicht, M. Schwenker, W. Biberacher, and A. Lerf* Walther-Meissner-Institut, Walther-Meissner-Str. 8, 85748 Garching, Germany ReceiVed: January 7, 2001
The specific heat in the normal and superconducting states of single-crystal intercalation compounds of the host material 2H-TaS2 was measured from 1.7 to 9 K by use of a thermal relaxation method. By studying two extreme cases of charge transfer n, namely the 9 Å methylene blue intercalation compound (9 Å MB+TaS2) (n ) 0.06) and K0.33TaS2 (n ) 0.33), and comparing the results with literature data, it is seen that charge transfer has only minor influence on the electronic specific heat in the normal state. This is in drastic contradiction to the expectation from a rigid band model. The contribution of the phonon-parameter β, however, varies with intercalation. No direct correspondence between Tc and the Debye temperature θD can be seen, but if θD is multiplied by a factor, characterizing the intercalation compound, scaling between Tc and the corrected Debye temperature θcorr D is found. Furthermore, it is observed that the superconducting transition temperature of the methylene blue intercalation compound is sensitive to cooling rate.
1. Introduction Shortly after the beginning of intercalation chemistry of the layered metal dichalcogenides, a large number of organic and inorganic cations have been intercalated in 2H-TaS2 and the products have been tested for superconductivity.9 Intercalation in the host 2H-TaS2 raises the Tc from 0.6 to 2-5.5 K.8 This effect was attributed to the suppression of a structural instability by intercalation.7 The structural instability is usually assumed to be driven by a CDW; however, recent theoretical calculations consider it as a metal-metal bond formation.26 There have been a number of questions raised concerning the nature of quasi-two-dimensional superconductivity and the role of the intercalated atoms and molecules in determining Tc. The mystery of an anomalous curvature of the upper critical field perpendicular to the layers has recently been solved:19 The phase line in the H-T-diagram, which shows an upward curvature, is identified as the irreversibility line, whereas Hc2⊥ depends linearly on temperature near Tc. But the statement that intercalation compounds belong to the class of the most anisotropic superconductors is still true. Many attempts have been made to relate the superconducting transition temperature to the layer separation (thus to the anisotropy of the crystals?)9 or to the charge transfer (thus to the density of the states at the Fermi level?).23,18,16,17 But none of them gave unambiguous evidence for an influence on the Tc. The intercalation compounds are an interesting system to study, because comparative investigations concerning the superconductivity in these compounds can be done. The reason for this is the unchanged structure of the TaS2 layers by intercalation. To study the influence of charge transfer n on the density of states and to get information on the Debye temperature of the intercalation compounds, measurements of the specific heat are very useful. K0.33TaS2 and the recently produced methylene compound 9 Å MB+-TaS2 (MB+ is a cationic phenothiazine derivative, see Figure 1) are two extreme examples of intercalation compounds with charge transfer n, with n )
Figure 1. Methylene blue.
