THE MAGNETIC ANISOTROPY OF Ni AND THE MEAN FREE PATH OF THE ELECTRONS

HAL Id: jpa-00214004

https://hal.archives-ouvertes.fr/jpa-00214004

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.

THE MAGNETIC ANISOTROPY OF Ni AND THE MEAN FREE PATH OF THE ELECTRONS

K. Hausmann, M. Wolf

To cite this version:

K. Hausmann, M. Wolf. THE MAGNETIC ANISOTROPY OF Ni AND THE MEAN FREE PATH OF THE ELECTRONS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-539-C1-540.

�10.1051/jphyscol:19711181�. �jpa-00214004�

JOURNAL DE PHYSIQUE Colloque C 1, supplement au n° 2-3, Tome 32, Fevrier-Mars 1971, page C 1 - 539

THE MAGNETIC ANISOTROPY OF Ni AND THE MEAN FREE PATH OF THE ELECTRONS

K. HAUSMANN and M. WOLF

Zentralinstitut fur Festkorperphysik und Werkstofforschung. Dresden, DDR

Résumé. — On avance l'hypothèse, que l'anisotropie magnétique de Ni dépend fortement du libre parcours moyen des électrons. En adoptant cette hypothèse, il suit de la règle de Matthiessen sur le libre parcours moyen que dans le K\

les dépendances de la température et de la concentration se factorisent, ce qui est en bon accord avec les données expé- rimentales obtenues pour^NiCu et J^iMo. Ainsi les dépendances de la température et de la concentration extrêmement fortes qu'on observe pour les Ki des alliages riches en nickel, se montrent étroitement liées l'une à l'autre.

Abstract. — The hypothesis is proposed, that the magnetic anisotropy of Ni depends strongly on the mean free path of the electrons. Using this hypothesis the Matthiessen rule for the reciprocal mean free path leads to a factorization of K\ with respect to its temperature and concentration dependence. This is in accordance with measurements on NiCu and NjMo. The anomalously strong dependences on temperature and concentration of K\ in nickel rich alloys are thus connected with each other.

There are some peculiarities of the magnetic aniso- tropy of Ni which suggest the supposition [1, 2] of a strong dependence of the anisotropy of Ni on the mean free path (mfp) of the electrons :

1. The dependence on purity. — Two samples with the resistance ratios ^273/^4.2 ⁼ 610 and 230 exhibit according to Franse [1] essentially different torque curves at low temperatures. The sample with the lower purity has a value of | Kt | which is about 25 % less than that of\K^t | for the pure nickel. A similar reduction of \KX | by impurities has been found by Hofmann [3].

2. The dependence on concentration. — All kinds of alloying metals (Me = Cu, Mo, V, Co, Fe) reduce the anisotropy of Ni. This reduction is anoma- lously strong. One iron atom compensates e. g. the contribution of ten nickel atoms.

3. The dependence on temperature. — Kt of Ni decreases much faster with increasing temperature T than expected from the magnon part of the tem- perature dependence. Thus K1V, defined by

K(T) = K1V(T). I ^ g - j , T<d (1)

for temperatures much lower than the Curie tempera- ture 0, decreases rapidly with increasing temperature (M = spontaneous magnetization).

The aim of the present paper is to compare the working hypothesis of a strong dependence of the anisotropy of Ni on the mfp of the electrons and its consequences in more detail with experimental data.

For small concentrations c^t < 1 and low tempera- tures r < ^ 9 we use the following formula

K^iV(T,cⁱ)KK^lv[rⁱ(T,cⁱ)~]. (2) It is not easy to prove experimentally, whether (2) is

correct or not, since (2) cannot be understood physi- cally, unless X is interpreted as the real mfp of the electrons, connected with the uncertainty of the qua-

simomentum of the electrons Ak and defined by the uncertainty relation

XAk = 1 . (3) Hence A- 1 is obtained from the differential cross

section <r(9) by a simple integration with respect to the scattering angle &

A- 1 ~ f"d9sind(T(a). (4)

•> 0

On the other hand the « mean free path » / following from the resistivity is given by

r¹ ~ \ d9 sin 9(1 - cos9)<r($). (5)

J 0

Therefore, at low temperatures the real mfp X must be much shorter than the « mean free path » / connec- ted with resistivity.

