PHYSICAL REVIEW B 85, 035125 (2012) Temperature dependence of structural and electronic properties of the spin-liquid candidate κ-(BEDT-TTF)2Cu2(CN)3 Harald O. Jeschke,1 Mariano de Souza,2,* Roser Valentı́,1 Rudra Sekhar Manna,2 Michael Lang,2 and John A. Schlueter3 1Institut für Theoretische Physik, Goethe-Universität Frankfurt am Main, D-60438 Frankfurt am Main, Germany 2Physikalisches Institut, Goethe-Universität Frankfurt am Main, D-60438 Frankfurt am Main, Germany 3Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA (Received 21 November 2011; revised manuscript received 10 January 2012; published 27 January 2012) We investigate the effect that the temperature dependence of the crystal structure of a two-dimensional organic charge-transfer salt has on the low-energy Hamiltonian representation of the electronic structure. For that, we determine the crystal structure of κ-(BEDT-TTF)2Cu2(CN)3 for a series of temperatures between T = 5 and 300 K by single crystal X-ray diffraction and analyze the evolution of the electronic structure with temperature by using density functional theory and tight binding methods. We find a considerable temperature dependence of the corresponding triangular lattice Hubbard Hamiltonian parameters. We conclude that even in the absence of a change of symmetry, the temperature dependence of quantities like frustration and interaction strength can be significant and should be taken into account. DOI: 10.1103/PhysRevB.85.035125 PACS number(s): 61.05.cp, 61.66.Hq, 75.10.Jm, 71.15.Mb I. INTRODUCTION The two-dimensional organic charge-transfer salts based on bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF or even shorter ET) molecules in a κ-type lattice arrangement have been intensively studied over the past 30 years due to their complex interplay between electron correlation and the effects of low dimensionality and spin frustration.1 In particular, the discovery of spin-liquid behavior in κ-(BEDT- TTF)2Cu2(CN)3 (Ref. 2) has fascinated experimentalists and theorists alike. Issues of current interest concern the nature of the low-temperature spin-liquid realized in this material3–5 and the various anomalies observed upon approaching the spin-liquid state from high temperatures. These anomalies include drastic changes in the 1H-NMR relaxation rate around 200 to 150 K (Ref. 6), the thermopower at 150 K (Ref. 7), relaxor-type ferroelectricity around 60 K (Ref. 8), and a mysterious phase-transition anomaly at 6 K (Ref. 9). The latter feature, which manifests itself in anomalies in thermodynamic2,3 and transport4 quantities, is accompanied by pronounced lattice effects.9 Various scenarios have been suggested for the 6 K anomaly including a crossover from a thermally to a quantum disordered state,3 an instabil- ity of the quantum spin-liquid,3,10–16 or a distinct type of charge ordering.17 Theoretically, the spin-liquid properties have been investigated on the basis of the anisotropic triangular-lattice Hubbard Hamiltonian.12,18–21 The parame- ters t , t ′, and U of this Hamiltonian have been determined with semiempirical7 as well as first principles methods22,23 based on the experimental structure at room temperature. Missing in such investigations is, however, the consider- ation of a possible temperature dependence of the model parameters. In this work, we find by a combination of single crystal X-ray diffraction at various temperatures and density func- tional theory calculations that even in the absence of structural phase transitions, the temperature dependence of the structural parameters is significant enough to influence the electronic behavior and the determination of the Hamiltonian model parameters in κ-(BEDT-TTF)2Cu2(CN)3. We suggest that this has subtle effects on the degree of frustration and interaction strength. In 1991, the crystal structure of κ-(BEDT-TTF)2Cu2(CN)3 was reported,24 and the unit cell parameters confirmed,25 on twinned crystals at room temperature. The crystal structure was redetermined in 1993, also on a twinned crystal at room temperature.26 The crystal structure of the very similar κ ′- (BEDT-TTF)2Cu2(CN)3 structure, which is reported