CRITICAL PHENOMENA IN THE SPECIFIC HEAT OF MAGNETICALLY ORDERED COMPOUNDS

HAL Id: jpa-00214048

https://hal.archives-ouvertes.fr/jpa-00214048

Submitted on 1 Jan 1971

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

CRITICAL PHENOMENA IN THE SPECIFIC HEAT OF MAGNETICALLY ORDERED COMPOUNDS

A. Cooke, D. Martin, M. Wells

To cite this version:

A. Cooke, D. Martin, M. Wells. CRITICAL PHENOMENA IN THE SPECIFIC HEAT OF MAG-

NETICALLY ORDERED COMPOUNDS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-644-

C1-645. �10.1051/jphyscol:19711221�. �jpa-00214048�

CRITIQUES S TA TIQUES

CRITICAL PHENOMENA IN THE SPECIFIC HEAT OF MAGNETICALLY ORDERED COMPOUNDS

A. H. COOKE, D. M. MARTIN and M. R. WELLS The Clarendon Laboratory, Parks Road, Oxford, England

R&ume.

- On a mesure les chaleurs spkifiques

⁸

basses temgratures de DyA103, TbAlOs, GdAIO3, GdV04 et GdCI3 et de manikre plus detaillee au voisinage de

1 1-T/TN

I

^=S 10-1.

Au-dessus du point

I.

les donnks expenmen- tales se

conferment a

une loi du type

C / R ⁼ A

I 1-

TITx

I -" et on observe que la valeur de

a

est du mCme ordre pour plusieurs composes et approche

113.

On compare ces resultats avec des prkvisions rkcentes pour le modele ferromagn6- tique d'Ising, qui suggerent une valeur

a = 118.

Abstract.

-The specific heats at low temperatures of DyAIO3, TbA103, GdAlO3, GdV04 and GdCls have been measured, and their variation in the region

^I ~ - T / T N i ^,(10-1

has been examined in detail. Above the ordering tempe- rature the data have been fitted to a law of the form

C / R = A I 1-TITN

I -" and

it

is observed that the value of

a

is very consistent for several compounds and approximately equal to

113.

These results are compared with recent predictions for the Ising ferromagnet which suggest a value of

a = 118.

Introduction. -

Specific heat measurements have been made on five rare earth compounds which become magnetically ordered at low temperatures and exhibit A-type anomalies at their ordering temperatures. High resolution measurements in the close vicinity of the ordering temperature have enabled the detailed varia- tion of the specific heat with temperature to be deter- mined. In this paper we discuss the limitations of the experimental technique and describe the procedure adopted when analysing the results. Above the transi- tion temperature, the results show remarkable simila- rity when fitted to a power law variation with critical index

a.

Furthermore this value of

a

is different from the recent predictions by Sykes et al. [I] for the Ising model, even though two of the compounds investigated approximate quite closely to an Ising system of magnetic ions in many other respects.

The Experimental Equipment. -

To make accu- rate, high resolution specific heat measurements we require 1) a reproducible, sensitive thermometer with associated measuring equipement of sufficiently high resolution, 2) very low drifts of temperature between heatings, 3) crystal specimens which are chemically and physically highly homogeneous. Wetonsider these points in turn.

1) We have used doped germanium thermometers giving a rapid resistance variation in the helium range (e. g. 5 000

R at 1.3 O K

to 680 R at 4.2

OK).

The resistance is measured by an A. C . Wheatstone bridge with a resolution of 1 in lo5 at a thermometer current of 2 PA. At 2 OK, the resistance variation is of order I R/m deg., so that temperatures may be resolved to 0.01 m deg. The thermometers were calibrated against the vapour pressures of He3, He4, Hz and against a gas thermometer, and the results fitted by computer to a power series in In R containing as many as six terms. The error in fitting to the formula was of the order 1 m deg./deg.

2) Low drift rates are necessary not only to obtain accurate values for the temperature rise on heating, but also to ensure uniformity of temperature within the specimen. In our system the crystal specimens were sealed at room temperature into a copper calori- meter containing He3 gas at a pressure of 10 mm Hg.

This was suspended in an enclosure which was eva- cuated at 20 OK, the calorimeter then being cooled via a mechanical heat switch. For high resolution work the heat switch was opened at a temperature just below the transition point. With this arrangement, tempera- ture drifts between heating were approximately 5 % of the temperature rise on heating near the A-point, and 2 O/, elsewhere. Taking considerations 1) and 2) toge- ther, our system is capable of meaningful measure- ments using a heating interval of 1 millidegree, with an accuracy of about 5 %, when I 1

-

TITN I < lo-'.

3) Our samples are grown by a method [2] in which the compound crystallizes out from solution in molten flux (typically a mixture of PbO and PbF,) which is slowly cooled. Gross flux inclusions can be detected by inspection, but even clear well-formed crystals may contain flux impurities due to ionic substitution for the rare earth ions. Thus, a sample of GdAIO, grown from a Bi203 flux was found to contain 5.5 %

Bi and

to have a Neel point of 3.69 OK, whereas a sample grown from a PbO flux contained only 0.32 % Pb, and had a Neel point of 3.87 OK. Even so, the impure specimen gave a sharp R-point in the specific heat with a maximum C / R

=

3.4, as against 5.0 for the purer material, suggesting that though impure it was highly homogeneous. The effect of crystal impurities remains the greatest uncertainty in high resolution work

;

our best results have been obtained on specimens consisting of carefully selected small crystals all from the same batch.

