The magnetic field dependence of the low temperature specific heat in single crystals of YBa2Cu3O7

Physica C 168 (1990) 363-369 North-Holland

THE MAGNETIC FIELD DEPENDENCE OF THE LOW TEMPERATURE SPECIFIC HEAT IN S I N G L E C R Y S T A L S O F YBa2Cu307 J. BAAK, C.J. M U L L E R a n d H.B. B R O M Kamerlingh Onnes Laboratorium, Leiden University, PO Box 9506, 2300 RA, Leiden, The Netherlands

M.J.V. M E N K E N , K. K A D O W A K I a n d A.A. M E N O V S K Y Natuurkundig Laboratorium, Universiteit van Amsterdam, PO Box 20215, I000 HE Amsterdam, The Netherlands

Received 14 March 1990

Specific heat measurements in magnetic fields up to 5 T and at temperatures below 1 K are performed on single crystals of YBa2Cu307_~ with a transition temperature of 89 K. The specific heat goes through a maximum with increasing magnetic field strength. This behavior and the temperature dependence of the zero field data, C= aTn+ bT 3 and with n = 0.42, are characteristic for localized spins coupled via random Heisenberg antiferromagnetic exchange. The results are analyzed with the semi-empirical random exchange model of Bulaevskii. Only two free parameters are available, which are completely determined by the zero-field data. Using these values the field behavior is correctly predicted. Representative data of other groups are analyzed with the same model. Defect states that are not related to the high-To mechanism are seen as an origin of this excess contribution to the lattice specific heat.

1. Introduction Recently the specific heat d a t a o f La-, Y-, Bi- a n d Tl-based high-To s u p e r c o n d u c t o r s were reviewed by J u n o d [ 1 ]. After an extensive c o m p a r i s o n o f d a t a J u n o d concludes that the so often o b s e r v e d linear term in the low t e m p e r a t u r e specific heat (Coc T) is not extrinsic but atypical: it does not stem from an impurity phase but it tends to d i s a p p e a r in more ideal samples. The analytic form o f this " l i n e a r " t e r m is ill defined: empirically it resembles a T n term with 0 < n < 2. The best p o w d e r samples seem to be less affected by this atypical c o n t r i b u t i o n than single crystals. The first low t e m p e r a t u r e specific heat d a t a on single crystals were published by y o n M o l n a r et al. [2 ]. An appreciable linear c o n t r i b u t i o n in C was observed. Single crystal d a t a [ 3 ] o v e r a larger t e m p e r ature regime ( d o w n to 0.4 K ) r e p r o d u c e d the d a t a o f von M o l n a r et al. The " l i n e a r " t e r m followed a T °42 dependence. Recent data on single crystals with a T~ o f 93 K gave an even lower value o f the " l i n e a r " term [4 ]. At 1 K the total value o f C a m o u n t e d to 0921-4534/90/$03.50 © Elsevier Science Publishers B.V. ( North-Holland )

10 m J / ( m o l K ) , c o m p a r a b l e to the best p o w d e r samples. As an explanation for the Tn-term we have suggested that r a n d o m exchange interactions between residual spins not involved in the superconducting pairing were responsible [ 3 ]. To check the magnetic origin o f the linear term, m e a s u r e m e n t s in field are elucidating. This is particularly true for the r a n d o m exchange interactions. In the s e m i - p h e n o m enological m o d e l o f Bulaevskii [ 5 ], which we follow here, the in-field d a t a are even directly related to the zero-field results. In this c o m m u n i c a t i o n we present and analyze the field dependence o f the low temperature specific heat on our single crystals with a Tc o f 89 K and make a c o m p a r i s o n with similar d a t a on p o w d e r samples o f other groups (as far as we know there are no other field d a t a sets on single crystals a v a i l a b l e ) . F r o m the relation between field and zero-field results, it is argued that r a n d o m exchange interaction plays an imp o r t a n t role in all data. The advantage o f single crystals in this study is the reduction o f the influence o f grain b o u n d a r i e s and surface c o n t a m i n a t i o n (e.g. by oxygen depletion o f surface layers).