to be an ambient pressure superconductor, was described in 1992.27,28 The crystal structure of the κ phase was subsequently redeter- mined in 1997,29 and the unit cell redetermined in 2001, both at room temperature.30 Already in 1991, the unit cell parameters were reported at 300 and 30 K, with a(30 K)/a(300 K) = 0.9964, b(30 K)/b(300 K) = 0.9932, c(30 K)/c(300 K) = 0.9900, and β(30 K)/β(300 K) = 1.0146 (Ref. 31). Our comparable con- traction values between 300 and 20 K are a(20 K)/a(300 K) = 0.9988, b(20 K)/b(300 K) = 0.9958, c(20 K)/c(300 K) = 0.9905, and β(20 K)/β(300 K) = 1.0148 and agree well with the previous results. In addition, we find evidence for an ordering of the ethylene groups in a staggered conformation between 200 and 150 K. Despite the current interest in this material as a spin-liquid candidate, no low-temperature structural determinations have yet been reported. Herein, we present a detailed characterization of the crystal structure as function of temperature determined on a single crystal with very high agreement factors. II. SINGLE CRYSTAL X-ray DIFFRACTION A black, platelike crystal of κ-(BEDT-TTF)2Cu2(CN)3 with dimensions 0.4 × 0.4 × 0.4 mm3 was placed onto the tip of a glass fiber and mounted on a Bruker APEX II three-circle diffractometer equipped with an APEX II detector. Temperature control in the 100–300 K region was provided by an Oxford Cryostream 700 Plus Cooler, while below 100 K it was provided by a Cryocool-LHE cryogenic system (Cryo Industries of America). The sample temperature below 100 K was confirmed by installing a Cernox thermometer (Lakeshore) in the immediate vicinity of the crystal and 035125-11098-0121/2012/85(3)/035125(7) ©2012 American Physical Society http://dx.doi.org/10.1103/PhysRevB.85.035125 HARALD O. JESCHKE et al. PHYSICAL REVIEW B 85, 035125 (2012) FIG. 1. (Color online) Structure of κ-(BEDT-TTF)2Cu2(CN)3 at T = 5 K. Note that the disordered CN− group in the inversion center is only shown in one conformation. stabilizing the temperature immediately prior to data collec- tion. In order to reduce adverse thermal effects, the thermome- ter wires (twisted manganin wires, 0.5-mm diameter, supplied by Lakeshore) were anchored on the surfaces of the cryostat exposed to the 4He stream. The data were collected using MoKα radiation (λ = 0.71073 Å) with a detector distance of 50 mm. Unit cell parameters were determined upon cooling in 10 K increments between 100 and 290 K, with a frame exposure time of 10 s. Full data sets for structural analysis were collected at temperatures of 5, 20, 100, 150, 200, 250, and 300 K. The uncertainties in the temperature determination are typically ±0.2 K down to 100 K, while for the 20 and 5 K data points, an error bar of ±1 K has to be accepted. These data collections nominally covered over a hemisphere of reciprocal space by a combination of three sets of exposures. Data to a resolution of 0.68 Å were considered in the reduction. The raw intensity data were corrected for absorption [SADABS (Ref. 32)]. The structure was solved and refined using SHELXTL (Ref. 33). A direct-method solution was calculated, which pro- vided most of atomic positions from the electron-density map. Full-matrix–least-squares/difference-Fourier-cycles were per- formed, which located the remaining atoms. All nonhydrogen atoms were refined with anisotropic displacement parameters. The hydrogen atoms were placed in ideal positions and refined as riding atoms with relative isotropic displacement parameters. As a representative example, in Fig. 1 we show the structure of κ-(BEDT-TTF)2Cu2(CN)3 at a temperature of T = 5 K. In the bc plane, the BEDT-TTF molecules form their typical κ-type arrangement. One of the cyanide (CN−) groups resides on an inversion center, thus requiring it to be disordered with a 50% carbon and 50% nitrogen distribution on these two atomic positions.24 Analysis of the low-temperature structural data (see Table I) indicates that overall, a, b, and c axes decrease with temperature, while the β angle increases monotonically upon cooling. We find that the orthogonal projection of the a axis, a⊥ = a sin β, has the greatest