Low temperature specific heat of the spin-density-wave compound (TMTSF)2PF6

Solid State Communications,

Vol. 91, No. 7. pp. 523-527, 1994 Elrvier Science Ltd Printed in Great Britain 0038-1098(94)$7.00+.00

0038- IOY8(Y4)00401-3 LOW TEMPERATURE

SPECIFIC HEAT

OF THE SPIN-DENSITY-WAVE J. Odin*, J.C. Lasjauniasl,

COMPOUND

K. Biljakovipl2,

P. Monceaul

‘Centre de Recherches sur les Tres Basses Tern eratures, 8 , France Fourier, C.N.RS., BP 166,38042 Grenoble-Cedex &tstitute

of Physics of the University,

tT-MTSFl2PF6 and K Bechgaard3

laboratoire

associe a I’UniversitC

Joseph

41001 Zagreb, P.O. Box 304, Croatia

3Dept. of General and Organic Chemistry, (Received

H.C. CErsted Institute, 5 Efiy

DK-2100 Copenhagen,

Denmark

1994, 6y P. Burlet)

We re ort on specific heat measurements of the SDW compound (TMTS&PF6 between 2 and 25 K performed by two different techni ues. We discuss the two successive transiiions which occur in this T-range : 9, t e SDW ordering transition at T = 12.1 K, and a lass transition around 3-3.5 K. The latter is very dependent on the kinetics o7 measurements, and has all characteristic features of freezing of supercooled liquids.

the slowing down behaviour of the dielectric constant. Taking into account these new features, we re ort and discuss the specific heat C of (TMT!!F)zPFb in a wider T-range (2 K < T < 25 K) which now includes the SDW ordering transition tern rature (TSDW = 12.1 K). (kTSF)2PF6 is a uasi 1D metallic compound (Bechgaard salt) whit*9, undergoes a SDW metalinsulator transition at T8Bw. Instead of a stabilization of the insulating state by a honon softening, like in the Peierls transition of e DW compounds, the electronic ground state corresponds to an antiferroma netic order. It is characterized b a modulation o B the spin density with the 2kF SD W wave vector component and without modification of the underlying Iattice.ll

1. Introduction Density-wave (DW) s stems-includin both charge-density wave (E DW) and spin- %ensity wave (SDW)-exhibit glassy behaviour over a wide temperature ran e and in very different energy-time windows. B-3 The disorder in the DW ground state is due to the randomly distributed impurities or defects which pin the DW phase. Low-temperature thermodynamical pro erties of CDWs and, more recently investigated BDWs, are very sensitive to this disordered character. They are, almost systematically, characterized by two typical features : (i) additional excitations to regular honons which contribute to the s cific heat C Lr T below 0.5 K 4 reminiscent of $ow-energy ex$itations in glasses: and (ii) slow, non-exponential heat relaxation, with “aging” effects,8 which rove the non-linearity of the specific heat in this ! -range. These two properties have been observed in the SDW model corn ound (TMTSF)ZPF~.~,~ Up to now, it was dl.P.flcult to connect the “high” temperature behaviour, which is satisfactorily described bv theories of elastic deformation of the pinned CDW,2 with the very low-T (c 1 K) relaxational behaviour. But recently, a strong temperature and frequency dependence of the real part of the dielectric function, interpreted as a critical slowing down of the mean ielaxation time, has been demonstrated successivelv in the CDW state of TaS3 7 and in the SDW state of (TMTSF)~l’F~,W with characteristic temperatures of 13 K and 2.3 K respectively. On the other hand, a jump in the phonon specific heat of (TMTSF)zPFh was detected around 3-3.5 K,6 which was initially ascribed to a SDW sub-phase transition. Subsequent systematic investigations of this anomaly have pointed out the crucial role of the kinetics of measurements and of the previous thermal history in the variation of the specific heat. These facts have enabled us to establish the similarity between this transition and the usual glass transition in su ercooled liquids.Y,l” This interpretation was rein farced by

2. Experimental We used two different techniques : (a) A unsi ndinbatic (Q.A.) technique between 2.5 and 22 K in a He4 cryostat. The sample in form of a lot of small needles (408 mg) was embedded in a resin and thereafter placed in the s’lver ‘R”“;y sample 01 er. After cooling down to the lowest temperature, the sample was isolated from the thermal bath and heated adiabatically step by step. Each heating process (by about 3 “/u of T) was used to measure the heat capacity. Duration of heating was about 100 s and total data acquisition including the new thermal e uilibrium- was about 45 mm. In the T-range of 3-‘5 K, the heating rate was -1.3 K/h. (b) A tmnsient he& pulse technique between 2 and 7 K. We used a similar arrangement as in our previous experiment in the same cryostat,6 with a sample (110 mg) originating from a new batch. The samole was looselv connected to the heat sink bv a therinal link. Temberature of the sink was regilated step by step (either by cooling or heating) corres onding to relative variations of temperature of s to 5 ‘%,. Heating (or coolin ) rate was about 0.5 K/h between 2 and 4.5 K an % duration of heat 523

