HAL Id: jpa-00214337
https://hal.archives-ouvertes.fr/jpa-00214337
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.
CONCENTRATIONAL DEPENDENCE OF THE MAGNETIZATION OF SOME TRANSITION-METAL
ALLOYS
S. Sidorov, A. Doroshenko, S. Dubinin
To cite this version:
S. Sidorov, A. Doroshenko, S. Dubinin. CONCENTRATIONAL DEPENDENCE OF THE MAGNE- TIZATION OF SOME TRANSITION-METAL ALLOYS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-870-C1-871. �10.1051/jphyscol:19711306�. �jpa-00214337�
JOURNAL DE PHYSIQUE Colloque C 1, supplbment au no 2-3, Tome 32, Fbvrier-Mars 1971, page C I
-
870CONCENTRATIONAL DEPENDENCE OF THE MAGNETIZATION OF SOME TRAN SITION-METAL ALLOYS
S. K. SIDOROV, A. V. DOROSHENKO, S. F. DUBININ Institute for Metal Physics, Sverdlovsk
RCsumC. - Le changement de l'aimantation dans des alliages de differentes compositions est explique par un mkanisme d'orientation apparaissant comrne le rbsultat de la competition entre les interactions d'echange positives et negatives entre paires d'atomes voisins. Les formules pour le calcul de (c) sont Btablies. Les resultats des calculs de fi (c) sont compares avec Ies valeurs experimentales pour les alliages Mi-Mn, Ni-Fe et Pt-Mn.
Abstract. - The magnetization changing upon the alloys contents is explained by orientation mechanism rising as a result of competition of negative and positive exchange interactions in the pairs of the nearestbour atoms. The formulas for calculation of ,ii(c) are adduced. The results of calculation of p(c) are compared with the experimental data for Ni-Mn, Ni-Fe and Pt-Mn alloys.
A peculiar dependence of saturation magnetization at O°K upon the contents of alloy is observed in Ni-Mn, Ni-Fe, Pt-Mn and some other alloys. When the second component increases the magnetization increases approximately linearly, then its increase lessens and then after achieving the maximum value it rapidly decreases and at some concentration goes to zero. This behaviour of magnetization may be explained by changes in electron structure of atoms and the resulting lessening of atomic magnetic moments of the components. But such an explanation meets some obstacles.
Another and more natural explanation, as it seems to us, may be proposed if one takes intoaccount that exchange integrals of these alloys yield to the condi- tion :
J l l > O , J 1 2 = J21 > O , J 2 2 < O ,
where Ni and Pt atoms are denoted by index I and index 3 refers to Mn and Fe atoms. When atomic magnetic moments are considered as classic vectors the two contrary tendencies of their orientation will increase with the increasing of the second component in the alloy. On one hand atoms of the first and the second types will tend to orientate their moments parallelly to one another for J , , > 0 and J,, > 0. On the other hand an opposite tendency to an antiparallel orientation will increase for J,, < 0 and J,, > 0. As a result of these two contrary tendencies there should appear inhomogeneous noricolinear magnetic structure with the variable in the alloy volume local magnetiza- tion. The average magnetic moment per atom of alloy will be determined by vector sum of all atomic magne- tic moments. At a certain concentration co whose value depends upon the relation of absolute values J , , , J12 and J,, and upon the nearest environment the average magnetic moment per atom of alloy equals to zero. The more the ( J2, I and more the probability of neighbouring of atom of the second type by atoms of the same type-P,, the less co. Probability P22 in general case of arbitrary state of order is defined by the concentration, long-range order degree and corre- lation parameters of the alloy.
On the basis of these considerations the following formula for average magnetic moment per atom of alloy at 0 OK had been derived [l-31 :
where p , and p, are the atomic magnetic moments of the alloy component ; c is the concentration of atoms of second type ; z is the first lattice coordinate num- ber ; P,, = 1 - P,,. Functions 1.,(P2,) and ?,2(P22) as it was shown in the papers [2,3] may be expressed as :
where P;I and P : ~ are the values P2, and PZ2 at c = co and P,(n, P,,) is the probability of atom 2 to be surrounded by n = 0, 1, 2, ... z atoms 2 and in the absence of correlation in the alloy the binomial distri- bution satisfys the relation
The first two terms in formula (1) give the concen- trational dependence of the average magnetic moment of the alloy upon the mere replacement of atoms of the first type by atoms of the second type when there moments are parallel. The third term describes the decreasing of the average magnetic moment for non- colinearity of magnetic structure increases when the concentration of atoms of the second type increases.