relative contraction with temperature. One ethylene group is disordered at room temperature with a staggered conformation 77% of the time. As the temperature is lowered, the ethylene group remains partially disordered down to a temperature of 200 K and is fully ordered in a staggered conformation at 150 K. The anion layer becomes slightly more buckled at low temperature: at room temperature, the Cu1 atom lies 0.050 Å out of the TABLE I. Crystal data and structure refinement of κ-(BEDT-TTF)2Cu2(CN)3. Formula = C23H16Cu2N3S16, formula weight MW = 974.43, monoclinic, wavelength λ = 0.71073 Å, effective number of electrons in the crystal unit cell contributing to F(000) = 978, space group P 21/c, Z = 2. Residual factor for the reflections R1 = ∑ ||Fo| − |Fc||/ ∑ |Fo|, weighted residual factors wR2 = [ ∑ w(F 2 o − F 2 c )2/ ∑ w(F 2 o )2] 1 2 , I > 2σ (I ), least-squares goodness-of-fit parameter GoF = [ ∑ w(F 2 o − F 2 c )2/(Nd − Np)] 1 2 . Staggered (%) is the percentage of ethylene groups that are in the staggered conformation. Note that in eclipsed and staggered conformations, the two ethylene end groups have the same or opposite twist angle with respect to the plane of the molecule, respectively. dCu−NNC (Å) is the distance that the Cu(I) ion is out of the plane defined by the coordinated N, N, and C atoms. The ET tilt angle ϑ is measured against the bc plane. dintradimer is the orthogonal distance between BEDT-TTF dimers. 300 K 250 K 200 K 150 K 100 K 20 K 5 K a (Å) 16.0919(3) 16.0848(3) 16.0781(3) 16.0703(3) 16.0746(6) 16.072(4) 16.062(3) b (Å) 8.5722(2) 8.5749(1) 8.5737(1) 8.5664(2) 8.5593(3) 8.536(2) 8.544(2) c (Å) 13.3889(2) 13.3373(2) 13.2964(2) 13.2698(3) 13.2678(5) 13.262(3) 13.271(2) β (◦) 113.406(1) 113.853(1) 114.273(1) 114.609(1) 114.852(1) 115.088(3) 115.093(2) V (Å3) 1694.93(6) 1682.43(4) 1670.86(4) 1660.72(6) 1656.51(1) 1647.8(6) 1649.3(5) ρ (g/cm−3) 1.909 1.923 1.937 1.949 1.954 1.964 1.962 μ (mm−1) 2.266 2.283 2.299 2.313 2.319 2.331 2.329 GoF 1.057 1.053 1.091 1.157 1.293 1.261 1.109 R 0.0311 0.0269 0.0238 0.0225 0.0220 0.0182 0.0204 Rw 0.0838 0.0735 0.0654 0.0627 0.0629 0.0503 0.0515 staggered (%) 77 86 93 100 100 100 100 dCu−NNC (Å) 0.050 0.056 0.064 0.069 0.073 0.072 0.072 ET tilt angle ϑ 66.55 66.25 66.00 65.79 65.64 65.53 65.52 dintradimer 3.558 3.538 3.518 3.500 3.488 3.470 3.473 035125-2 TEMPERATURE DEPENDENCE OF STRUCTURAL AND . . . PHYSICAL REVIEW B 85, 035125 (2012) C11-C12-N12 plane, increasing to 0.072 Å at low temperature. For the purpose of performing density functional theory calculations, the original symmetry of P 21/c has been lowered to P 21 by choosing one of two possible orientations of the CN− group in the inversion center. III. TEMPERATURE-DEPENDENT STRUCTURAL PARAMETERS In Fig. 2, we show the evolution of the lattice parameters with temperature. Over the large investigated temperature range from T = 300 down to T = 5 K, the volume is monotonously decreasing with temperature [see Fig. 2(a)]. The monoclinic angle β between a and c lattice vectors [see Fig. 2(b)] first rapidly increases upon cooling down to a temperature of T = 200 K, below which it increases more gradually. In Fig. 2(c), the lattice parameters are displayed as symbols, normalized by their values at T = 20 K (see Table I). We also include the relative b and c lattice constants along the two principal axes as obtained by thermal expansion 1660 1680 1700 V (Å3) (a) 113.5 114 114.5 115 β (°) (b) 1 1.01 0 100 200 300T (K) re la tiv e la tti ce p ar am et er s X−ray | |a−/a− 20K b/b20K c/c20K 1 1.01 0 100 200 300T (K) re la tiv e la tti ce p ar am et er s (c) Δx/x | | FIG. 2. (Color online) Structural parameters of κ-(BEDT- TTF)2Cu2(CN)3 between T = 5 and T = 300 K. (a) and (b) show the volume and monoclinic angle, respectively. In (c) relative lattice parameters are given with the T = 20 K structure as the reference. a⊥ = a sin β. Symbols refer to the new data from X-ray diffraction (this work), while lines are measured thermal expansion data from Ref. 9. The experimental error bar is comparable to the size of the symbols. measurements in Refs. 9 and 34. The out-of-plane expansivity data shown there