ANISOTROPIC MAGNETIZATION IN Zn2Y

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ANISOTROPIC MAGNETIZATION IN Zn2Y

C. Voigt, M. Alker, K. Hempel

To cite this version:

C. Voigt, M. Alker, K. Hempel. ANISOTROPIC MAGNETIZATION IN Zn2Y. Journal de Physique

Colloques, 1971, 32 (C1), pp.C1-857-C1-858. �10.1051/jphyscol:19711300�. �jpa-00214331�

JOURNAL DE PHYSIQUE

Colloque C 1, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 857

ANISOTROPIC MAGNETIZATION IN Zn2Y

C. VOIGT, M. ALKER and K. A. HEMPEL

Institut fiir Angewandte Physik der Universitat Miinster, Germany

RBsumB. -

On a mesure le couple d'anisotropie sur un monocristal de ZnzY (Zn2BazFel2022) entre 22,5 OC et le point de Curie jusqu'a H

16 kOe. Le couple maximal Tmax depend presque lineairement de H pour H

9 kOe.

D'apr6s Schelleng et Rado on peut kcrire pour les petites valeurs de M I (composante anisotrope de l'aimantation) T,,, - ^{- V(K1.--}

^V

volume de l'Bchantillon. La premi6re constante d'anisotropie K I decroit de - 7,9 x x

erg cm-3 a 22,s OC jusqu'a

OC. Les variations de MI avec la temperature sont faibles (MI - ^{5,s G a 22,5 OC).}

Les valeurs de la rigidite magnetique (couple/radian) mesurkes 22,5 OC confirment les resultats des mesures du couple.

Abstract.

- Torque measurements were performed on a single crystal of Zn2Y (ZnzBazFe12022) between 22,s OC and Curie point up to H

kOe. The maximum torque Tmax depends almost linearly on H for H

9 kOe. According to Schelleng and Rado one has for small values of MI (anisotropic part of the magnetization)

Tmax

-V(KI - MlH)

V

sample volume. The first order anisotropy constant K1 decreases from

x

erg cm-3 at 22,5 OC to

at

Ml varies slowly with temperature (MI -- ^{5,5 G} at 22,5 oC). Measurements

the magnetic stiffness (torquelradian) at 22,5 OC confirm the results of the torque measurements.

Anisotropy of magnetization has been determined in many cases directly by magnetization measure- ments. However, torque measurements have proved to be a valuable method as well, especially when the anisotropy was small. As a consequence of non- isotropic magnetization the torque maximum, at high fields usually assumed to be constant, will change with increasing field. Although this effect can easily be measured the evaluation of the anisotropic part of the magnetization is not as easy and usually requires extensive numerical calculations. In this paper we report on torque measurements on Zn,Y between room temperature and Curie point. Approximate formulae are used for the interpretation of the expe- rimental data in order t o get a rough estimate for the magnitude of the anisotropy of magnetization.

The ferrite Zn2Y (Zn2Ba2Fe12022) has hexagonal crystal structure. At zero applied field the magne- tization lies in an easy n plane perpendicular to the c-axis as has been shown by resonance measure- ments (Verweel [I, 21). At room temperature the anisotropy can be described using only a first order constant of anisotropy Kl -- ^{- 1,l x lo6 erg ~ m - ~}

(Agapova 131). The very weak sixfold anisotropy in the easy plane [2] will be neglected.

Following Schelleng and Rado [4] we write for the free enthalpy E of the sample

V

volume of the sample

HM

H cos 8

H

exter- nally applied field

8

angle between the magne- tization and the field direction

8,

angle between the c-axis and the field direction. KO,, M,,

K1 and M1 are independent of H and isotropic. It is assumed that the sample is in the single domain state. M1 repre- sents the anisotropic part of the magnetization M :

M

M, + ^xHM

M I sin2 (8, + 8). (2)

(*)

Present address

Institut fiir Werkstoffe der Elektrotech- nik, Technische Hochschule Aachen, Germany.

The torque exerted by the field on a sample which is rotated about an axis perpendicular to the field direction and to the c-axis can be written as

T

- V(K1 - M1 HM) sin 2 (8, + ⁸⁾ . (3) For not too large values of M I the torque has its maximum a t 8,

450

8

00, so that

Tmax - V(Kl - M I H ) . (4) We have used this equation to obtain a formal descrip- tion of our experimental results.

The single crystal investigated had spherical shape, the deviation of the diameter from its average value of 1.25 mm was smaller than 1 %. The measurements were carried out with a non-compensated torquemeter.

As can be seen from figure 1 T,,, depends linearly on H in the high field region. Using (4) for H 2 9 kOe we obtain approximate values for K , and M1 which are shown in figure 2. Kl varies strongly with tempe- rature t, in contrast to M I , and becomes zero when t is equal to the Curie temperature [2]. The results for K, agree sufficiently well with those obtained by magnetization measurements on oriented polycrys- talline material (Belov [5]). Defining Kl,

- M I H as the field-dependent fraction of the total anisotropy constant Ki

Kl - M I H , we have at t

75 OC KIH

- 7 x lo4 erg ~ m ( H - ~

10 kOe).

The fact that I K,, I is much smaller than the value given in [5] is probably caused by the approximations made in evaluating the constants from the experi- mental data.

The difficulty of determining Kl and M1 arises because 9 in general cannot be calculated explicitly as a function of 8,. This can be overcome by per- forming measurements a t a known and fixed value of 8. An easy way t o do this is to keep 9, constant at O0 or 90°. In the first case

is equal to zero for all values of H, in the second case only for H 2 - 2 K1/Mo.

Since the torque is also zero in these positions we consider its derivative, the magnetic stiffness

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711300

C 1

-

FIG. 1.

-

Assuming only E to be a function of HM and

8, + 0, one can show that

in case that 8

00. Using (1) we thus get for 8,

O0

c - l = v-1

{ C2 (Kl - MI

+

+ [HMO + X H ) I - - ~ ) (6)

FIG. 2.

-

and for 8,

900 :

The magnetic stiffness was measured at room tem- perature using the torsion pendulum method (Voigt [6]).

From measurements a t 8,

00 and

900 we obtain K ,

- 8.45 x lo5 erg ~ m

- Mo ~

201 G

M I

5.9 G ; x

0.4 x

The values for Kt and M I agree well with those from the torque measurements. The small discre- pancies may be due to the fact that demagnetizing effects have been neglected. Furthermore, the field dependence of T,,, at high fields is not exactly linear so that the value for M I is only an approximate one.

We assume that experiments at very high fields, currently in progress, will reveal more detailed information.

Acknowledgements. -";The authors are indebted to Dr. W. Tolksdorf (Philips Forschungslaboratorium Hamburg) who kindly provided the single crystal sample.

References

[I]

VERWEEL (J.), J. Appl. Phys., 1967,

[4] SCHELLENG (J. H.), RADO

T.), Phys. Rev., 1969, [2] VERWEEL (J.), Philips Res. Rep. Suppl,

9. 179, 541.

[5] BELOV (K. P.), KOROLEVA (L. I.), MITINA (L. P.),

AGAPOVA

N.), PEREKALINA (T. M.), SOV. Phys.- Sov. Phys.-Sol. State, 1969, 10,

Sol. State, 1968, 9 , 1825.

VOIGT

Angew. Phys., 1969,26,160.