Specific heat of TMMC in the region of low temperature magnetic phase transition

Solid State Communications,Vol. 15, pp. 1765—1768, 1974.

Pergamon Press.

Printed in Great Britain

SPECIFIC HEAT OF TMMC IN THE REGION OF LOW TEMPERATURE MAGNETIC PHASE TRANSITION B. Vist, C.K. Chau and H. Weinstock Physics Department, Illinois Institute of Technology*, Chicago, illinois, 60616, U.S.A. and R.E. Dietz Bell Laboratories, Murray Hill, New Jersey, 07974, U.S.A. (Received 31 May 1974 byA.G. Chynoweth)

Specific heat measurements on the one-dimensional linear chain antiferromagnet TMMC in the temperature range 0.4—4.0 K show an anomaly at 0.83 K indicative of a three-dimensional magnetic phase transition. Above 0.83 K, that part of the specific heat not related to the phase transition, shows a linear and quadratic dependence on temperature in agreement with measurements at higher (T> 1.5 K) temperatures. The interchain coupling does not appear to be responsible for the observed low value of the linear term. Application of a 15 kG magnetic field along the c-axis broadens the specific heat anomaly and shifts the maximum value from 0.83 K to about 1.0 K. AN EARLIER communication1 presents evidence of a major contribution to the specific heat of TMMC** from thermal activation of magnons associated with linear magnetic chains along the c-axis. At temperatures less than about 1.5 K, an additional specific heat contribution appears and seems to be increasing toward lower temperatures. From earlier studies of susceptibility,2’3 which showed a singularity at 0.84 K, and from neutron scattering data,4 it has been concluded that a transition from the one*

The portion of this investigation carned out at illinois Institute of Technology was supported by the U.S. Atomic Energy Commission under Contract AT(l 1—l)—1629.

.

magnetic field were carned out, with two different sample holders. For the zero field measurements there were almost no restrictions in the positioning of the sample. This, in turn, permitted one to make the holder of two thin copper plates, so that the correction for additional heat capacity was l~ssthan 7% of the total. For the other case (H ~ 0), positionmg was critical as the sample had to be placed in the uniform field

t Submitted in partial fulfillment of the requirements ~ ~ ~ Institute of Tech**

dimensional short range correlated state to a threedimensional long range ordered state takes place (at the above mentioned temperature). The current investigation is an extension to lower temperatures of the specific heat of TMMC, using the same specimen as used in the previous work,1 in an effort to study the effect of the magnetic phase transition. Preliminary reports of the observation of the phase transition have been made elsewhere by several groups, all of which are in qualitative agreement with one another.5’6’7 Experi’nents in zero and in an externally applied

TMMC is the abbreviation for ‘tetramethyl ammonium manganese chloride’ or (CH 3)4NMnCI3.

region of the surrounding superconducting solenoid. 1765

1766

SPECIFIC HEAT OF TMMC

Consequently, a correspondingly larger holder was used, but which contributed no more than 30% to the total heat capacity. In the zero field work, two carbon thermometers with nominal values of 12 and 68 ~2,respectively, were used. These two values conveniently cover the temperature range between 0.3 and 4.2 K with averlap in the region of 1 K. Since a sharp anomaly was found for H = 0 at T~= 0.83 K, additional measurements were0carried out to study the influence of a magnetic field on the specific heat in this temperature region. For this specific region a carbon thermometer with a nominal value of 28 ~2was used to provide maximum sensitivity in the limited temperature range. A superconducting solenoid supplied a field for which both the drift per second and the gradient over 1 cm were less than 0.01%. A magnetic field of 15 kG was applied to the c-axis of the crystal. The measurements were carried out on a single crystal of (1.000 ±0.001)g and approximate dimensions of 5 X 11 X 23 mm3, where the c-axis is along the longest dimension. As TMMC is very hygroscopic, the sample holder was constructed such that the sample could be mounted without being exposed to the atmosphere for more than one minute. The sample, having flat parallel surfaces, was clamped between two copper plates held together by nylon string or nylon screws, thus thermally isolating the two plates. A heater was attached to one of the plates with GE7031 varnish, which was also used to glue the thermometers to the other plate. A gold foil was connected to one of the plates for making thermal contact between the sample and its environment. The zero field results are in good agreement with previous measurements1 performed (on the identical specimen) at higher temperatures. An overall view of the temperature dependence between 0.4 and 4.0 K is shown in Fig. 1. In this figure one notes a sharp anomaly occurring at 7~= 0.83 K, presumably associated with the expected phase transition. A~ expanded plot of this anomaly is given in Fig. 2. The temperatures at which the maximum value for the specific heat has been observed in zero field have been averaged over four different runs. The result is =

0.829 ±0.002 K,

Vol. 15,No. 11/12

where the error represents the rms deviation from the mean value. For temperatures higher than 0.83 K, the specific heat data have been fitted to a variety of polynomial expressions in temperature, plus a function indicative of the singularity. These fits have been carried out over different temperature ranges. The functional fits are represented in their most general form by 2+cT3+z~C(T), (T>T~), (1) C(T) = aT+bT where I~C~T) represents the contribution due to the phase transition. The criterion used to select the best fit is that ~~T) should be of little importance for temperatures much above T~. To obtain the functional form of z~C(T),which is singular at T~,use has been made of three well known forms to find the best fit, i.e., a power law dependence, a logarithmic and a cusp-like singularity. The last of these gives by far the best fit, and setting (T— T~)/T~e, this fit yields, using 95 data points from 0.84 K ~ T~ 1.7 K, and the linear and quadratic terms found at higher temperatures,1 C(T)

=

0.088 T + 0.047 T2 +

(0.298 ±0.002)11 in the units J/mole K.