were taken in a direction perpendicular to the bc plane. They are shown together with the corre- sponding quantity from the X-ray diffraction measurement, a⊥ = a sin β. IV. TEMPERATURE-DEPENDENT ELECTRONIC STRUCTURE In the following, we determine the electronic properties for the resolved crystal structures at different temperatures by em- ploying the all-electron full-potential local orbitals (FPLO)35 basis. We perform all calculations on a (6 × 6 × 6) k mesh with a generalized gradient approximation functional.36 In Fig. 3 we present the electronic band structures for the various crystal structures. In the calculation, we used the staggered (majority) conformation of the BEDT-TTF molecules at all temperatures. The changes as function of temperature for the two bands at the Fermi level, corresponding to the antibonding combinations of the BEDT-TTF highest occupied molecular orbital (HOMO) levels, are relatively small. On the other hand, the occupied bands down to −0.7 eV below the Fermi level show a significant dependence on temperature. These bands derive from the bonding combination of BEDT-TTF HOMO levels and from the [Cu2(CN)3]− anion layer. Overall, these bands show a bandwidth that decreases with increasing temperature. This can be explained by the volume increase as function of temperature [see Fig. 2(a)]. Further analysis of the electronic structure requires a reliable identification of the bands deriving from the BEDT- TTF molecules. For that purpose, band weights have been calculated for all structures and added up for all atoms corresponding to the BEDT-TTF cation layers and to the [Cu2(CN)3]− anion layers, respectively. In Fig. 4, blue circles and orange triangles stand for a predominance of the BEDT- TTF weight and [Cu2(CN)3]− weight, respectively. This identification allows us to fit the BEDT-TTF derived bands to a tight binding (TB) Hamiltonian HTB = ∑ ij,σ ti−j (c†iσ cjσ + H.c.), (1) where c † iσ (ciσ ) create (annihilate) an electron with spin σ at site i; the sites correspond to the positions of the BEDT-TTF molecules, shown as balls in Fig. 5. While a good overall fit of the band structure can be achieved by including six neighbor BEDT-TTF molecule distances up to d = 9.4 Å, a very good fit describing also the small dispersion along the B– direction, as shown by lines in Fig. 4, requires fourteen neighbor distances up to d = 14.5 Å. We now proceed to analyze the temperature dependence of the tight binding parameters corresponding to the network of BEDT-TTF dimers that are highlighted in Fig. 5. These dimers form a triangular lattice, with the hopping parameter t ′ connecting dimers to chains along the b direction and the hopping parameter t forming the 2D connections in c direction. We are interested in estimating the parameters of 035125-3 HARALD O. JESCHKE et al. PHYSICAL REVIEW B 85, 035125 (2012) −0.6 −0.4 −0.2 0 0.2 C Y Γ Z C Γ en er gy ( eV ) 5 K 20 K 100 K 150 K 200 K 250 K 300 K FIG. 3. (Color online) Band structures of κ-(BEDT-TTF)2Cu2(CN)3 from T = 5 to T = 300 K. the Hubbard Hamiltonian for the anisotropic triangular lattice H = ∑ 〈ij〉,σ t(c†iσ cjσ + H.c.) + ∑ [ij ],σ t ′(c†iσ cjσ + H.c.) +U ∑ i ( ni↑ − 1 2 )( ni↓ − 1 2 ) , (2) where 〈ij 〉 and [ij ] indicate summations over nearest and next- nearest neighbors, respectively. t and t ′ can be obtained from the molecular overlap integrals t2 to t4 by considering the geometrical formulas t ≈ t2 + t4 2 , t ′ ≈ t3 2 . (3) −0.6 −0.4 −0.2 0 0.2 C Y Γ Z C Γ A B Γ D E Γ en er gy ( eV ) FIG. 4. (Color online) Band structure of κ-(BEDT- TTF)2Cu2(CN)3 at T = 20 K. Blue circles and orange triangles indicate bands with a majority of BEDT-TTF and [Cu2(CN)3]− character, respectively. The TB fit is shown with lines. For the definition of the overlap integrals tn = ti−j , see Ref. 22. Note that inclusion of longer-range hopping into these formulas (for example, including t5 into t ′) has no influence on the results reported in the following. V. DISCUSSION Figure 6 summarizes our findings from the tight binding analysis. The nearest-neighbor hopping parameters t , forming a square lattice, increase upon cooling down to a temperature of T = 200 K, then decrease again [see Fig. 6(a)]. The frustrating hopping parameters t ′ show the opposite behavior FIG. 5. (Color online) Network formed by the BEDT-TTF molecules in the bc plane of κ-(BEDT-TTF)2Cu2(CN)3. Each gray ball represents the center of gravity of a BEDT-TTF molecule, with gray bonds indicating the intermolecular distances that were taken into account for the tight binding fit. BEDT-TTF dimers are highlighted by ellipses, and the paths forming the triangular lattice paths are shown with bold lines. The unit cell is marked as a rectangle. 