364

J. Baak et al. / Field dependent specific heat of YBaeCu~07

2. Experimental The specific heat data were obtained via a thermal relaxation method. A mosaic of about 80 crystals with a total weight of 50 mg was mounted on a sapphire plate on to which a heater of NiCr was sputtered. A slice of an Allen&Bradley l0 ~ carbon resistor was used as a thermometer. The plate was connected via a thermal resistance (a thin Cu wire) to a heat sink. On the sink a heater and two thermometers were mounted: a Ge-thermometer and an Allan&Bradley resistor with a calibrated field dependence for the infield measurements. In every run the A&B resistor was calibrated in zero field against the Ge-thermometer. In an improved version used for the 93 K samples, the A&B resistor was replaced by a ruthenium oxide thermometer, which showed excellent reproducibility. The samples were mounted with a precisely determined amount of Apiezon-N grease, which was also used in the run with the empty apparatus to facilitate a correct subtraction of its heat capacity. Method and sample were checked via a run with a Pd-sample in zero field. No deviations were found from values quoted in the literature [6]. The heat capacity of the empty apparatus, i.e. thermometer, grease and heater, was measured in the same fields as where the sample data were taken and amounted to about 20% of the total heat capacity. During a heat pulse, typically of 1 nW, the temperature increased by a relative amount of 2%. The pulse duration time was always at least a factor of 5 longer than the intrinsic time constant of the sample, which was a few seconds. The inaccuracy of the data points in zero field is 3% below 2 K. Above this temperature the relative weight of the Apiezon-N grease in the total specific heat and the increase in relaxation time lower the inaccuracy gradually to about 10% around 10 K. For the data in a magnetic field, to achieve optimal field penetration of the sample, the field changes were made above To. The error in the in-field data points amounts to 10%. All single crystals were prepared in ZrO2 crucibles, starting from off-stoichiometric composition of the constituents Y203, BaCO3 and CuO [ 7 ]. The quality of the samples was checked by measuring the diamagnetic susceptibility. The susceptibility curves showed complete diamagnetic shielding. The midpoints were 89 K with a width of 1 K for the 89 K

batch and 93 K with the same 1 K width for the 93 K batch.

3. Results The specific heat of the 89 K batch in a magnetic field B at T=0.5 K and T=0.9 K is shown in fig. I. The error in the data point amounts to 10%. The specific heat goes through a maximum with increasing magnetic field strength B. The location of the maximum is at a higher field in the higher temperature scan. At T=0.5 K the value of C in a field of 5 T is reduced by more than a factor of 2 compared to the zero-field value. The drawn lines are the predictions of BM (the Bulaevskii model) based on the zero-field data, as will be explained below.

4. Comparison to other data Before discussing the consequences of our data, we make a comparison to the single crystal data of yon Molnar et al. [2] for B = 0 T; and to representative data of Caspary et al. [8] for 50 m K < T < 4 K in zero field and a field of 8 T, of Reeves et al. [9] for 2 K < T < 6 K and B < 3 T and of Phillips et al. [10] for 0.4 K < T < 3 0 K and B < 8 T. 4.1. Single crystal data o f yon Molnar

The usual way to analyze the zero-field specific heat

20 A

E

0

1

2

3

t~

5

B T) Fig. 1. Specificheat as function of field at fixed temperatures of 0.5 K (squares) and 0.9 K (triangles). The solidlines are predictions of the Bulaevskii model. The dotted line corresponds to a Schottkyanomalyof 2.6 X 1021free spins.

J. Baak et al. / FieM dependent specific heat of YBaeCu307

365

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~

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~

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80

100

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Fig. 3. Data of Caspary et al. The random exchange expression C = T ° S T - 0 . 0 1 2 T -2 is shown by a dashed line.

6 o

DI O

0

q0

20

/

3. In this plot the data are "corrected" for the lattice and the hyperfine and quadrupolar contribution of the nuclei. The dashed line is a fit based on C = 12T°'57-0.012T-2. In 8 T there is hardly any specific heat in excess to the lattice contribution.

i

060 ~ I

/

I-LD

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i

i

10

20

30

i

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q0 50 T 2 (K ~)

i

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70

80

Fig. 2. (a) The single-crystal zero-field C data o f von Molnar plotted as C/Tvs. T 2 on a linear scale. The drawn line is given by C/T=9.0+O.37T2+O.OO13T 4, and the dashed line by C~ T = 1 2 T ° S + 0 . 5 4 T a , with C i n m J / ( m o l K). (b) The data o f our 89 K batch, shown as in (a). The dashed line corresponds to C = 12.5T°-42+ 0.59 Ta; the insert gives the data between 2 K and 10 K, compared to C/T=8.0+0.41T2+0.0025T 4 m J / ( m o l K2).

