The specific heat of TbPO4 from 0.5 to 10 K

Solid State Communications, Vol. 26, pp. 17—20. © Pergamon Press Ltd. 1978. Printed in Great Britain.

0038—1098/78/0401—0017 $02.00/U

THE SPECIFIC HEAT OF ThP04 FROM 0.5 TO 10K R.W. Hill, J. Cosier and S.H. Smith Clarendon Laboratory, Oxford University, Oxford OX1 3PU, England (Received 26 October 1977 by C. W. McCombie) Measurements on an unstrained specimen show that: (a) there are transitions at 2.11 and 2.27 K, (b) the hyperfme specific heat requires ~ in the low temperature limit, (c) the specific heat and entropy above 4K are consistent with crystal field levels at 3.8, 7 and 21 cm 1. INTRODUCTION

that of its contents over much of the temperature range. The measurements were made with the primary object of studying the transition or transitions in an unstrained sample with high temperature-resolution, but were extended down to 0.5 K so that the hyperfine specific heat could be studied, and up to 10K to investigate the effects of higher crystal field levels.

THE MAGNETIC and thermal properties of TbPO4 have been extensively studied in the past few years. Like some other rare-earth phosphates, vanadates and arsenates it crystallizes in the zircon structure, suffers a Jahn— Teller distortion [1, 2] below a temperature TD, and becomes antiferromagnetic [1] below the Néel temperature TN. Unlike the other compounds, its low-field, low2. MEASUREMENTS temperature antiferromagnetic phase is one in which the magnetic moments are neither parallel nor perpendicular The measurements were made in a cryostat which to the c-axis [3], but canted at an angle [4] of 40°. has been described elsewhere [9]. Two germanium The specific heat of this material has been measured resistance thermometers were used with an overlap several times, with inconsistent results: near 1.3 K. The thermometer for the lower tempera(1) Lee, Moos and Mangum [3] report a specific tures was calibrated by DT. R. Rusby at the National heat with a single sharp maximum at 2.17 K, but give no Physical Laboratory, while the higher temperature one data. was calibrated 3He and by 4He ourselves from against 1 to 4.2the K. vapour It was also pressure (2) Schopper et al. [5] also report a single maximum, of liquid but at 2.05 K. This is for a powder sample. calibrated in the range 4—20 K shortly after the con(3) Schopper [6] reports two specific heat maxima, clusion of these experiments by Dr. B.W.A. Ricketson one at 2.20 K which is taken to be TN, and another, (Cryogenic Calibrations, Pitchcott, Nr. Aylesbury, smaller, one at 3.5 K which is identified with TD. This Bucks, U.K.). The temperature increments used were specimen was a powder, pressed into a metal conas small as 2.5 mK near the lower peak and 8 mK near tamer, the upper one. Elsewhere, increments of the order of (4) Suzuki, Ohtsuka and Yamadaya [7] report two 5% of the actual temperature were used. maxima, a large one at 2.12 K and a smaller one at The results obtained near 2K are shown in Fig. 1. 2.24 K. The specimen was a single crystal of 7mg mass, Two heat capacity peaks are clearly seen, with maxima attached to the apparatus with Apiezon grease. of over 100 J K’ mor’ at 2.112 ±0.002 K, and The inconsistencies between these measurements 24 J K’ moF’ at 2.27 ±0.01 K, in good agreement may well be caused by strain, to which ThP0 4 is very with the results of Suzuki et al. The lower temperature sensitive, and it seemed desirable to make new measurepeak is of the A-type, very high, narrow, and roughly ments in a strain-free manner. This was easily done, symmetrical, while the upper one is asymmetrical with since we had at our disposal a supply of crystals grown a near-discontinuity; these features are not revealed by in a single batch, each of—’ 100mg mass. The crystals the earlier work. were grown from Pb3P2O7 flux by slow cooling and Measurements below 1.5 K are shown in Fig. 2. It recovered by hot-pouring [8]. About 3 g of this material can be seen that there is an upturn in the specific heat was sealed into a copper vessel with helium gas to below 0.7 K which3”must duereasonable to the hyperfine ion.be Any extrapolation effect the heat exchange. The heatexperiment, capacity ofbut the coupling of the Tb from above 1 K leads to the convessel was measured in a separate of the measurements turned out to be almost negligibly small compared with clusion that contributions other than the hyperfme one 17

18

THE SPECIFIC HEAT OF ThP04 FROM 0.5 TO 10K

Vol. 26, No. 1

00 0

30

8

0

80

0 I

~6 E2-

0 0 0

0.

60•

C)

0

0 0

c~)

0 0 0

I-

o E ‘40 0

0. C)

o

0

o0 0 0

20

0_

1.5

‘

:

Q

I 2 Temperature K

I

0

° 0 0 0o

0)

E

are negligible at and below 0.5 K. On this assumption, and using the approximate Hamiltonian

1.5

Fig. 2. The specific heat of TbPO4 below 1.5 K. ~

2.5

Fig. 1. The specific heat of TbPO4 near 2 K.