Analysis of Experimental Results.

- The choice of TN _{or Tc} is important in analysis of the data in the region 1 1

-

TITN I < lo-'. This was effected by choosing either the temperature for which C/R has its maximum value or the result obtained by making use of the Mangelsdorf retarded function plot [3]. The former method can cause difficulties when

⁽⁽

rounding

^)>

at the kpoint is pronounced

;

the Mangelsdorf plot defines the critical temperature unambiguously but presumes the variation in specific heat with temperature is logarithmic above and below the discontinuity. A particularly good result was obtained on GdVO, by Cashion et al. [4] where TN-

=

2.496 0 OK and TN+

=

2.496 8 OK. For other compounds with poorer

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711221

CRITICAL PHENOMENA IN THE SPECIFIC HEAT OF MAGNETICALLY ORDERED COMPOUNDS C 1

-

⁶⁴⁵

agreement, it is necessary, to try values of T N between Similar behaviour, indicating a discontinuity in the T N - and T N + in all subsequent log and semi-log specific heat which is logarithmic in form below T N

plots. and a power law above T N , has been found for other

In the antiferromagnetic compounds DyAlO,, recently investigated compounds such as D. A. G. [6], GdAIO,, TbAlO,, GdVO, and the ferromagnetic DyPO, [7] and MnCI2.4 H 2 0 [8], all of which are compound GdCI, we have attempted to fit the data included in the Table. Moreover we see that there is to a law of the general form remarkable consistency in the coefficients and in

C / R

=

A'ln

(

1

-

TITN

(

+ B , particular the critical exponent

r .

With the exception of ferromagnetic GdCI, all the by plotting CIR against In I 1

-

TITN I. In each case compounds listed order antiferromagnetically and there is a linear portion of the curve extending over their value of critical exponent

a

is approximately 113.

the range l o - , < I 1 - TIT, I < lo-' for tempera- No distinction is noticed between compounds which tures less than TN

;

from this linear portion of the in many other ways may be interpreted as examples curve the value of A' is measured and the result is of Ising (highly anisotropic) or Heisellberg (isotropic) given in the Table. Above T N the graph is continuously models.

curved and we presume that such a variation is not There is at present a considerable amount of evi- valid in this region. dence [ I ] that the value of a for the Ising (s

=

112) Consequently attempts were made to fit the data ferromagnet is 118 and this value should be directly to a divergence law of the other commonly accepted comparable with the values of

^u

obtained for D. A. G . , form

:

- CIR

⁼

A I

1 -

TIT, I-". Plots of In CIR DyPO,, DyAlO, and TbAIO,, there being no distinc- versus In I 1 - TITN 1 showed linear regions extending tion between the thermodynamic behaviour of Ising over approximately two orders of magnitude in ferro- and antiferrornagnets. From the limited experi-

I 1 - TITN I

^;

see for example GdVO, [4] and GdAlO, mental evidence that we have to hand there appears [5]. From these regions of linear variation the values to be little evidence for supporting the value of

u =

118, of A and

a

may be ascertained and these are listed in except for the Heisenberg ferromagnet GdCI, whose the Table. value of

a

falls close to this theoretical prediction.

Compound Model T N

a

A A' Reference

-

-

-

-

- -

D. A. G.

I ^{2.540 0.31 - - 0.48} Keen et al.

DyPO4 Ising S

=

112 3.391 0.31 0.155 - 0.54 Colwell et al.

DyA103 3.53 0.40 0.17 - 0.50

TbAIO, 3.955 0.26 0.21 - 0.46 ( Cashion et

GdAIO, 3.870 0.29 0.32

GdVO, I Heisenberg

=

7 / 2 2.495 0.30 0.32 - - 0.72 oJ50 \

M ~ c I , : ~ H 2 0 Heisenberg S

⁼

512 1.625 5 0.35 0.167 - 0.73 Dixon and Rives

(*)

GdC13 Heisenberg S

=

712 2.219 0.13 0.30 - 0.24 Cooke et al.

(*)

GdCI, is ferromagnetic.

References

[I]

SYKES (M.

F.),

MARTIN

(J. L.)

and HUNTER

(D.

L.),

[5]

CASHION

(J. D.),

COOKE

(A. H.),

THORP (T.

L.)

and

Proc. Phys. SOC., 1967,

91,

671.

WELLS (M.

R.),

to appear in

Proc. Roy. Soc.

[2]

WANKLYN

( B .

M.) and GARTON

(G. J.), CrysfaI [6]

KEEN

( B . E.),

LANDAU (D.

P.)

and WOLF

(W. P.), Growth, 1967, 1, 164. J . Appl. Phys., 1967,

38,

967.

[31

MANGELSDORF

(P. C.), J. AppI Phys., 1959, 30, 442. [73

COLWELL (J.

H.),

MANGUM

(B.

W.), THORTON (D.

D.), [4]

CASHION (J.

D.),

COOKE

(A. H.),

MARTIN

(D.

M.), WRIGHT

(J.

C.) and Moos

(H.

W.),

Phys. Rev.

HOEL

(L. A.)

and WELLS (M.

R.),

Colloques

Letters, 1969,

23,

1245.

Internationaux du CNRS, Les Elements de

[8]

DIXON (G.

S.)

and RIVES

(J. E.), Phys. Rev., 1969,

Terres Rares,

1969, No 180,

Tome

2, 417. 177, 871.