To circumvent the difficulties mentioned above we use Matthiessen's rule for the reciprocal mfp in order to test the hypothesis (2). Since the scattering of the electrons by impurities and elementary excitations is incoherent, the differential cross sections, are additive.

Thus it is possible to divide the reciprocal mfp of the electrons in nickel rich alloys NiMe for small concen- trations Ci -4 1 into a temperature dependent «ideal » part and a part depending only on the concentrations

^jMeCT, C,:) = X^(T) + AM^C.) • (6) The temperature dependence of Xfy calculated using

Kt{T) of [4] and M(T) of [5] can be described accord- ing to figure 1 by the following empirical formula

K1N4(T) = K1( 0 ) e -( r / r°) 3 / 2 . (7) We interpret (7) in accordance with the hypothesis (2)

as

Kiva-l)=K1(0)e-"X (8) with y as an unknown but temperature and concen-

tration independent length. From (6) and (8) the fol-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711181

C 1

-

t

tj? TO

s

mh h 6.0-

a ⁹

?$ .p ^5.0

'E

d. ^h h 5.0

4.0 m

1 2 3 4 5 P

( T / I O O ~ K ) % - \ k-

FIG. I. - Temperature dependohce of the first magnetic ani-

2

sotropy constant of Ni in the magnon vacuum state.

lowing temperature and concentration dependence 3.0

of K,, in =Me is obtained ^{1 2 3 I 5 6 7}

( T / ~ O O ~ K )

4 -

KFMe(T, ci) = K~;(T) e-yf"e(ci)

.

Since is proportional to the concentrations of the alloying atoms the following expression for the anisotropy constant of nickel rich alloys is obtained finally

K?~"(T, ci) = K?(T).

x exp

[- ²

^.

S I 2 3 4 5 6

For low temperatures and small concentrations (10) ^{c / a t % Mo - - - -} can be simplified to

FIG. 3. - Dependence of K I on the concentration of Mo K?M'(T, ci) = K:~(T) exp

(- 7

It was shown in [3] by comparing the temperature dependence of K, for nickel samples of different purity (99.9 % and 99.99 % Ni), that it is possible to fac- torize K1 into a purity dependent factor and a factor depending only on the temperature. The purity depen- dent factor decreases with increasing content of impu- rities. These observations are clearly in accordance with (I I).

The measurements done by Williams and Bozorth [6]

on NiCu show, that the factorization of the tempera- ture and concentration dependence of K1 isfulfilled experimentally up to 24 % Cu. The same holds for the predicted exponential form of the concentration dependence. Eq. (11) is in accordance with experi- ment also for NiMo as is obvious from figure 2 and figure 3.

Thus using the hypothesis of a strong dependence of the magnetic anisotropy of Ni on the mean free

path of the electrons it is possible to unterstand, why NiCu and X M o exhibit the same temperature depen- -

dence of K, as pure Ni. An exponential decrease of the anisotropy with increasing concentrations of alloying metals is predicted and confirmed by experi- ment. Furthermore the extremly strong temperature dependence of K , in Ni implies an analogously strong dependence on concentration in nickel rich alloys. A microscopic foundation could be based either on the band model [8] or on the s-d-exchange model. In the frame of the latter model it is possible to unters- tand qualitatively the exponential form of the depen- dence of the magnetic anisotropy constant of Ni on the mean free path of the electrons.

Acknowledgments. - The authors wish to thank M. Bernhardt, Prof. G. Heber, Dr. H. Hemschik and Prof. U. Hofmann for their helpful discussions.

References

[I] FRANSE (J. J. M.) and DE VRIES (G.), Physica, 1968, [5] KAUL (R.) and THOMPSON (E. D.), J. Appl. Phys.,

39, 477. 1969, 40, 1383.

[2] HAUSMANN (K.), Phys. Stat. Sol., 1970, 38, 809. [6] WILLIAMS (H. J.) and BOZORTH (R. M.), Phys. Rev., 1939, 55, 673.

[3] HOFMANN Phys. Stat. (u.), HANDSTEIN Sol., 1970, (A.) 40, and HAUSMANN K81. (K.1, _{[7] HOPMAW} and WOLF (u.), BERNHARDT (M.), to be published. (M.), HAUSMANN (K.) [4] HOFMANN (U.), private communication. [8] MORI (N.), J. Phys. Soc. Jap., 1969, 27, 307.