~~0~101 ±0.003)1

(2)

The fit is relatively insensitive to changes in the coefficients of the linear and quadratic terms, but is far better than fits attempted in which a T3 term in eq. (1) is added. For temperatures below 0.83 K, a logarithmic dependence for ~T) is noted. However, the high temperature linear and quadratic terms do not contribute in this region since the experimental data actually cross the extrapolated linear and quadratic curve. These data appear to suggest that the interchain coupling affects the one-dimensional spin fluctuations over a temperature range extending considerably above 7,. If, to the contrary, the effects of the interchain coupling were appreciable only near T~,and below, then

f TA dT c/T

= JTA

dT [aT+ bT2] IT

Vol. 15,No. 11/12

SPECIFICHEATOFTMMC

1767

1.2

7

H~0 RUNS

0.9-

.1H53

THU2 ~1NS1 1106 110

C(J/ ~Ie

2

K)

-00858T. O.0480T

~

1

2

I 3

4

T (K)

FIG. 1. Specific heat vs temperature of TMMC in zero field.

04

.

H =0

:

RUNS

:

03

/

~=

.~=

02

$

C(J moleK)

/

/

0 1

for observed spinthe wave result.1small value of a as compared to the

~ 7 /

When the influence of a magnetic field on the

/ /

-~

I

T (K)

05

10

versus 185 mi/mole K for the integral on the right. The additional 41 mi/mole K involved in the interchain ordering apparently has been taken from the intra-chain fluctuations, possibly by reducing slightly the value of the linear T coefficient, a. If such a reduction were made uniformly over the 4 degree interval over which the value of a was established,’ this would correspond to a decrease in the value of a of only 0.010 i/mole K. This is not sufficient to account

1.5

2.0

FIG. 2. Expanded plot of Fig. 1, centered around T 0 = 0.83 K. where TA is some temperature just above T~(say 1.5 K), above which the effects of the interchain coupling are not significant. The integral on the left was evaluated from the experimental data by extrapolating CIT linearly to CIT = 0 at 0 K from the last data points at 0.43 K. This yielded 226 for the integral on the left

specific heat was studied, several data points in zero field (interspersed with those taken for H = 15 kG) were also taken again, particularly in the critical region, in order to see whether hysteresis would be obseived as in the susceptibility data.3 However, the singularity resulting from these zero field data shows no noticeable deviation from that obtained in the runs where no magnetic field was applied at all. In the presence of an externally applied magnetic field of 15 kG parallel to the crystallographic c-axis, a broadening of the peak was observed and the specific heat maximum was shifted to a higher temperature. For temperatures above 1.9 K, the heat capacity is not measurably affected by the presence of the magnetic field, and data in that temperature region are shown in Fig. 3. This is consistent with the weak,

1768

SPECIFIC HEAT OF TMMC

C(J/~IeK)

Vol. 15,No. 11/12

~~~O~5BT,OO48OT2

~

~‘_R

———

c-~ 0

T (K)

I 1

I 2

I 3

4

FIG. 3. Specific heat vs temperature of TMMC in an applied magnetic field of 15 kG parallel to the c-axis. quadratic field dependence for the dispersion relations in the preceeding paper. The maximum value of C in the applied field of 15 kG is 0.25 i/mole K, occurring at a temperature T= 1.0 K. This compares with the maximum observed zero field value of C = 0.39 i/mole K at T~= 0.83 K. The shift of the maximum C to a

1. 2. 3. 4.

higher temperature and its broadening in applied field is qualitatively in agreement with fundamental thermodynamic arguments applied to the known susceptibility temperature behavior.3 Acknowledgements The authors are grateful to R. Dingle who supplied the crystal used in this work, and to L.R. Walker and P.C. Hohenberg for helpful discussions. —

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REFERENCES DIETZ R.E., WALKER L.R., HSU F.S.L., HAEMMERLE W.H., VIS B., CHAU C.K. and WEINSTOCK H., Solid State Commun. 15, 1185 (1974). DINGLE R., LINESM.E. and HOLT S.L.,Phys. Rev. 187, 643 (1969).

5.

WALKER L.R., DIETZ R.E., ANDRES K. and DARACK S., Solid State Commun. 11,593 (1972). BIRGENEAU RJ., SHIRANE G. and KITCHENS T.A., Thirteenth International Conference on Low Temperature Physics, August 1972, Boulder, Colorado, abstract DaM2. VIS B, CHAU C.K. and WEINSTOCK H., Bull. Am. Phys. Soc., 18,450(1973).

6.

WHITE H.W., MILANJ.M., LEE K.H. and HOLT S.L.,Bull. Am. Phys. Soc., 18, 450 (1973).

7.

TAKEDA K.,Phys. Lett. A47, 335 (1974).