I Temperature K

0.5

/

0

3

~

_____

C) =

a’12 +P{I~—.~I(I+ 1))

I

=

5/2

it is found that (a)if P = 0, a’=0.l2OK, (b) ifP/a’ = 0.108, as in Tb metal [10], a’ 0.128 K.

b~ 2 =

/2

Since P is proportional to J~—~J(J+ 1), and j~ assumes its greatest possible value of 6 in Tb metal, (a) and (b) give the extreme possibilities for P and hence for a’. It is concluded that4.9, a’ =and 0.124 ±0.004K, corresponding to (~~> of a magnetic moment of 7.4 Bohr magnetons. These values are in good agreement with the results of measurements of saturation magnetization in fields of about 3 T parallel to the [Ill] and [0011 directions at 0.5 K [11]. By 2.5 K the heat capacity has dropped to the

4

6 8 10 Temperature K Fig. 3. The specific heat of TbPO4 above 2.5 K; Q experiment; the curves=are10cm’, calculated= from the energy levels of Fi~. 4 withy 0=(curve 1 (curve xb);y 7 cm a?; 10 cm = 3.1c). cm xy == 3.8 cm1 x(curve relatively small (but absolutely large) value of S J K1 moF’, and only falls off slowly with increase of temperature thereafter, reaching 2.5 J K’ mol1 at 10K as shown in Fig. 3. The same trend is shown by

Vol. 26, No. 1

THE SPECIFIC HEAT OF ThP04 FROM 0.5 TO 10 K 2/R = (~o~2 — ~Di4 1 and CT where ~,, = ~ exp (— O~/T)

and the O~are the various energy levels of Fig. 4, expressed in temperature units. This interpretation leads to an entropy approaching R lii S at high temperatures (T’-’ 20 K) faffing to R lii 2 when the temperature is sufficiently reduced. At the

21 cm~

I ___________

_____________

19

1

will is transitions, reflected be lifted, in theallowing the degeneracy experimental the entropy of the entropy ground to tend curve, state to zero. but doublet isThis outside the scope of the independent particle calculation which we imagine to be valid above 4 K. Here both the entropy and specific heat may be compared with the predictions of this theory, but some allowance must be made for the lattice contribution when comparing specifIc heats. The value used was 3.6 x l0~T3 J K1 mor’

1

2

Fig. 4. Low lying energy levels of ThP0 4 at temperatures above the transitions. earlier work, though the absolute values are somewhat smaller here. The only possible explanation of a specific heat which is so large, and falling so slowly with increase of temperature, is the repopulation of a series of higher energy crystal field states. Spectroscopic studies in the far infra-red reveal the existence levels with 1, which isofthe order ofenergies magniof about 10 and 20 cm tude required. 3. DISCUSSION The entropy was calculated by integration of CP/T values from the lowest temperatures up to temperature T(but excluding the nuclear spin entropy). At 4K it is close to R ln 3 and is rising rapidly; at 10 K it is nearly R in 4, and stifi rising, though more slowly. The entropy due to lattice vibrations should be relatively unimportant, and may be ignored. The figure of R in 4 for the entropy implies that there are at least 4 energy levels for the Tb3’ ion which are occupied appreciably at these temperatures. This is consistent with the fIndings of Lewis and Prinz, according to whom the tetragonal electric field splits the 7F 6 state of the ion as shown in Fig. 4 withy 10 cm’ and x relatively small. The level at 21 cm’ is well determined, and is taken to be exact in the analysis that follows, The remaining 8 states of the J = 6 manifold are too high in energy to be significant here. Above the transitions ThP04 is paramagnetic, and we assume that the terbium ions may be treated as independent particles, an assumption which should become increasingly valid as the temperature is raised. Then the entropy and specific heat may be calculated from S/R

=

ln~0+~1/~0T

as for GdVO4 [13], a correction of 15% at 10K. A similar allowance can be made in the entropy, but as previously noted it is found to be small, not more than 1% of the total. Figure 3 includes a specific heat curve [curve(a)] calculated from=the levels ofwith Fig. 4experiment withy = is 10 cm’ andx 0. energy The agreement poor. Varying the value of x withx ,with a singlet state which is mainly l/..J2(16> + —6>) nearby. Magnetic ordering would lift the degeneracy and also increase (JZ) above 5, while crystallographic distortion would reduce it by admixing states of smaller (Jr). The observed value is therefore a reasonable one, and provides some evidence that both distortion and magnetic ordering do occur. The two transitions give rise to very different

20

THE SPECIFIC HEAT OF ThPO4 FROM 0.5 TO 10 K

behaviour in the specific heat: the lower temperature one gives a maximum whose height is probably limited by the finite temperature increment (2.5 mK) used in its measurement, while the upper one yields a finite specific heat which drops by a factor of two between consecutive points taken with 8 and 15 mK increments. These are features which any model of the magnetic and structural properties of ThPO4 must explain, but they do not in themselves say what that model should be. A full understanding will necessarily involve all relevant properties of ThP04, and measurements of susceptibility,

Vol. 26, No. 1

magnetization and the magneto-electric effect are in progress in this laboratory, using material from the same batch.

Acknowledgements The authors are indebted to Dr. A.H. Cooke, M.R. Wells andhelpful Mr. N.J: England for suggesting theMr. problem and for discussions, to Professor H. Suzuki for communicating results prior to publication, and to Professor B. Bleaney for his continuing interest and encouragement. —

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