0.33 and n ) 0.06, respectively. By comparing these data with data from earlier work, it is possible to test a rigid band model for intercalation compounds and relate the result to the observed Tc value. In disagreement with the prediction of a rigid band model, we find that the electronic part of the specific heat is constant for all intercalation compounds regardless of the charge transfer to the superconducting layers, but the phonon specific heat and the resulting Debye temperature depend on the intercalation species. We present a model in which the phonon spectrum is decisive for the Tc value of the compounds. 2. Experimental Details 2H-TaS2 has been prepared by iodine vapor transport at 900° C and a subsequent annealing procedure. The intercalation reactions were carried out by an electrochemical method under galvanostatic conditions out of deaerated aqueous solutions. Details on the preparation and characterization of the methylene blue intercalation compound and K0.33(H2O)0.66TaS2 has been published recently.13,3 The intercalation process is a reduction reaction of the host lattice: for charge compensation of the cations between the layers electrons are transferred to the conduction band. The charge transfer n is given in electrons per TaS2, and in the case of a fully ionized (this has been shown for the lithium intercalation compound LiTaS2 by Silbernagel22) monovalent cation intercalation compounds, is equal to the cation content x. In case of the MB+ intercalation compound, the charge transfer has been determined to n ) 0.06. The layer distance of this compound is d ) 9.07 Å, therefore we called
10.1021/jp010089a CCC: $20.00 © 2001 American Chemical Society Published on Web 05/05/2001
4868 J. Phys. Chem. B, Vol. 105, No. 21, 2001
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TABLE 1: Specific Heat Data of 2H-TaS2 and Its Intercalation Compounds Measured in this Work and for Comparison Data from Literature
9 Å MB -TaS2 (not pumped) 9 Å MB+-TaS2 (pumped) K0.33(H2O) y≈0TaS2 (pumped) (py)1/2TaS2 +
(dmpy)1/5TaS2 (coll)1/6TaS2 2H-TaS2
Tc [K]
γ [mJ/mol K2]
β [mJ/mol K4]
θD [K]
5.05 4.3/3.5 3.94 3.7 3.30 2.8 2.80 0.8 0.6
8.9 ( 0.7 7.4 ( 1.1 8.7 ( 0.6 8.9 ( 0.4 9.1 ( 0.2 9.5 ( 0.4 9.5 ( 0.4 8.5 ( 0.1 8.6 ( 0.1
0.95 ( 0.03 1.07 ( 0.03 0.99 ( 0.03 2.07 ( 2% 2.32 ( 2% 1.65 ( 2% 1.65 ( 2% 0.37 ( 2% 0.31 ( 0.03
184 176 180 141 136 152 152 251 265
it the 9 Å MB+-TaS2 phase to distinguish it from the other phases we obtained under slightly changed reaction conditions.13 The samples used for the measurements of the specific heat had an approximate mass of 3 mg and were cut out of larger crystals before intercalation. Measurements of the specific heat were made using an automated calorimetry system that operates on the basis of the relaxation method.1 The thermometer is a bare thick-film-resistor (Lake Shore: cernox 1050) and the heater a minimized precision strain gage. The thermal coupling of the system (thermometer, sample, heater) to a heat bath is achieved by eight manganin wires of diameter 25 µm, which were used for the resistance measurements of the thermometer and the heater. The crystals were attached to the thermometer using a thermally conducting grease (Apiezon N). During the measurement the sample was overheated by 3% of the bath temperature. The addenda is typically 30-40% of the measured signal. The absolute accuracy of the data is ( 3%. For specific heat measurements, the sample chamber is usually evacuated at room temperature before cooling. Doing this in the case of intercalation compounds causes the cointercalated water in the potassium-intercalation compound to be pumped out. It will be shown later that even the methylene blue intercalation compound is influenced by pumping. Therefore, we applied also another cooling procedure to some of the samples: we cooled the sample quickly in nitrogen atmosphere down to the freezing point of N2. By further cooling, the N2 gas freezes out and the vacuum becomes good enough for measuring the specific heat. Additional experiments for studying the transition to superconductivity were carried out with an ac-susceptometer working through the influence of the susceptibility on the frequency of a tank circuit. With this equipment it is possible to quench the sample from room temperature down to 4 K.
µ0Hc(0) [mT]
∆C/γTc
ref
13.3
0.79
19.4
0.80 0.8 0.96 0.65
this work this work this work 5 20 5 20 5 10
28.8
6
1.2
Figure 2. Specific heat of K0.33TaS2 with a fit to the normal state parameters in a C/T vs T2 plot.
molecule. For all samples, N ) 3 is assumed (only the host material is taken into account). The specific heat is discontinuous at the phase transition from the normal to the superconducting state. This jump at T ) Tc was determined from a plot of C - βT3 using the method of equal entropy and is tabulated as ∆C/γTc. The thermodynamic critical field Hc(0) at T ) 0 can be calculated via the Rutgers equation
V Hc(0)2 ∫0T (CS - CN)dT ) 8π c
assuming that the specific heat in the superconducting state can be reasonably extrapolated to T ) 0 with an exponential decay of the electronic part.
CS(T) ) Ae(- bTc/T) + T3
3. Results The normal state specific heat at low temperatures is a sum of the electronic and lattice contributions with the coefficients γ and β, respectively.