524

LOW TEMPERATURE SPECIFIC HEAT

pulses between 0.5 and 1 s. Thermal transienms,$ res onse to heat pulses were always ex .tK time constant varying from 12 s at p” =2Kto . 8wdsat T = 5 K. In both techniques, heat capacity of addenda was determined by another experiment (in particular the silver epoxy-resin in experiment (a) [ref. 121) and then subtracted. In the Q.A. ex eriment (a), the ratio of heat capacity of the adden 1 a to the total heat capacity varied between 47 “/o at T = 2 K and 57 7d at T = 25 K, and in experiment (b), this ratio varied between 39 YUat 2 K and 33 X at 6 K. With technique (b), the experiment was performed down to 150 mK and results are in good agreement with the previous experiment, but analysis and discussion in the T-range below 2 K are out of scope of the present report. In comparison to our previous measurements performed on 150 mg of material,6 the present specific heat data are reduced by 4-5 ‘Y,,in the T-range 2-7 K, corres onding to a change of total heat capacity of - 3 ‘%. his can be partly accounted for by the uncertainty on the sample mass.

Vol. .91, No,. 7

med in the vicinity of the glass transition (T8). It is also known for glasses that the temperature of the jump is sensitive to the frequency of the measurement. Specific heat spectroscopy has shown that the anomaly occurs at lower temperature when the frequency decreases.‘3 The Q.A. techni ue is per definition characterized by the absence o? relaxation of the temperature of the sam le after the energy input. B comparison, in t Re transient technique, first, t Ke duration of energy input (heat pulse) is about lo2 times shorter, and, second, there is a relaxation of temperature towards its initial value after each heat ulse with a time constant of several tens secon dps. In that sense the latter techni ue, despite its moderate frequency (10-l to 10-&z), is . more similar to an a.c. one, compared to the d.c. adiabatic technique. This can explain the absence of CP jump down to 2.5 K in the Q.A. measurements. rees of freedom, vibrational

f.

3. Results Data obtained with the two different techni ues . are reoorted in Fin. 1. The first obvious resu 9 t IS

CPe obeys a cubic law like the vibrational specific heat. In comparison to usual glass forming systems, where T, occurs at several lo2 K, here T. appears at very low T, in the liquid helium ?hrange. In this re ion, C is dominated by the lattice specific heat (- l#3) an 8 the transition appears as a jump in a C/T3 diagram ; whereas in usual glass

f

20 ;

E ?3

-at 7; 20 E 2 e 15 2 ;

o

(TMTSF),FfS

18

16

14

10

2

3

4

5

6

7 T (to

0

5

10

15

20

25

30 r (K)

Fig. 1 : Total specific heat of (TMTSF)zPFh, from 2 to 25 K, reported as C,/T3. Symbols (0) indicate technique. data obtained with the uasi-adiabatic heat-pulse Symbols (A) correspon 8 to transient techni ue, with the lump at T = 3.4 K which indicates t1 e glass transition. The two frames refer to Figures 2 and 3.

Fig. 2 : Total specific heat in a C,/T3 diagram obtained in ver different kinetic conditions : Data technique (e) are obtaine d with the quasi-adiabatic as in Fi 1 and correspond to the equilibrium state. Ot8’er data are obtained with the transient heat pulse technique. (A) corres ond to regular at a rate of 0. s K/h (reversible heating or coolin 4 .9 and 4.5 K, for unannealed cycle) between sample, as in Fig. 1. (+) indicate the cooling cycle from 4.5 K for the sample in a high1 relaxed state obtained after a long stabilisation at $= 2.77 K.