4.3. The field data of Reeves The field data of Reeves et al. are only available in the limited temperature regime between 2 K and 6 K for B < 3 T (drawn lines in fig. 4 ( a ) ) . For the drawn lines in fig. 4 ( b ) , the effects of random exchange have also been included.

4.4. The field data of Phillips results is to plot the data as C / T versus T 2. Figure 2 ( a ) shows von Molnar's data between 2 K and 10 K. The drawn line is given by C/T=9.0+0.37 T 2 + 0 . 0 0 1 3 T 4 with C i n m J / ( m o l K). A fit of similar quality is obtained with the random exchange expression C = 12T°'5+0.54T 3 (dashed line in the figure). Figure 2 ( b ) gives our zero-field data between 0.4 K and 10 K. The upturn in C~ T a t the lowest temperatures has been found by many groups. The dashed line in fig. 2 ( b ) corresponds to C=12.5 T°'42+0.59T 3. In the insert of fig. 2 ( b ) the data between 2 K and 10 K are fitted with the expression C/T=8.0+O.41T2+O.OO25T 4. The two different sets of data agree quite well.

4.2. The low temperature data of Caspary et al. The zero-field data of Caspary [8 ] are given in fig.

These powder data, which were published at an early stage of the high-To research, overlap with our temperature and field regime. In fig. 5 the Phillips data (drawn lines) are reproduced, where the dashed lines are again predictions of the random exchange model, and dotted lines also incorporate the vortex contributions (see section 5.3. ).

5. Discussion

We first address the influence of the lattice term, summarize the random exchange model of Bulaevskii and explain the fitting expressions used for our and the other data. The magnitude of the fluxoids is estimated thereafter and finally the nature of the localized spins is considered.

J. Baak et al. I FieM dependent specific heat of YBaeCu307

366

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i

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Fig. 4. Reeves' data. The lines 1-4 in (a) are the original data in fields of 0, 1, 2 and 3 T, respectively. (b) shows that similar curves are obtained by including a random exchange contribution.

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lows then for our 89 K batch, see the insert in fig. 2(b). This value compares well with the best Y B a 2 C u 3 0 7 - a samples [ 11 ]. A fit of similar quality is obtained with the expression C = a T l-ot.~bT 3, which can be based on the random exchange interaction [ 3 ]. The parameter values for yon Molnar's and our data set (value in parentheses) are a = 12.0(12.5) m J / ( m o l K2-a), a = 0 . 5 0 ( 0 . 5 8 ) and b=0.54(0.59) m J / ( m o l K4). These b-values imply Debye temperatures of 360 K and 350 K, respectively. Due to the lower value for OO in the random exchange expression, the 20% drop in On between 10 K and 20 K [ 11 ] is absent. Also Lasjaunias et al. [12 ], who fitted their zero-field single-crystal data with an expression C = a T - 2 + b TO.S+ c T 3+ Cscho,ky, obtain a Debye temperature of 350 K. For the analysis below, it suffices to note that below 1 K the lattice contribution in the field data is of minor importance.

Fig. 5. Phillips' dam. The full lines correspond to the original data,

the dashed lines to the random exchangeprediction, based on the zero-field data. Inclusion of the vortex contributions (see text) leads to the dotted lines. 5. I. The Debye temperature

For his data set, von Molnar arrives at a Debye temperature of about 400 K from the (commonly accepted) fitting expression C= aT+ b T 3+ cT 5 with a = 9 . 0 , b=0.37 and c=0.0013. A similar value fol-

5.2. The random exchange model

Bulaevskii has shown that a chain of spins with a random antiferromagnetic exchange interaction is equivalent to a system of free spinless Fermi particles with energies e+g#aB and chemical potential -glzaB. Here/tn denotes the Bohr magneton and g the Land6 factor. The internal energy of such a system is given by:

J. Baak et al. / Field dependent specificheat of YBa2Cu~Oz

U = N i p(E)(e+gltBB) --oo

X

1

1+ e x p ( ( 1 / k T ) ( ~ + g ~ B ) }

de.

