Heat capacity of [(CH3)3NH] CuCl3.2H2O below 1 K

Physica 78 (1974) 314-318 © North-Holland Publishing Co.

LETTER TO THE EDITOR HEAT CAPACITY OF [(CH3)3NH] CuC13.2H20 BELOW 1 K H. A. ALGRA, L. J. DE JONGH, H. W. J. BL()TE, W. J. HUISKAMP,

Kamerlingh Onnes Laboratorium, University of Leiden, Leiden, The Netherlands and R. L. CARLIN

Department of Chemistry, University of Illinois at Chicago Circle, Chicago, lllinois 60680, U.S.A. (Commun. Kamerlingh Onnes Lab. No. 414c) Received 10 January 1975

Synopsis Specific-heat data on [(CH3)3NH] CuC13.2H20 below 1 K are reported. The results agree qualitatively with a model of weakly coupled, ferromagnetic Heisenberg chains. A )t-type anomaly, indicating the onset of long-range order is found at T c = 0.165 + 0.005 K.

Recently a n u m b e r of experimental studies 1-3) have been reported on the series of isostructural c o m p o u n d s [(CH3)3NH] MC13.2H20, where M = Co, Cu or Mn. The results have been interpreted in terms o f a model of magnetic chains (intrachain interaction J1 ), that are weakly coupled in the second dimension (interaction J2), and even more weakly in the third dimension (interaction J3). Support for the assumption that J1 > > J2 > > J3 can be found from the crystal structure, by comparing the different superexchange paths connecting the M 2÷ ions along the various crystallographic directions ~). Accordingly, Losee et al.2) have analysed their specific-heat data on the Co 2 ÷ c o m p o u n d in terms of a 2-dimensional array of weakly coupled Ising chains. Concerning the copper salt, on the other hand, Stirrat et al. 3) report that their susceptibility measurements are better fitted to the 314

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prediction for the 2-dimensional Heisenberg ferromagnet than to that for the ferromagnetic Heisenberg chain, from which it would appear that in this c o m p o u n d J, and J2 are o f comparable magnitude. Be that as it may, it is clear from their X data that the main interaction in the Cu 2 ÷ salt is ferromagnetic, and that the ferromagnetic components (whether layers or chains) become ordered antiparallel to one another at a transition temperature T c = 0.157 + 0.003 K. In view o f the above we thought it would be worthwhile to further investigate the magnetic behaviour of [(CH3)3 NH] CuCI3.2H2 O, by extending the specific-heat measurements of Losee et al. t ) into the region below 1 K. The experiments were performed with a 3 H e - 4 H e dilution refrigerator, using the conventional heat-pulse technique, the temperature being measured with a CMN thermometere. The investigated samples weighed about 0.5 g and included one single-crystal and two powdered specimens. The heat-capacity data, obtained after subtraction o f the (separately measured) contributions of the addenda, are shown in fig. 1. The transition to long-range order appears as a X-anomaly at T c = 0.165 -+ 0.005 K in all samples. Since the t h e r m o m e t r y in the present experiments was such as to allow for a possible error o f a few per cent in the a b s o l u t e

~A detailed description of the experimental outfit will be given elsewhere.

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temperature (if related to the 4He scale), the agreement with the T c value of ref. 3 is good. Above 1 K the results smoothly join those of Losee et al. 1 ). For T < 0.4 K the single-crystal data are seen to fall below those of the powdered samples. Tiffs is attributed to (the observed) spin-lattice relaxation effects. Also the powder experiments were hampered by increasing relaxation times as T was lowered below T c, preventing meaningful measurements to be taken below T ~- 0.06 K. An immediate conclusion to be drawn from fig. 1 is that the data are in better agreement with the Heisenberg chain model than with the quadratic Heisenberg model. This may be inferred from the flatness o f the curve in the region above T c and from the value reached at the broad maximum, Cmax/R ~ 0.19, which is much closer to the chain prediction of 0. 1344,~ ) than to the value of 0.38 obtained for the 2-dimensional Heisenberg model 6,7 ). In estimating the lattice contribution to the data above 1 K, we have therefore assumed the total specific heat in this region to be represented b y a ferromagnetic chain contribution plus a T 3 lattice term. Curve (a) in fig. 1 is the prediction for the ferromagnetic (S=½) Heisenberg chain 4,s), the fit to the experiment yielding J ~ / k = + (0.80 + 0.05)K, whereas curve (b) corresponds to a T3 dependence with a Debye temperature o f about 86 K. It is seen that curve (c), which is the sum of b o t h contributions, reproduces rather closely the experimental data of Losee e t al. ~ ). Subsequently, we have estimated the magnetic entropy associated with the experimental curves by using: (i) the chain prediction (curve (a)) for T > 3 K; (ii) the experimental data for T < 3 K down to t h e lowest temperature reached; (iii) a T 3 dependence as an extrapolation to T = 0, since such a behaviour is followed by the powder data for 0.06 < T < 0.15 K. We thus obtained the magnetic entropy change as ~XS/R = 0.69 and 0.56 for the powdered samples and the single-crystal, respectively, which may be compared to the theoretical value of 0.693 for S=½. The incorrect result for the single-crystal is ascribed to the enhanced relaxation effects observed in this case. The entropy change below T c is about 0.20 R for the powdered samples. As is evident from fig. 1 we are left with some substantial differences between the experimental data below T ~- 1.2 K and the chain curve (a), that need to be explained. We have attempted a further analysis in fig. 2, where for T < 0.5 K we only consider the experimental data on the powdered samples. Curve (a) is again the prediction for the ferromagnetic Heisenberg chain with J ~ / k = 0.80 K, curve (b) represents Bloembergen's 6,7) result for the quadratic, S = ½, Heisenberg ferromagnet, scaled to the data above 1.2 K, the "fit" yielding J ~ / k = ,12/k ~ 0.5 K. The fact that the 2-dimensional model cannot adequately fit the data in this region is further evidence for the predominantly 1-dimensional character of the system. Lastly, curve (c)