CN ) γT + βT3
(1)
The values of γ and β given in Table 1 were obtained from a least-squares fit of eq 1 to the normal state specific heat given per (intercalate)xTaS2 formula unit. The Debye temperature θD is given by
12 4 π RN 5 β) θ3D
(2)
where R is the gas constant and N is the number of atoms per
(3)
(4)
The value of b was determined by fitting a straight line to a plot of ln[(C - T3)/Tc] vs Tc/T and A by scaling the resulting exponential to the actual data at 1.7 K. Figure 2 shows the specific heat of K0.33TaS2 in the form of C/T versus T2 together with the fit of eq 1 to the normal state data points. The values of the above-mentioned parameters for the measured intercalation compounds are listed in Table 1 together with data from measurements of the specific heat available in the literature. In Figure 3, the electronic part of the specific heat Cel of the 9 Å MB+ intercalation compound is plotted as Cel/T vs T. The difference between the two transition curves of the same sample is due to the fact that one time the sample chamber was pumped at room temperature and the other time not. In the first case one has a broad transition to superconductivity which looks like
Superconducting Transition Temperature of 2H-TaS2
J. Phys. Chem. B, Vol. 105, No. 21, 2001 4869 4. Discussion
Figure 3. Electronical part of the specific heat of 9 Å MB+TaS2 (top) when the crystal was in a vacuum before cooling and (bottom) when the crystal was cooled under normal preassure.
4.1. Superconducting State. The assumption that the measured potassium intercalation compound has no cointercalated water between the layers after pumping at room temperature can be confirmed by the observation of a Tc value of 3.94 K, which is comparable to the value of 3.8 K reported by Lerf et al.15 for K0.33TaS2. As the layered transition metal dichalcogenides and their intercalation compounds are taken to be anisotropic BCS superconductors, the results of the measurements should be compared with BCS theory. In the isotropic case the predicted value of the jump in the specific heat C should be ∆C ) 1.43γTc. For anisotropic superconductors the value should be less. The theoretical value in the weak coupling limit for the case of an anisotropic linear variation of the superconducting gap is 0.7923 × g(R) × γTc2.6 Here g(R) ) (1 + R + R2)2/(1 + R + R2 + R3 + R4); R ) ∆min/∆max. The intercalation compounds are very anisotropic, so the discontinuity of the electronic specific heat should be closer to the lower approximation R ) 0 (Hc2|/Hc2⊥ ) 50).19 So values of the jump in the specific heat of 0.8 to 1 γTc are realistic. As the coupling mechanism of the electrons should be via exchange of phonons the effective electron-electron coupling constant could be estimated from the McMillan formula in the limiting case of strong coupling:
Tc )
Figure 4. Superconducting transition curves measured with acsusceptibility for a 9 Å MB+-TaS2 crystal. If the crystal is slowly cooled, it has a high Tc (a); if it is quenched Tc is lower (b). The transition to superconductivity is much broader (c) when the crystal was in a vacuum before cooling.
a double transition at 4.3 and 3.5 K. The other, in comparison, has a sharp transition at 5.05 K. To verify the influence of pumping, we also measured the ac-susceptibility of the 9 Å MB+ intercalation compound (Figure 4). A sample pumped on (10-2 mbar) at room temperature has a broad transition between 3.5 and 5 K. If the sample is cooled at ambient pressure, the transition is very sharp (∆T ) 0.2 K). The effect of pumping is reversible: If a pumped sample was at normal pressure (air or helium atmosphere) for a longer time, approximately 4 h, the transition width is small again. We also observed that a further parameter has an influence on the transition temperature, namely the cooling rate. To study the influence of cooling, a quenched sample with a Tc of 4.5 K was tempered stepwise at higher temperatures and cooled again. The transition to the phase with the higher Tc of 5.2 K takes place at approximately 80 K.