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LOW TEMPERATURE SPECIFIC HEAT

forming systems, the jump occurs in a re ion where the lattice C, saturates into Dulong- b etit limit. In Fig. 2 are reported data for two different runs with the transient technique, which correspond to two different thermal histories, or degrees of annealing, of the system. Whereas the triangles correspo?ld to the initial “unannealed” state,-for described, which the jump at T = 3.4 K is reversibl the crosses correspond to the cooling o r the system of in a hi hly relaxed state (after a stabilization 40hat H = 2.77 K. the samole has been reheated LID to 4.5 K and thereafter c&led down). In the inteE pretation with the glass transition, the relaxed s stem can follow the equilibrium curve down to #= 3.0 K (note the excellent agreement with the Q.A. experiment), and then falls out of equilibrium. In the Q.A. conditions, the equilibrium state is followed down to 2.5 K. 4. Discussion roperNow, we intend to discuss these uoted ties of the SDW phase of (TMTSF)z 9 F6 witX*in the eneral framework of the lass transition. At the we have to outel.me the very unusual SDW glassy phase as it concerns the collective electronic modes in a system essentially characterized by the properties of the Fermi surface.

a) CLss

From the temperature dependence of the dielectric relaxation71n,ive can obtain information about the of SDW glass. Indeed, the class of universalit resistance towards t b e changes Induced by tempeives the insight into the “fragility” of the rature glass. Hhe most rapid changes of the relaxation time T in the transition range characterize the

stren vth” of the s stem. For a stron glass as SiO2 D - 180, and for tyragile ones D - 3 fief. 141. In the case of (TMTSF)2PF6,8 - 1.1 [ref. 141. As for (TM%F)zPFh this ratio IS ‘ilbout 1.25-1.28, and is consistent with more fragile character obtained from dynamics. Finally, due to the lack of information about the microscopic nature of entities liquid, which corres onds here to a glass-forming drawn we have to 1 e cautious with conclusions from a classification established for well defined atomic structures.

525

b)w: The conceot o correlation length scale t and its possible drvergence at the Vogel temperature T is

a central question for the glass transition. 15,16*n fact, diverging len th scales have never been observed in glassesltand an arrest for the growing of 5 occurs on cooling well above Tc ; in the dynamic scaling analysis,*5 it happens at a temperature where a cross-over occurs for the parameter zv from a “fragile” value towards a “strong” values (zv - 15-20 or =). In the approach by the concept, originally *pro ose;! by copc$zdit & ibbsl7 to interprete the rePaxational behaviour of glass-forming liquids, the correlation length SC has a different meaning, other than the correlation length for phase transition.ls From the standpoint of a fluctuation theorv for the dvnamic glass- transitionls, it characterizes a region in which molecular motions in suoercooled liauids are cooperatively correlated thrdugh some temporary structure. kc decreases for increasing temperatures and at some temperature the cooperativity volume becomes too small to define coo erativity at all. At Tc, cc is of the order of 1-2 nm. ‘Isa From the specific”heat jump at Tg (Fig. 2), the degree of coooerativitv N, can be calculated usine the formula Na 2 R d’C (T/CZiT)z [ref. 18~1 whsh is adapted from Eq. 1 of ref. 18a, with R the universal as constant, AC the step height of C at T = T* C = 8 P (T,$ and 28T the width of the {ass transition. s r stem (T = +8 = 3.4 K, 6T < For the unannealed 0.2 K, AC = 10-I J/ma .K) Na 2 700, which means region conthat each cooperatively rearrangin tains more than 700 units and eat % one contributes by one kr, to the C . In the case of the highly relaxed state, N,, is muc R larger. We do not know how many degrees of freedom correspond to one ko in our case, but from the general observation that in glasses the number of de rees of freedom coooerativelv connected bv & is o Bthe order of 100. [ref: 18~1, w’e come to the (Ateresting conclusions that there might be collective degrees of freedom and/or that the cooperativity volume is much larger than for ordinary glasses.18

iemphrature C/T3 decreases monotonously, with a very small anomal at the SDW ordering transition (see Fig. 3) at +!SDW. This value of Ts~w is in excellent agreement with other data in the literns ecific heat measurements b ture. Other Coroneus rt nl. Py in K give a variation ver up to the transition at 12.1 K, and t ereafter a progressive downward deviation ; however the’ lafiice B term is 7 ml/mol.K4. about two or three times smaller than our value in the corresponding T-range. We technique have measured b the same transznt the specific heat o tya 150 me samole of the isostructural’ Bechgaard salt (TMl%F)2Cl04 and obtained an excellent agreement (up to I %) with data of ref. 20 above the superconducting transition temperaof 213 K ture anal sed with a Debye kmperature lref. 201. F rom the cubic regime of the vibrational specific’ heat of (TMTSF)zI%h below T,, with a = 14.5f0.5 mJ/mol.K4 (these data and ref. 6a) one obtains a Debye temperature 0~ = 2OM3 K. The similarity of the B values we have measured in

526

LOW TEMPERATURE

SPECIFIC HEAT

nal contribution should cease at TSDW. A minimum value of the configurational entro y of the “supercooled” state can be estimated Prom the extrapolation above TR of the vibrational specific . = aT3 defined for the “glassy” system ~~~~h~~ne in Fig. 1) :