In BM a semi-empirical expression is assumed for the density of states as a function of energy ~: p (~) = A k - ~+~1~1 -'L k being Boltzmann's constant, and N the number of spins per mole. The two constants A (not dimensionless) and ot are the only two unknown parameters in BM, which is our main reason for preferring BM above more sophisticated treatments [ 13-16 ]. The results of all these models do not essentially differ. From the internal energy and the density of states, the specific heat can be calculated: C( T, B) = A N k ( g l t a B / k )~-c'Ya( t), t= 2kT/gllBB , oo

y c , ( t ) = t -2 f -,~[ (l+x) 2 3 x [coshZi (1--~x)/t ] 0

+

( l-x)2 cosh2i~)/t

j ] clx.

(2)

The integral Y ( t ) can be evaluated numerically. In the zero-field limit, eq. (2) becomes C( T, O) = flANkT 1-'~ ,

(3)

where fl can be calculated for a known value of or. 5.2.1. The random exchange model applied to our own field data From the zero-field data an or-value of 0.58 is obtained, which implies fl= 1.9. Using these values, A N k = 6.6 m J / ( mol K 2- ~). In fig. 1., the drawn lines are the predictions of BM, based on the zero-field data. The predicted values are in reasonable agreement with the experimental data. We emphasize that no fitting has been used to obtain these field curves. That the extra contribution in zero-field is exclusively of a magnetic origin is strongly suggested by the fact that the high-field excess term is even smaller than its zero-field value. Apart from the presence of "Curie-like" spins in the superconducting state, the analysis followed here in terms of BM requires in addition that these spins are antiferromagnetically cou-

367

pled via the Heisenberg exchange interaction and reside in one-dimensional chains (e.g. Cu 2+ spins caused by oxygen deficiency on the Cu ( 1 ) O chains). In contrast to e.g. quinolinium bistetracyanoquinodimethane [ 17 ], the standard example for a random exchange system, the normally applied susceptibility method fails to show these spins because of the diamagnetic shielding. In ESR experiments on YBa2Cu307, one-dimensional antiferromagnetic ordering fluctuations are indeed seen below 30 K [ 18,19 ], which are ascribed to localized d-holes on Cu 2+. Also neutron scattering experiments on YBa2Cu306.9 by the CENG-group at the ILL [ 20 ] in a magnetic field of 4.7 T and 1.5 K have shown the presence of an average spin density of the order of 10-3/tB at the Cu ( 1 ) sites. In BM the number of spins per mole, N, in the chains does not follow from the fit parameters A and or, only the combination A N k is fixed. In principle, N can be determined directly via the entropy content of the measured specific heat curves. The low temperature data can be extrapolated using BM, but for the extrapolation on the high temperature side a cutoff is needed, whicl~ again depends on N. For a minimal order of magnitude we have compared the data at 0.5 K with a Schottky anomaly as will be produced by free spins (dotted curve in fig. 1 ). Its maximum is at the same position as that observed experimentally. The number of spins needed to reproduce the height of the specific heat maximum amounts to 2.6 × 1021 per mole. Assuming an oxygen deficiency of a few percent, an upper limit for the number of spins on the Cu( 1 )O-chains would be about 1022 per mole. 5.2.2. The random exchange model and the C-data of other groups Reeves et al. [9 ] analyze their data (see fig. 4(a) ) in terms of a linear contribution which increases with B and a lattice contribution which decreases with field. Within the considered fluxoid model (see section 5.3), the observed linear contribution of C~ T = 0.8B mJ / (mol K 2 ) with B in tesla implies an unrealistically small value of the penetration depth of only 350 A, instead of the usual quoted value of 1200 /k or higher. Although the temperature range is relatively high and the magnetic fields are too small (in comparison to T) to show the clear features of the

