ANISOTROPIC MAGNETIZATION OF NICKEL AT LOW TEMPERATURE

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ANISOTROPIC MAGNETIZATION OF NICKEL AT LOW TEMPERATURE

G. Aubert, P. Escudier

To cite this version:

G. Aubert, P. Escudier. ANISOTROPIC MAGNETIZATION OF NICKEL AT LOW TEMPERATURE. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-543-C1-544.

�10.1051/jphyscol:19711183�. �jpa-00214006�

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JOURNAL DE PHYSIQUE Colloque C I , suppl6ment au no 2-3, Tome 32, Fe'vrier-MarSI971, page C 1 - ⁵⁴³

ANISOTROPIC MAGNETIZATION OF NICI(EL AT LOW TEMPERATURE

G. AUBERT and P. ESCUDIER

L. E. P. M., C. N. R. S., Grenoble, France

R6sumB. - Nous avons ktudi6 par mesure de couples de 4,2 OK A la tempkrature ambiante l'anisotropie de l'knergie et de l'aimantation du nickel. La prkision relative des mesures de l'anisotropie de l'knergie est meilleure que 10-4. Les anisotropies intrinskques de l'knergie ( M a = Ee. < 111 > - Ea < 100 >) et de l'aimantation

(AM = M < 111 > - M < 100 >) sont indkpendantes du champ pour les champs internes supkrieurs a 10 kOe. La

variation de AEa avec la tempkrature est monotone mais beaucoup plus rapide qu'une ^Kloi en puissance dix ¹⁾alors que AM passe par un maximum dans cette gamme de tempkrature et ne s'annule pas a 0 OK (AM - ^0,lu. e. m./cm3 21 4.2 OK).

- .,- --,-

Les possibilitbs d'interprktation thkorique de ce comportement sont envisagkes.

Abstract. - The anisotropy of energy and magnetization of nickel has been studied by a torque method from 4.2 OK to room temperature. The anisotropy of energy was measured as a function of field and temperature with a relative accuracy better than 10-4. The intrinsic anisotropies of energy (AEa = Ea.< 111 > -Ea. <I00 >) and magnetization ( A M = M < 111 > - ^M< 100 >) are found to be field ~ndependent for internal fields higher than 10 kOe. .AEa varies monotonously with T much faster than a ⁽⁽tenth power law ⁾⁾whereas AM goes through a maximum in thls temperature range and does not vanish at zero OK (AM - ^0.1^e.^m.^{u./cm3 at}^{4.2 OK).}

Further theoretical developments for the interpretation of such a behavior are proposed.

As already published [I], the free energy of the unit volume of a spherical single crystalline ferroma- gnetic sample can be written in the form

H is the applied field and we call E, the magnetocrystalline anisotropy energy.

I. Experimental method of measurement. - The torque exerted by the sample on the torquemeter is measured as a function of the direction of the applied field, with five significant figures for the maximum measurable torque. All the results presented here are taken from measurements in the { 110 ) plane of the sample. In the (Oil) plane, let @ be the angle of the applied field with the [loo] axis and 8 be the angle of the magnetization vector of the sample (uniformly magnetized) with the same axis. The measured torque

r(@) is related to H, M and F by

r(@) ⁼^{HM sin}^(@ ^-⁸⁾⁼^-dF _ae (2) at constant H (applied field) and T (temperature). By a numerical method, we get from 72 values of the torque taken for @ = i ?h 7c (0 < i < 35) at given H and T, the Fourier expansion of the torque as a function of @ and 8. The table 1 shows two examples of the results of this procedure at liquid helium temperature with two different values of the applied field (the internal field Hi = H - 7 ^Mis quoted as HH

are still significant for P higher than 18. So a pheno- menological expansion of the anisotropy energy using spherical harmonics or direction cosines of the direction of the magnetization must imply more than 8

ct anisotropy constants ^D.Contrary to the method used by J.-J.-M. Franse [2], it is not necessary, with our procedure to fix a priori neither the number of constants involved in such an expansion nor its form, this number must only be smaller than or equal to 16 (for we take 72 equidistant points of the curve).

We shall discuss elsewhere the problem of the form to be given to the expansion and limit ourselves to the differences in free energy (AF), magnetocrystalline anisotropy energy (AE,) and magnetization (AM) between the two directions of highest symmetry in a cubic crystal, namely < ¹⁰⁰> ^and< ¹¹¹>.