θD 1.04(1 + λ) exp 1.45 λ - µ*(1 + 0.62λ)
(5)
The parameter µ* is a pseudopotential of the effective electron repulsion and is taken to be 0.13 for transition metals. For all intercalation compounds listed in Table 1 we calculated a λ value around λ ) 0.7, which means that these materials are not really strong coupling superconductors. Whereas the variation of the coupling parameters of the intercalation compounds are not large, the value for the host is much lower, namely 0.45. The reason for this deviation could lie in the structural instability of the host lattice. The 9 Å MB+-TaS2 is the first intercalation compound for which a dependence of the superconducting transition on cooling rate and pressure is reported. The dependence on cooling rate could be due to a disorder-order phase transition at approximately 80 K. At this temperature it seems to be more likely that the methylene groups of the individual dye molecules order than that the whole methylene blue cations rearrange in the interlayer gap. Arguments for this interpretation are the observation that the slowly cooled sample has the higher Tc and that a disorder-order transition (of ethylene groups) in the organic superconductor κ-(BEDT-TTF)2Cu[N(CN)2]Br, also observed at 80 K, causes a comparable shift of the superconducting transition temperature of ∆Tc ) 1 K.14 Even more surprising is the effect of pumping on Tc. It could not be put down to the fact of pumping out additional intercalated water (methylene blue was intercalated out of an aqueous solution), because the influence of pressure is reversible in waterless helium atmosphere. As this effect is not immediate but takes 4 h, it is more likely to be a kinetic effect. 4.2. γ-Parameter. The most important result of the normal state specific heat data of the intercalation compounds is the fact that the γ-parameter is constant within a resolution of 8-10%, and even the empty host 2H-TaS2 shows nearly the same value. Thus, looking at such different compounds as the host with its structural instability and intercalation compounds
4870 J. Phys. Chem. B, Vol. 105, No. 21, 2001
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TABLE 2: Electronic Part of the Specific Heat of 2H-NbS2 and Its Intercalation Compounds Taken from Literature 2H-NbS2 (mpy)1/3NbS2 (en)1/3NbS2 (py)1/2NbS2 Cs1/2NbS2 K1/2NbS2
Tc [K]
γ [mJ/mol K2]
ref
6.53 6.10 3.01 2.45 4.1 3.95 3.24 3.14
18.9 17.64 9.07 8.71 9.48 11.6 4.9 5.4
21 12 12 12 12 21 21 21
having charge transfers from 0.06 to 0.33, there is no considerable variation in γ. In the case of the intercalation compounds, a constant γ is in conflict with the expectation from the rigid band model. This model is the simplest way to discuss the electronic normal state properties of intercalation compounds, because band structure calculations exist for none of these compounds. The starting point is the calculated band structure of 2H-TaS2 (see e.g. refs 11 and 4). For the intercalation compounds, these bands are kept rigid and the charge transfer is thought to fill up the conduction band. As the conduction band of 2H-TaS2 is filled beyond the maximum of the density of states, every further inserted electron should cause a decrease in the density of states at the Fermi level. This means that the γ-parameter should decrease with increasing charge transfer. A reasonable explanation for such a wide range of charge transfer, where γ is almost constant, is not easy to find. Perhaps there is a complex relation between charge transfer and a narrowing of the band due to an increased layer separation and sulfur-sulfur distance in the layer. Other normal state parameters, such as the magnetic susceptibility, the temperature dependence of the electrical conductivity, the Hall constant,24 the Seebeck coefficient,24 and Shubnikov-de Haas oscillations2 predict a two-band model for intercalation compounds. This assumption would make the system even more complex. Surprising is the observation that the host 2H-TaS2 has almost the same γ-value as its intercalation compounds. This may be due to a chance coincidence of two effects: namely the increase of the density of states at the Fermi level because of the suppression of the structural instability in the intercalation compounds and the decrease of the density of states as a consequence of the charge transfer. The influence of the structural instability on the density of states can be demonstrated by comparing the γ-value of 2H-NbS2 (no structural instability!), which is 17.64 mJ/(mol K2) with the electronic part of the specific heat of 2H-TaS2 (structural instability Ttrans ) 77 K), which is much smaller, even though these compounds are isostructural. The pure influence of the charge transfer on the electronic specific heat of intercalation compounds of 2H-NbS2 can be seen from Table 2. In these compounds an obvious decrease of γ with increasing charge transfer is observed. From the fact that the host lattice 2H-NbS2 has a higher γ-value and a higher Tc than 2H-TaS2, the conclusion was drawn that the lower Tc of 2H-TaS2 is a consequence of the lower γ due to the structural instability. But by comparing Tc and γ of 2H-TaS2 and its intercalation compounds, this conclusion is seen to be not totally correct. Even though there is no evidence that in intercalation compounds a structural distortion takes place, the γ is not changed by intercalation although Tc rises. But as noted above, the effective electronelectron coupling parameter λ is much smaller in the host, indicating a smaller electron-phonon interaction because of the structural distortion of the lattice.