368

J. Baak et al. /Field dependent specific heat of YBa2CusO7

random exchange model, we have estimated from the zero-field data the random exchange parameters or=0.51 and ANkfl=6.2 (C in m J / ( m o l K ) ) . For the lattice contribution, 0.53T 3 is used. The combination of a fluxoid term of C~ T= O. 1B m J / ( m o l K 2) with the random exchange contribution (drawn lines in fig. 4 ( b ) ) permits the penetration depth to be about three times larger than in the original paper of Reeves et al. (see also section 5.3). Phillips et al. [ 10 ] have analyzed the data of fig. 5 in terms of a linear contribution due to a fraction of the sample that remains in the normal state and a Schottky contribution due to magnetic impurities. We have used the zero-field data to calculate the field dependence according to the random exchange model (dashed line in fig. 5 ); the heights and widths of the observed anomalies are as expected, but the location of the maxima is at somewhat higher temperatures than calculated. At the highest temperatures the random exchange model gives too low a value. Apparently a field dependent "linear" term is needed, which partly stems from the fluxoids. The dotted line in fig. 5 incorporates this effect via a C/T=O. 1B m J / ( m o l K 2) term, see also section 5.3. We would like to stress that the assumption of a simple Schottky anomaly together with a linear term as originally proposed by Phillips et al. is insufficient to reproduce their data. As illustrated in fig. 1 for our own data, the distribution of Schottky anomalies, implicit in the random exchange model, is essential for an explanation of the observed width of the anomalies; the width of a single Schottky anomaly (dotted line) is too small. The zero-field data of Caspary et al. [ 8 ] (see fig. 3 ) show an upturn in ( C - Cnuclea r - Clattic e ) / T similar to that of Phillips and our own data. They attribute these observations to a spin-glass behavior (a similar statement has been made by Urbach et al. [21 ] for Bi2SrCa2Cu20 s and Tl2Ca2Ba2Cu3Oio ) on top of a nuclear hyperfine contribution. The "glass temperature" is calculated to be 1.7 K [22 ]. The data for B = 0 T can be reproduced by eq. (3) - C~ T = 12T-°'43 _ down to 0.4 K. Below 0.2 K, like Caspary, we have to include a tail of a hyperfine splitting. The final expression used for the dashed line in fig. 3 is C / T = 1 2 T - ° ' 4 3 - O . O 1 2 T - 3 . The negative T - 3 term means that our hyperfine contribution is somewhat smaller than that used by Caspary. At the lowest temperatures the deviations between fit and

data points are of the order of 1 m J / ( m o l K), which is only a few percent of the total specific heat. The merit of the random exchange mechanism is the natural explanation for the temperature dependence of the "linear term" below 1.7 K (the calculated glass temperature) [23 ]. The 8 T data show the suppression of the heat capacity, as expected in the random exchange model. However, eq. (2) predicts a C / T value of about 6 m J / ( m o l K 2), which is larger than that actually observed. In a spin-glass model far below the glass temperature of 1.7 K, the in-field and zero-field data are expected to differ even less [23 ].

5.3. The Ginzburg-Landau field contribution A magnetic field above He2 creates vortices, which means normal electrons and a linear contribution to C at low temperatures: C/TocB. Using the Ginzburg-Landau theory in the London limit, Reeves et al. have calculated the field dependence of the specific heat of a uniaxially symmetric superconductor. For a penetration depth of 1200 A, the estimated increase of the linear term with field due to the growing number of vortices is C~ T= O. 1 B m J / ( m o l K 2 ) with B in tesla. In a field of 3 T, this contribution is 0.3 m J / ( m o l K2), which is comparable to the random exchange contribution (see fig. 4 ( b ) ) . The combination of the random exchange contribution with the vortex term removes the need for the unrealistic short coherence length of about 350 A, see above.

5.4. Nature of the localized spins Within the BM different values for n are allowed. Because the difference in transition temperatures is most likely connected to a difference in oxygen content, different spin distributions and hence different n-values have to be expected. Still we would like to point to another factor which can play a role. The value of n = 0.42 found for the 89 K superconductor is very close to the value calculated for the temperature dependence of C in doped semiconductors below the metal-insulator transition: n = 0.40 [ 24 ]. The main difference with the one-dimensional BM is that the spins in the doped semiconductors are randomly distributed in three dimensions. It is likely that not only the dependence of C on T, but also of C on B

•I. Baak et al. / F i e M dependent specific heat o f YBa2Cu30z

will be analogous to BM. In these disordered systems, near the metal-insulator transition the presence of conduction electrons will increase n from 0.4 to 1 in the final metallic limit. By analogy the value found in the 93 K batch might be also influenced by such an effect. If so, an n-value even closer to 1 might be expected for oxygen defect regions with more charge carriers decoupled from the superconducting bulk, as possibly present at the surface of grains.

6. Conclusion We have

shown

that

in

single crystals of

Y B a 2 C u 3 0 7 _ 6 there is an extra contribution in the

low temperature specific heat of the form a T n, which is characteristic for spins coupled via a random antiferromagnetic Heisenberg exchange. Within the Bulaevskii model, it is possible to predict the field dependence of the specific heat from the two zerofield parameters a and n. Although BM is a crude approximation for the antiferromagnetic exchange interactions between the localized spins in a real highTc superconductor, it gives a fair description of the observed field dependence of the low temperature C in our single crystals and the powder data of other groups. The localized spins have to be associated with oxygen defect regions in the material and are not involved in the superconducting mechanism.

