CRITICAL BEHAVIOUR OF THE UNIAXIAL DIPOLAR FERROMAGNET LiHoF4

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CRITICAL BEHAVIOUR OF THE UNIAXIAL

DIPOLAR FERROMAGNET LiHoF4

P. Beauvillain, J. Renard, I. Laursen, P. Walker

To cite this version:

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JOURNAL DE PHYSIQUE Colloque

C6,

supplPment au no

8,

Tome

39,

aoar

1978,

page

C6-745

CRITICAL

BEHAVIOUR

OF

THE UNIAXIAL DIPOLAR FERROMAGNET

LiHoF,

* i

P. Beauviilain, J.P. Renard, I. ~aursen* and P.J. Walker

I n s t i t u t dlEZectronique Fondamentale, Laboratoire a s s o c i S au CNRS, U n i v e r s i t d Paris-Sud, BBtirnent 220, 91405 Ursay Cedex, France

* ~ e ~ a r t m e n t o f EZectrophysics, Building 322, The Technical U n i v e r s i t y o f Dewnark, DK-2800

,

Lyngby, Denmark

**

Clarendon Laboratory, Parks Road, Oxford, U.K.

Resum6.- On a mesur6 la susceptibilitg magnetique et l'aimantation suivant l'axe facile de LiHoFt, prGs de la temp6rature de Curie : Tc = 1,527 K. La variation thermique critique de la susceptibilite et l'aimantation ii T = TC en fonction du champ sont bien dgcrites par les lois classiques avec les corrections logarithmiques prevues theoriquement pour les ferromagnetiques dipolaires uniaxes. Abstract.- The magnetic susceptibility and the magnetization parallel to the easy axis have been measured near the critical point of LiHoFr : T c = 1.527 K. The critical behaviour of the susceptibility and the field dependence of the magnetization at T = Tc are well described by the classical laws with logarithmic corrections, which are theoretically predicted for uniaxial dipolar ferromagnet S.

LiHoF,is ferromagnetic below Tc = 1.53 K /I/. The easy spin axis is the fourfold c crystal axis. Since in the ground state g// (along c) c 14.1,

g 2 0 / 2 / and the dipolar interactions are about

I

three times larger than the exchange ones, it may be considered as a fairly good uniaxial ferromagnet. Such system is very interesting since it corresponds to ther marginal dimensionality d* = 3. For d = d*, logarithmic corrections to the classical (Landau) behaviour are predicted 1 3 1 . We have tried here to observe this particular critical behaviour by accurate susceptibility and magnetization measurements near Tc. The experiments have been carried on two monocrystalline samples l and 2 grown by the Stock- barger method : l/ a 53.2 mg ellipsoid with its long axis parallel to c and 2 1 a sphere weighting 339.8 mg.

MAGNETIC SUSCEPTIBILITY.- AC susceptibility was measured using a mutual inductance bridge operating at 70 Hz. The amplitude of the AC field was kept as low as 2 Oe. Measurements were done in a superf luid '~e bath. Temperature was electronically stabilized and accurately measured with a germaniwn resistor cali- brated against the 4 ~ e vapour pressure (sensitivity 0.1 mK). The measured parallel susceptibility per gram

~ 7 ,

of .the sample 2 is shown in the figure 1. Below 1.526 K, it reaches a plateau at h a x = (NO)-' where N is the demagnetizing factor and P the crystal density. Close to Tc, corrected from the demagnetizing field effect is well fitted by the theoretically predicted law

xC

=

r

t-'1 log t

1

li3where

Fig. 1 : Experimental parallel susceptibility per gram versus temperature. Full line represents the classical law with logarithmic corrections and das- hed line the power law

xc

= 6.216 X 10-' (t1-I . O S

.

t = (T

-

Tc)/Tc with Tc = 1.5269(6) K , r = 6.19(5) x

10-'. A careful statistical analysis shows that the temperature range of the fit might be limited to 2 X 10-'<t < 1.1 X 10-'

.

The lower limit is related to the rounding of the transition, due to strains or impurities while the upper one is the extension of the critical region.

MAGNETIZATION MEASUREMENTS.- Static magnetizations were measured by a fluxmetric method versus applied field along c up to 2.5 kOe. The isothermal magnetization curves M(H ) displayed on a recorder were systematically studied around and below Tc. Below T,

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the beginning of M(Ho) consists of a straight line until M reaches the spontaneous magnetization M

S'

For M > MS, M(Ho) becomes non-linear ; this allows

the determination of MS(T). For T > Tc, M(Ho) is

non-linear at every field, the maximum curvature

occuring for

T

= Tc. The critical isotherm M(H) at

T a Tc, where H is the effective field in the sample

H

.

-

NV-'M (v sample volume) is shown in the figure 2. Table I _{vely the susceptibility,the critical isotherm and}: Critical amplitudes T, D and B of respecti- the spontaneous ma netization and the universal

ratio

o3

(B' T.

%)-'

of LilloP,

.

Fig. 2 : Reduced critical magnetization M/MS(0) ver-

sus the reduced field h. Full line represents the

theoretical law M D h1l3 llog h

I

'I?

At low fields, H < 300 Oe, M(H) per gram is correctly

fitted by the theoretical law M = D h1/3110g hI1I3

where h is the reduced field H/HN with

%

= 2 kBTc/

gNuB = 3260 G.

The measured spontaneous magnetization per

gram MS(T) is shown in figure 3 and compared to the

theoretical law M S (t) = ~(-t)'/~ Il~g(-t))~'~

.

Since the experimental data were only obtained for I-tl >

1oe2

and were not very accurate close to T C' we could not check the theoretical law and could only determine an approximate value of the critical amplitude B (table I).

DISCUSSION.- The critical behaviour of the susceptibility and the critical isotherm of LiHoF, are well described by the classical laws with logarithmic corrections. The universality hypotesis implies

four universal relations among thermodynamic critical

amplitudes /4,5/. We have determined three critical

amplitudes B,

I'

and D which are consistent with the

theoretical predicted universal ratio : D' (B2

r

%)-l

= 213.

Fig. 3 : Reduced spontaneous magnetization MS(T)/

MS(0) of sample 2 versus temperature. Full 11 e

represe ts the theoretical law MS(T) = B(-t)lP2

I

log

(-t)

1

l 7 3

.

References

/ l / Cooke, A.H., Jones, D.A., Silva, J.F.A., and

Wells, M.R.,

J.

Phys. C,

5

(1975) 4083

/ 2 / Hansen, P.E., Johansson, T. and Nevald, R., Phys.

Rev. B

2

(1975) 5315

~a~ariiio, J. and Tuchendler,

J.,

Physica = B

(1977) 1233

/3/ Larkin, J.A. and Kmel'Nitskii, D.E., Sov. Phys.

JETP

2

(1969) 1123

/4/ Aharony, A. and Hohenberg, P.C., Phys. Rev. B

2

(1976) 3081