035125-4 TEMPERATURE DEPENDENCE OF STRUCTURAL AND . . . PHYSICAL REVIEW B 85, 035125 (2012) 49.5 50 50.5 40 41 42 t (meV) t’ (meV) (a) 0.8 0.82 0.84 0.86 t’/t (b) frustration 340 350 360 U (meV) 2t1 ≈ U (c) 6.8 7 7.2 0 100 200 300T (K) U/t (d) interaction FIG. 6. (Color online) Temperature dependence of Hamiltonian parameters of κ-(BEDT-TTF)2Cu2(CN)3. as a function of temperature, decreasing upon cooling down to a temperature of T = 150 K, then increasing. Interestingly, these two effects enhance each other when we consider their ratio t ′/t as shown in Fig. 6(b). t ′/t , which quantifies the degree of frustration in the system, decreases from t ′/t = 0.82 at T = 300 K to t ′/t = 0.80 at T = 150 K, then increases to a maximum value of t ′/t = 0.86 at T = 5 K. A rough estimate for the Coulomb interaction strength U can also be extracted from the dimer approximation U ≈ 2t1, where t1 is the BEDT-TTF intradimer hopping integral [see Fig. 6(c)]. We find that the measure of the interaction strength U/t estimated in this way monotonously falls by 7% as the temperature is increased from T = 5 to T = 300 K. In order to rationalize the observed temperature dependence of the Hamiltonian parameters in (2), we analyze the crystal structure in more detail. For that purpose, we determined the orientation of the BEDT-TTF molecules in space by finding the plane of the TTF part of the molecule and measuring its angle with respect to the bc plane, cf. inset of Fig. 7. This yields the inclination of the BEDT-TTF molecules against the anion layer shown as squares in Fig. 7 and the intradimer distance shown as circles (see also Table I). Both quantities show a nearly monotonous increase over the studied temper- ature range. The decreasing intradimer distance explains the increase of the intradimer hopping integral t1 with decreasing temperature. Apparently, the nonmonotonous evolution of the overlap integrals t , t ′, especially the distinct extrema in both quantities around 150 to 200 K, has to be of a different origin. FIG. 7. (Color online) (a) Orientation ϑ and dimerization d of BEDT-TTF molecules as a function of temperature. The inset illustrates how ϑ and d are measured. (b) Ratio c/b between c and b lattice vectors as a function of temperature. The overall trend can be understood by considering the temperature dependence of the lattice parameters; from Fig. 5 it is clear that changes in the b lattice parameter should have an impact on t ′, while changes in c should affect t . In Fig. 7(b), we see that the c/b lattice parameter ratio decreases with temperature down to T = 150 K, then increases with falling FIG. 8. (Color online) The Cu1 coordination sphere at 5 K. The Cu1 is 0.072 Å out of the plane defined by N12, C11, and C12. Thermal ellipsoids are drawn at the 50% probability level. 035125-5 HARALD O. JESCHKE et al. PHYSICAL REVIEW B 85, 035125 (2012) 0.97 0.98 0.99 1 1.01 100 150 200 250 300 re la tiv e la tti ce p ar am et er x /x (2 90 K ) T (K) a b c β V a b c β V FIG. 9. (Color online) Plot of the unit cell parameters as a function of temperature between 100 and 290 K. temperature until T = 20 K. This has an immediate impact on the degree of frustration t ′/t as it should be approximately proportional to the c/b ratio. Indeed, a comparison of Figs. 6(b) and 7(b) confirms this expectation, and thus explains the nonmonotonous temperature dependence of the frustation. An increasing frustration upon cooling, reaching t ′/t values at low temperatures in excess of those at room temperature, is an interesting finding which may help us to better