The magnitudes in the formula for the average magnetic moment depends upon c, (the concentration when the average magnetic moment is equal to zero).
Therefore for using of our formula it is necessary to know this concentration from experiment. In the papers [I-41 it was shown that a local perturbation of spin-system decreasing average magnetic moment appears when the number of the second type neigh- bours of an atom of the second type is not less than a certain number x.
On the figure 1 and figure 2 and figure 3 there are shown the calculated concentrational dependencies of the average magnetic moment and the experimental data for Ni-Mn, Ni-Fe and Pt-Mn alloys. In all calcu-
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711306
CONCENTRATIONAL DEPENDENCE O F THE MAGNETIZATION O F SOME TRANSITION-METAL C 1
-
871lations it had been assumed that atomic magnetic moments did not depend upon an alloy concentration.
FIG. 1. - Concentrational dependence of ji for Ni-Mn alloys for different degrees of long-range order. The calculated curves (solid lines) and experimental data. Light symbols correspond to the disordered state, dark symbols (and x ) - to the ordered
state.
On figure 1 there are shown the calculated jI(c) for Ni-Mn alloys with different degrees of long-range order. Experimental values of the average moment having been brought to zero temperature are also shown here. As it is seen the curve for completely disordered alloy is in good agreement with experiment.
The comparison of experimental values of the average magnetic moment for ordered alloys with calculated curves allow us to draw certain conclusions about the degree of order in the alloys [2, 51.
On figure 2 there are shown the calculated curve and experimental data of F(c) for disordered Ni-Fe alloys. As it is seen the agreement is rather well.
On figure 3 there are shown the calculated curve for p(c) and experimental data for completely ordered Pt-Mn alloys. In the region of y-phase existence the calculated curve concords with experimental data rather well [6].
These results allow us to draw a conclusion that atomic magnetic moments in the above mentioned alloys practically are not changing. Desorientation of atomic magnetic moments due to exchange interaction of the opposite signs plays obviously the main role in explanation of concentrational dependence of magne- tization.
Because of the short-range character of these inter- Refere [l] SIDOROV (S. K.) and DOROSHENKO (A. V.), Fiz. Metal-
lov i Metallovedetzie, 1964, 18, 81 1.
[2] SIDOROV (S. K.) and DOROSHENKO (A. V.), Fiz. Metallov i Metallovedenie, 1965, 20, 44.
[3] SIDOROV (S. K.) and DOROSHENKO (A. V.), Phys.
stat. sol., 1966, 16, 737.
at?'. Fe FIG. 2. - Concentrational dependence of ,E for disordered Ni-Fe alloys. Solid line corresponds to the calculated data,
symbols -- to the experiment.
0 20 25
30
3540
4550
at'6 Mn
FIG. 3. - Concentrational dependence of for completely ordered Pt-Mn alloys. Solid line corresponds to the calculated
curve, symbols -- to the experimental data.
actions the statistical fluctuating environment of atoms gives rise t o inhoinogeneous magnetization in micros- copic scale. It should be expected that it would influence on neutron scattering. In reality, we obtained from experiment that invar Ni-Fe alloys had anormal small, angle magnetic neutron scattering.
[4] SIDOROV (S. K.) and DOROSHENKO (A. V.), Fit. Metal- lov i Metallovedenie, 1965, 19, 785.
[5] SIDOROV (S. K.) and DOROSHENKO (A. V.), Fiz. Metal- IOV i Metallovedenie, 1965, 20, 850.
[6] SIDOROV (S. K.) and DUBININ (S. F.), Fit. Metallov i Metalloveder~ie, 1968, 26, 503.