11. Variation with temperature and field of A, AE, and AM. - One can get

A F = I ; < 111 > ^-F < 100>

from both the experimental series as functions of @ and 8, because 8 = @ for symmetry directions. Indeed let 8, = @, be the angle between [loo] and [ I l l ] in the (071) plane :

Changing the variable 8 into @, we get through relation (2) :

d

on the table). The first column is the order P of the and the second integral in (5) vanishes because Fourier coefficient of the expansion r(0) = r(G3) = 0. As a checking of our numerical method for calculating the DpYs from the Bp9s, AF is

r ⁼ Bpsin P@ = Dpsin P8 (3) calculated by using @ and 0, and the results are res-

P P pectively quoted as E and F i n table I : the agreement Bp and Dp being measured with the same arbitrary is perfectly satisfactory within our experimental unit. At liquid helium temperature, the coefficients Dp accuracy.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711183

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G . AUBERT AND P. ESCUDIER

22 8.85 - 1.79 22 3-38 - .61 FIG. 2. - Variation with temperature of BEa and AM.

24 5.20 - ^2.80 ²⁴ ^5.36 - 1.89

TABLE I

Fourikr expansions of the torque in the { 1 10 } plane at 4.2 O K

- 3

T H HH T H HH -

4.20 19 179 16 981 4.20 12495 10297

P BP DP P BP DP

- - ⁷ - - - ^;^* ^2-

2 -4 935.31 -5 194.45 2 -4 780.95 - 5.186.95 -O

4 - 7 553.66 - ^{7 485.81} ⁴ - ^{7 528.95} - ^{7 472.96}

6 - ^1081.90 - 457.49 6 - 1 352.81 - 453.51 '

8 - 774.57 - 29.45 8 - 1 162.51 - ^25.79 '

10 - 194.65 38.33 10 - 388.76 39.28 12 - ^98.10 ^37.03 ¹² ^-^264.55 ^37.47

14 - 15.76 26.97 14 - 104.55 27.06

At a given temperature AF is found to vary as a linear function of Hi for internal fields higher than 10:,kOe (see Fig. 1 for T = 4.2 O K ) . Thus it follows from reference [l] that AF = AE, - ( A M ) Hi (6) with field independent AE, and AM.

- A E ~

-

7

^AM ^{4 3}⁹²₄₁

^*!

^I:⁴^I^:

I I I

10 12 14 16 18

INTERNAL FIELD [ K i L o a R s r E D l

FIG. 1. -Variation with field of A F at 4.20K.

16 3.13 16.36 16 - 58.06 16.54 0 100 200 300

18 12.61 7.71 18 - 18.71 8.24 TEMPERATURE (KI

20 11.84 1.74 20 - 5.14 2.54

The variations of AE, and AM with temperature from 4.2 ^O^Kto 273.15 OK are shown on figure 2. The possible error on AM is very difficult to evaluate for a drift in temperature can be interpreted as a variation with the field (in the worst case 1 OK gives the same variation of F as 10 kOe) : in our experiments, tempe- ratures are kept constant during several hours within 0.01 OK.

111. Interpretation of the results. - The behavior of AE, and AM as functions of the temperature (Fig. 2) cannot be interpreted by any of the theoretical models proposed till now. AE, does not follow a power law and if one tries to fit the experimental results with a power law, the less poor adjustment gives a power far higher than 10. The order of magni- tude and the thermal variation of AM cannot be accounted for by the model of E. R. Callen and H. B. Callen [3], particularly the rather large value at 0 "K (- 0.1 e. m. u./cm3). In the model that we proposed previously [I] on the basis of higher temperature and lower field measurements, the anisotropic magnetization AM should increase regularly as T decreases to zero. The low temperature results presented here make it necessary to improve this model. We think that only one part of the anisotropic magnetization is of orbital origin while the other part is a contribution of the spin system. To carry out further calculations and adjust some parameters we need accurate measu- rements of the g and g' factors as functions of the direction of magnetization and temperature. Measu- rements of 6; by resonance methods seem suitable for the first purpose at a given temperature but it seems to us that thermal variations of the magnetomechanical ratio g' with temperature would be easier to analyse than that of g.

A theoretical calculation of AE, appears to be a still more difficult problem, specially because the contribution of entropy terms to the free energy may be important.

Finally the calculation of the anisotropic magnetization in the model proposed by W.-N. Furey [4]

would be an excellent test for the validity of this new model.

References

[I] AUBERT (G.), J. A. P., 1968, 39 (Part I), 504-510.

[2] FRANSE (J. J. M.), thesis, Amstei-dam, 1969.

[3] CALLEN (E. R.) and CALLEN (H. B.), J. Phys. Chem.

Solids, 1960, 16, 310.

[4] FUREY (W. N.), thesis Harvard University, Cambridge 1967.