Acknowledgements It is a pleasure to thank Prof. J.L. de Jongh, Dr. G.J. Nieuwenhuys and Dr. A.J. Dirkmaat for useful discussions. This work is part of the program of the Leiden Materials Centre and ALMOS and is supported by the Foundation of Fundamental Research on Matter (FOM), which is sponsored by the Netherlands Organization for the Advancement of Pure Research (ZWO).

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References [ 1 ] A. Junod, to be published in Physica Properties of High Temperature Superconductors II, April 1990. [2] S. von Molnar, A. Torressen, D. Kaiser, F. Holtzberg and T. Penney, Phys. Rev. B37 (1988) 3762. [3] H.B. Brom, J. Baak, A.A. Menovsky and M.J.V. Menken, Synthetic Metals 29 (1989) F641. [4] J. Baak, H.B. Brom, M.J.V. Menken and A.A. Menovsky, Physica C 162-164 (1989) 500. [5]L.N, Bulaevskii, A.V. Zvarykina, Yu.S. Karimov, R.B. Lyubovskii and I.F. Shchegolev, Sov. Phys. JETP 35 (1972) 384; L.N. Bulaevskii, A.A. Gusseinov, O.N. Eremenko, V.N. Topnikov and 1.F. Shchegolev, Sov. Phys. Solid State 17 (1975) 498. [6] N.E. Phillips, CRC Critical Rev. in Solid State Sci. 2 (1972) 467. [7] M.J.V. Menken and A.A. Menovsky, J. Crystal Growth 91 (1988) 264; M.J.V. Menken, K. Kadowaki and A.A. Menovsky, J. Crystal Growth 96 (1989) 1002. [8] R. Caspary, M. Winkelmann and F. Steglich, Z. Phys. B77 (1989) 41. [9] M.E. Reeves, S.E. Stupp, T.A. Friedmann, F. Slakey, D.M. Ginsberg and M.V. Klein, Phys. Rev. B40 (1989) 4573. [10] N.E. Phillips, R.A. Fisher, S.E. Lacy, C. Marcenat, J.A. Olsen, W.K. Ham, A.M. Stacy, J.E. Gordon and M.L. Tan, Physica B 148 (1987) 360. [ 11 ] C.A. Swenson, R.W. McCallum and K. No, Phys. Rev. B40 (1989) 8861. [12]J.C. Lasjaunias, H. Noel, J.C. Levet, M. Potel and P. Gougeon, Phys. Lett. A129 (1988) 185. [ 13] W.G. Clark and L.C. Tippie, Phys. Rev. B20 (1979) 2914. [ 14] C. Dasgupta and S.-K. Ma, Phys. Rev. B22 (1980) 1305. [ 15 ] S.R. Bondeson and Z.G. Soos, Phys. Rev. B22 (1980) 1793. [ 16] J.E. Hirsch and J.V. Jose, Phys. Rev. B22 (1980) 5339. [ 17] L.J. Azevedo and W.G. Clark, Phys. Rev. B16 (1977) 3252. [ 18 ] C. Rettori, D. Davidov, I. Balaish and I. Felner, Phys. Rev. B36 (1987) 4028. [ 19] F.J. Owens, Solid State Commun. 70 (1989) 173. [20] J.X. Boucherle, J.Y. Henry, M. Jurgens, J. Rossat-Mignod, J. Schweizer and F. Tasset, Physica C 162-164 (1989) 1285. [21 ] J.S. Urbach, D.B. Mitzi, A. Kapitulnik, J.Y.T. Wei and D.E. Morris, Phys. Rev. B39 (1989) 12391. [22] R. Caspary, C.D. Bredl, H. Spille, M. Winkelmann, F. Steglich, H. Schmidt, T. Wolf and R. FliJkiger, Physica C 153-155 (1988) 867. [23] G.E. Brodale, R.A. Fisher, W.E. Fogle, N.E. Phillips and J. van Curen, J. Magn. Magn. Mater. 31-34 ( 1983 ) 1331. [24] R.N. Bhatt, M.A. Paalanen and S. Sachdev, J. Phys. (Paris) C8 (1988) 1179.