18 -1

l

16

Tww C,-aT3 As cwlf = T ‘n

J

14 i

I

10

Vol. ?I, No. 7

I

I

I

11

12

13

-.

ll; T(K)

Fig. 3 : Specific heat in a Cp/T3 diagram in the Tranee of the SDW orderine transition at T = 12.1 K. %d%ated b the arrow: The inset shows the amplitude o the anomaly, obtained after subtracting a continuous background approximated by the dashed line. these two isostructural compound systems raises some questions concerning the measurements of ref. 19. At higher temperature above 8 K, the progressive deviation of CP from the cubic regime can be partly accounted for b that of the vibrational contribution, as expecte d’ from the 80 value. d)&ctron_Dhonc:

The SDW transitiAn aooears as a very small bump superimposed to thh’ continuous ‘background, without any other detectable discontinuity (Fig. 3). In a reement with ref. 19, the relative am litude AC/ E- IS very small, at maximum - 1.5 ‘%of e P but the width of the transition is broader in our case, probably due to the much larger amount of material. From the jump AC at TSDW we estimate the electronic entropy in the condensed state below TSDV, If we take the mean field expression for the at the condensation tempera~~%‘!&$?a~~~p., fls4w21, the llrryrst possible also compitible with the value is y - 25 mJ/mol.K additional presence of a normal electronic term above TSDW [see Fig. 31. It ives the electronic .I?. ;iyp;;z; - 300 mJ/mol the equivalence of supercooled with t e SDW entity, then the configuratio-

dT = 1.52 J.mol-l.K-1

If we compare it with reviously calculated electronic entropy, we fin dp that ASconf is at least five times lamer then the electronic one. This fact raises an &tual and important question of the role of electron-alronon interaction In the SDW stabilization. Cohtrary to thk c& of CDWs, such a couling is supposed to be negligible in SDWs as no Pattice distortion has been detected up to now. A possible coupling to the lattice could occur via the phase deformation of the SDW, an interpretation proposed from s in-lattice T1 relaxation in N.M.R. experiments.22,29 Althou h our data may imply underlying electron-p a onon interactions in a SDW system, further investigations are clearly needed.

4. Conclusion This thermodynamical study has enabled the simultaneous observation of two successive transitions of very different nature : a metal-insulator transition with the formation of the collective

Acknowledgements - We thank Prof. E. Donth for ~e~;l~sa simple application of his model to our

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Vol. 9 1,.No. 7 11.

12. 13. 14. 15. 16. 17. 18.

LOW TEMPERATURE SPECIFIC HEAT

See, e.g., T. Ishiguro and K. Yamaji, Or anic Superconductors, Springer Series in P olidState Sciencr 88 (S ringer-Verlag, Berlin, Heidelberg 1990) p. 3s . Specific heat of “Eccobond Solder 56-C”, A. Berton, J. Chaus , J. Odin et B. Souletie, Cyosenics (Oct. 1d77) 584. N.O. Birrre and S.R. Naael, Phi/s. U Rn~. Left. 54 (1985) 2674. C.A. Angell, 1. Non-Cyst. Solids 131-133 (1991) 13. j. Souletie, j. Pllysi ue (Pliris) 51 (1990) 883. J.P. Sethna, J.D. S4,ore and M. Huang, Pli!ys. Rezr. B 44 (1991) 4943. G. Adam and 1.H. Gibbs, \. Chcm. Plrvs. 43 (1965) 139. ’ 4 E. Donth, a) 1. Non-Cyst. Solids 53 (1982) 325 ; b) j. Non-Cryst. Solids 131-133 (1991) 204 ; c) Private Communication.

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J. Coroneus, 8. Alavi and S.E. Brown, Pltys. _ -Rer?.Lctt. 70 (1993) 2332. P. Garoche, R. Brusetti, D. Jerome and K. Becheaard, I. Pltusiauc-Lettres 43 (1982) L147 ; “R. ‘P. Garoche. and Brusetti, K. Beth aard, j. Plrys. C : Solid State Pltys. 16 11983) 3 !!35. A ratio AC/yTc P 1.7 slightly larger than the BCS value (1.4) has been found in ref. 20, so that y calculated from the mean field theory has a largest possible value. E. Barthel, G. Quirion, P. Wzietek, D. Jerome, J.B. Christiensen, M. Jor ensen and K. Beth aard, Europliys. Left. 21 $ 1993) 87. W.G. CBark, M.E. Hanson, W.H. Won and B. Alavi, Proc. of Int. Workshop “ECR ? S-93”, ibid., p. 235.