understand the intriguing low-temperature magnetic and dielectric prop- erties of this material. Here we mention the distinct types of charge ordering, accompanied by dielectric anomalies, proposed in Ref. 17 for the present material as a result of an increasing degree of frustration. The nonmonotonous evolution of the in-plane distortion c/b, which adopts a minimum around 150 K, might be related to the ordering of the ethylene groups, uncovered in the present study.37 According to our structural analysis, the fraction of ethylene groups, ordered in the staggered conformation, gradually grows from 77% at room temperature to over 86% at 250 to 93% at 200 K. For temperatures below 150 K, the ordering is complete within the accuracy of our analysis/refinement. The large step size of 50 K employed in this study does not allow us to determine the ordering temperature more precisely. Likewise, we cannot say whether or not the ordering occurs continuously or sets in abruptly. An argument in favour of the latter possibility might be derived from a small steplike feature revealed in thermal expansion measurements around 150 K, see the out-of plane data shown in Fig. 1 of Ref. 9. We stress that a fully ordered staggered ethylene conformation below 150 K and a progressively disordered state above 200 K is fully consistent with the anomalous behavior revealed by 1H-NMR measurements be- tween 150 and 200 K (Ref. 6). The strong increase in (T1T )−1 above 200 K was attributed to thermally activated vibrations of ethylene groups.6 We suggest that the nonmonotonous temperature dependence in t ′/t might also be related to the drastic change in the thermopower around 150 K (Ref. 7). The thermopower is related to the energy derivative of the density of states at the Fermi level.38 However, for a strongly correlated system like κ-(BEDT-TTF)2Cu2(CN)3, density functional theory is not sufficient for the calculation of this quantity and more elaborate many-body calculations—which are beyond the scope of the present study—have to be done. In summary, we performed an analysis of the temperature dependence of the structural and electronic properties of κ-(BEDT-TTF)2Cu2(CN)3 by considering a combination of X-ray diffraction at various temperatures and density func- tional calculations. Our study shows that the temperature de- pendence of the structural parameters has significant influence on the electronic properties and results in a nonmonotonous behavior of the degree of frustration. Of special relevance is the increase of frustration at low temperatures in comparison to the behavior at room temperature. ACKNOWLEDGMENTS This work was supported by UChicago Argonne, LLC, Op- erator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. We also acknowledge support by the Deutsche Forschungsgemein- schaft (SFB/TR 49) and by the Helmholtz Association through HA216/EMMI. APPENDIX: ADDITIONAL CRYSTALLOGRAPHIC MATERIAL Crystallographic data for the κ-(BEDT-TTF)2Cu2(CN)3 structure at 5, 10, 100, 150, 200, 250, and 300 K has been deposited with the Cambridge Crystallographic Data Centre as supplementary publication Nos. CCDC 850022 to TABLE II. Unit cell parameters as a function of temperature in the temperature range from 290 down to 100 K. T (K) a (Å) b (Å) c (Å) β (◦) V (Å3) 290 16.248 8.655 13.516 113.56 1742 280 16.231 8.650 13.491 113.62 1735 270 16.235 8.647 13.483 113.79 1732 260 16.226 8.652 13.475 113.80 1731 250 16.227 8.652 13.463 113.90 1728 240 16.237 8.656 13.463 113.97 1729 230 16.234 8.657 13.453 114.04 1727 220 16.214 8.646 13.426 114.16 1717 210 16.207 8.639 13.414 114.26 1712 200 16.203 8.640 13.407 114.31 1710 190 16.205 8.639 13.399 114.42 1708 180 16.222 8.650 13.413 114.47 1713 170 16.200 8.640 13.397 114.56 1707 160 16.199 8.636 13.388 114.63 1703 150 16.183 8.627 13.372 114.70 1696 140 16.194 8.628 13.378 114.76 1697 130 16.165 8.611 13.348 114.82 1686 120 16.185 8.621 13.366 114.88 1692 110 16.187 8.621 13.367 114.90 1692 100 16.179 8.616 13.361 114.96 1689 035125-6 TEMPERATURE DEPENDENCE OF STRUCTURAL AND . . . PHYSICAL REVIEW B 85, 035125 (2012) 850028. 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