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HEAT CAPACITY OF [(CH3)3 NH] CuC13.2H20 BELOW 1 K

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Fig. 2. The magnetic specific heat of [(CHa)aNH] CuCI3.2H20. compared with different theoretical model predictions. Curves a, b and c are discussed in the text. The broken curve is a guide to the eye.

is the prediction s ) for an anisotropic ferromagnetic chain with J///k = 0.85 K and J± = 0.9 J#. We consider this curve to give a better approximation of the chain contribution to the specific heat, since it can be concluded from the × measurements3) * that there is an Ising type of anisotropy, favouring an alignment along the chain axis, with a magnitude of about 10% of J]. The remaining differences between the experiment and curve (c) are interpreted as follows. The long-range order peak at T c is ascribed to be due for the most part to the interaction in the third dimension (J3). A rough estimate of the interaction responsible for the occurrence of longrange order can be obtained from the experimental kTc/J1 value, using the relation derived by Oguchi s). This yields an interaction between the chains of the order of 1.5% o f J a , corresponding to 12 mK. This value is surprisingly close to the estimate of the antiferromagnetic interaction, jar/k, which produces an antiferromagnetic arrangement of the ferromagnetic components below T c, as evidenced by the x measurements3). We may estimate the antiferromagnetic interaction field from the peak value of the parallel susceptibility at To, in the manner described by De Jongh et al.9), finding Haf--~ 1.4 )~ 10 2 0 e . This yields Jaf/k "" - 1 0 mK or - 5 mK, depending on whether the number of antiferromagnetically coupled neighbours is assumed

*We acknowledge helpful correspondence with Professor Cowen on the subject.

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to be two or four, respectively. It is tempting therefore to associate J3 with jaf. Above the sign of J2 nothing can be said as yet. Since the 2-dimensional Heisenberg model is known to have no transition to long-range order at non-zero temperature 1°), the addition of an isotropic interchain interaction (J2) in a 2-dimensional array of Heisenberg chains will not produce a transition point. On the order hand, there is some anisotropy in both the interactions Ja and J2, so that we expect the interaction J2 to contribute also to the observed long-range order anomaly. In any case, J2 will certainly contribute to the energy stored in the short-range order processes above T~. We thus consider the presence of J2 to be responsible for the fact that the experimental results lie above the chain prediction (curve c) in the region 0.2 < T < 1.2 K. As to the relative strengths of the three interactions Ja, J2 and J3, the ratio Ja :J2 :J3 = 1:0.1:0.01 seems to be as reasonable an order of magnitude estimate as can be made at present. A more detailed discussion will appear elsewhere. A c k n o w l e d g e m e n t . This work was performed as part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie" (F.O.M.), with financial support from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk O n d e r z o e k " (Z.W.O.).

REFERENCES 1) Losee, D. B., Mc Elearney, J. N., Siegel, A., Carlin, R. L., Khan, A. A., Roux, J. P. and James, W. J., Phys. Rev. B6 (1972) 4342. 2) Losee, D. B., Mc Elearney, J. N., Shankle, G. E., Carlin, R. L., Cresswell, P. J. and Robinson, W. T., Phys. Rev. B8 (1973) 2185. 3) Stirrat, C. R., Dudzinski, S., Owens, A. H. and Cowen, J. A., Phys. Rev. B9 (1974) 2183. 4) Bonnet, J. C. and Fisher, M. E., Phys. Rev. A 135 (1964) 640. 5) B15te, H. W. J., Physica 78 (1974) 302. 6) Bloembergen, P., Tan, K. G., Lef~vre, F. H. J. and Bleyendaal, A. H. M., Proc. Int. Conf. Magn., Grenoble (1970), J. Phys. 32, suppl. C-l, p. 879. 7) Bloembergen, P. and Miedema, A. R., Physica 75 (1974) 205, and to be published. 8) Oguchi, T., Phys. Rev. 133A (1964) 1098. 9) De Jongh, L. J., Van Amstel, W. D. and Miedema, A. R., Physica 58 (1972) 277. 10) Mermin, N. D. and Wagner, H., Phys. Rev. Letters 17 (1966) 1133.