Figure 5. (a) No correlation of Tc and Debye temperature θD can be seen. (b) Tc scales with the corrected Debye temperature θcorr D .
Figure 6. The Debye temperature depends on the layer separation d (a) and on the molar mass M (b) on the same exponent.
4.3. β-Parameter and Debye Temperature θD. In contrast to the γ-parameter, the phononic part of the specific heat is quite different in the intercalation compounds, even though a correlation between Tc and θD cannot be recognized (Figure 5a). We give the following reasons why we were tempted to look for such a correlation. (a) The γ-parameter is constant for all measured intercalation compounds. (b) No influence of the anisotropy of the crystals on Tc was found. (c) The effective electron-electron coupling constant λ is the same for all intercalation compounds; the only parameter left according to the McMillan formula (eq 5) is the Debye temperature. Of course, we are aware of the fact that the Debye temperature, measured at low temperatures, is only a crude approximation of the relevant energy scale of the phonon spectrum responsible for superconductivity. However, the superconductivity of the intercalation compounds takes place in the TaS2 planes, and these planes are not changed by intercalation, thus a relation between Tc and the Debye temperature is reasonable and if there are changes in the high-frequency branch of the phonon spectrum the low frequencies should be modified, too. Figure 6 shows the dependence of θD on the layer distance d and on the molar mass M of the intercalation compounds, respectively. (Molar mass of the intercalation compound is M ) MTaS2 + xMintercalate.) In contrast to the Debye temperature, Tc does not depend on these parameters. Na0.33(H2O)1.8TaS2 and K0.33(H2O)0.6TaS2, for example, have the same Tc ) 5.5 K and nearly the same molar mass, but the layer separation is different: d for the sodium intercalation compound is 11.8 Å and 9 Å for the potassium compound. La0.11(H2O)2.1TaS225 on the other hand, has also a Tc ) 5.4 K but a molar mass different from the two intercalation compounds mentioned above. θD shows the same functional dependence on layer distance d and molar mass M of the intercalate, as can be seen from Figure 6. Therefore, a factor that would describe the d and M dependence of θD should be a product of both parameters. In Figure 5b, Tc is plotted versus the Debye temperature corrected
Superconducting Transition Temperature of 2H-TaS2
J. Phys. Chem. B, Vol. 105, No. 21, 2001 4871
by a factor xMd/(M0d0). M0 and d0 are the molar mass and the layer distance of 2H-TaS2. The data points can be fitted by a straight line represented by the following equation:
Tc )
Cθcorr D
- T0
(6)
where C ) 0.065 ( 0.002 and T0 ) 10.3 K ( 0.3 K. Hence the phononic specific heat can be written as
Cph(T ) Tc + T0) ) β(Tc + T0)3 ) 1.1 × 1014(Md)3/2
J mol 3/2 (7) mol K kg ‚ m
(
)
The phononic specific heat at Tc + T0 is then proportional to the square root of the product of molar mass and layer distance. Following McMillans equation, the scaling can be written
Tc + T 0 )
(
θcorr 1.04(1 + λ) D exp 1.45 λ - µ*(1 + 0.62λ)
)
(8)
where λ ) 1.09. The theoretical background of this scaling behavior is not understood at present. 5. Conclusions We have measured the specific heat of two intercalation compounds with extreme charge transfer, K0.33TaS2 and 9 Å MB+-TaS2, from 1.7 to 9 K. We showed that the dye intercalation compound is sensitive to low pressure at room temperature and verified this with ac-susceptibility measurements. The cooling rate has also an influence on the superconducting transition temperature. This may be due to a phase transition in the intercalate layer. The jump in the specific heat of intercalation compounds is a further sign that these compounds are very anisotropic superconductors. The electronic part of the specific heat in the normal state of all intercalation compounds is independent of the charge transfer. This is in strong contradiction to a rigid band model. The intercalation compounds differ in the phononic part of the specific heat, but the calculated Debye temperature cannot be related to Tc. Scaling
between Tc and θD was found when the Debye temperature is corrected by a factor characterizing the intercalation. References and Notes (1) Bachmann, R. ReV. Sci. Instrum. 1972, 43, 205. (2) Biberacher, W.; Joss, W.; van Ruitenbeek, J. M.; Lerf, A. Phys. ReV. B 1989, 40, 115. (3) Biberacher, W.; Lerf, A.; Besenhard, J. O.; Mo¨hwald, H.; Butz, T.; Saibene, S. Il NuoVo Cim. 1983, 2D, 1706. (4) Blaha, P. J. Phys.: Condens. Matter 1991, 3, 9381. (5) DiSalvo, F. J.; Schwall, R.; Geballe, T. H.; Gamble, F. R.; Osiecki, J. H. Phys. ReV. Lett. 1971, 27, 310. (6) Einzel, D. Lecture notes summer semester 1998: UnconVentional SuperconductiVity, unpublished. (7) Friend, R. H.; Yoffe, A. D. AdV. Phys. 1987, 36, 1. (8) Gamble, F. R.; DiSalvo, F. J.; Klemm, R. A.; Geballe, T. H. Science 1970, 168, 568. (9) Gamble, F. R.; Osiecki, J. H.; Cais, M.; Pisharody, R.; DiSalvo, F. J.; Geballe, T. H. Science 1971, 174, 493. (10) Garoche, P.; Manuel, P.; Veyssie, J. J.; Molinie, P. J. Low Temp. Phys. 1978, 30, 323. (11) Guo, G. Y.; Liang, W. Y. J. Phys. C: Solid State Phys. 1987, 20, 4315. (12) Hamaue, Y.; Aoki, R. J. Phys. Soc. Japan 1986, 55, 1327. (13) Hauptmann, A.; Lerf, A.; Biberacher, W. Z. Naturforsch. B 1996, 51, 1571. (14) Kund, M. Reihe Physik: Uniaxiale Effekte in organischen und keramischen Supraleitern, vol 50; Verlag Harri Deutsch: Frankfurt am Main, 1995. (15) Lerf, A.; Sernetz, F.; Biberacher, W.; Scho¨llhorn, R. Mater. Res. Bull. 1979, 14, 797. (16) Lerf, A. Habilitation: Interkalationsreaktionen und ihre Nutzung zur chemischen Manipulation elektronischer Transporteigenschaften, Technical University Munich, 1991. (17) Lerf, A.; Biberacher, W. Condensed Systems of Low Dimensionality; Beeby, J. L., Bhattacharya, P. K., Gravelle, P. Ch., Koch, F., Lockwood, D. J., Eds.; Plenum Press: New York, 1991; p 709. (18) Onuki, Y.; Yamanaka, S.; Inada, R.; Kido, M.; Tanuma, S.-I. Synth. Met. 1983, 5, 245. (19) Schlicht, A.; Lerf, A.; Biberacher, W. Synth. Met. 1999, 102, 1483. (20) Schwall, R. E.; Stewart, G. R.; Geballe, T. H. J. Low Temp. Phys. 1976, 22, 557. (21) Schwenk, H. Diploma thesis, Technical University Munich, 1977. (22) Silbernagel, B. G. Solid State Commun. 1975, 17, 361. (23) Somoano, R. B.; Woolam, J. A. Intercalated Layered Materials; Reidel Publishing Company: Dodrecht, 1979; p 307. (24) Thompson, A. H.; Gamble, F. R.; Koehler, R. F., Jr. Phys. ReV. B 1972, 5, 2811. (25) von Wesendonk, C.; Biberacher, W.; Lerf, A. Solid State Comm. 1990, 74, 183. (26) Whangbo, M. H.; Canadell, E. J. Am. Chem. Soc. 1992, 114, 9578.
