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Submitted on 1 Jan 1971
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MAGNETIC HYPERFINE FIELDS IN ALLOYS OF NON-TRANSITION ELEMENTS WITH IRON
G. Trumpy, E. Both, K. Sørensen
To cite this version:
G. Trumpy, E. Both, K. Sørensen. MAGNETIC HYPERFINE FIELDS IN ALLOYS OF NON- TRANSITION ELEMENTS WITH IRON. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-779- C1-780. �10.1051/jphyscol:19711272�. �jpa-00214104�
EFFET MOSSBAUER DANS LES ALLIAGES
MAGNETIC HYPERFINE FIELDS IN ALLOYS OF NON-TRANSITION ELEMENTS WITH IRON
G. TRUMPY, E. BOTH, K. S0RENSEN Laboratory of Applied Physics, Technical University
of Denmark, Lyngby, Denmark
R6sumB. - On fait une revue des donnks existant sur les champs hyperfins agissant sur les noyaux de fer dans des alliages de fer avec des klkments ne faisant pas partie de la skrie des klkments de transition. On y inclut de nouvelles donnkes sur les systkmes FeSn et FeSb obtenues par notre groupe. Les champs h. f. varient plus rapidement que les moments magnktiques. Le champ h. f. moyen est donn6 de manikre prkcise par une formule simple contenant uniquement les nom- bres de coordination des premiers voisins.
Abstract. - A compilation is made of the existing data for magnetic hyperfine fields at iron nuclei in binary alloys of iron with nontransition elements, including some new data on the Fe-Sn and Fe-Sb systems obtained by the present group. The h. f. fields vary more strongly than the magnetic moments. It appears that the average h. f. field is given quite accurately by a simple formula containing only nearest neighbour coordination numbers.
Introduction. - I n a study of the h. f. fields in iron-tin alloys we have observed that these fields are not in general proportional to the magnetic moments of the iron atoms, as is often assumed. This view is confirmed by reports on several other alloy systems.
In fact, the h. f. field at the iron nucleus tends to be less sensitive to alloying than the magnetic moment.
The present paper is concerned with the observa- tion that the h. f. magnetic field a t the Fe nucleus, He,,, is to a high approximation a simple function of nearest neighbour coordination, when the other alloy component is a nontransition element. This observa- tion may be of some value for the description and interpretation of ferromagnetic phenomena in general.
Ordered alloys. - In Table I are listed data of some binary iron-containing compounds, for which Mossbauer-effect measurements exist. These com- pounds are intermetallic in the sense that chemically equal atoms are roughly as closely associated with each other as are unequal atoms. The average nearest
neighbour coordination numbers, NFeFe, being the no. of n. n. Fe atoms, and zFe,,, being the total no.
of n. n. atoms, are given. ~f we form the ratio RFeFe/
%g,n, and plot it versus the experimental He,, figure 1 is obtained. The points all lie quite close to a straight line through the origin, which is given by
/ B ~ R Icalc = 120 N F ~ F ~ I ~ K , , k g a u s ~ . (1) As is well known, the greater part of He,, in Fe is caused indirectly by d-s exchange interaction [8].
This interaction favours parallel alignment of s and d electron spins. The negative h. f. field at the nuclear site is thus the result of a compensating distribution of negative s electron spin in regions where the d electron spin density is low. In ferromagnetic Fe-X compounds, where X is a nontransition element, the Fe-X bond will represent a low spin density, since the Fe-X-Fe bond generally favours antiferromagnetism.
Thus, one may say that the more X neighbours, the more space there is for the negative s electron spin
Average magnetic h. f. field at Fe,nuclei in binary compounds with non-transition elements
- -
Compound Magnetic Struc- I B I
N ~ e ~ e N~e,n [E:($ 1
zepp
I obs Referenceorder ture in kgauss in kgauss
Fe,Sn Fe,Ge Fe, Ge Fe,Sn, Fe,Ge, FeSn FeGe Fe1.1,Sb Fe,Si Fe3A1 Fe4N FezB
F bcc 8 8
] bcc
F 5.33 8
F sc 6 7.5
F D:: 7 11
340 (definition)
277 277 207 152 101 226 264 252
This work [21 I21 This work This work [31 This work 141
151 [51 I61 171
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711272
C 1 - 780 G . TRUMPY, E. BOTH, K. SDRENSEN
FeSn/ FeGe
FIG. 1. - Magnetic h. f. fields at the Fe nucleus in intermetallic compounds of iron with nontransition elements. The nearest- neighbour function on the abscissa is defined in the text.
distribution, and I YS1(0) l2 - l!PSt(0) I2 becomes com- paratively smaller. No calculations have been made of this effect, since all theories till now were concerned with a spherically symmetric d electron polarization.
If one considers a given overall lattice structure so that NFe,, is constant while NFeFe can be varied, it is intuitively easy, as in effective field theories, to accept the proportionality between Heff and NFeFe. This proportionality was directly observed by Stearns [9]
for one definite Fe site in ordered Fe-Si alloys.
Eq. (1) concerns the average fields and coordination numbers of an alloy. We have not found a correspon- dingly simple connection between h. f. fields on diffe- rent types of Fe sites in one compound. However, it seems to be a well-established rule that the ratios of single site h. f. fields are equal to the magnetic moment ratios.
Disordered alloys. - For the general case we now assume that the h. f. field in atom Fe' is a function of two main factors : (1) the no. of n. n. Fe'-Fe bonds, being NFe,Fe, and (2) the relative average no. of d electrons taking part in Fe-Fe binding, given by NF~F~,~/NF~,,,. We see that if this product is given the exponent 112, it contains eq. (1) above. For the general case, we tentatively write
where NFeFe,g is the general, or average, no. of Fe-Fe coordinations in the alloy.
Accordingly, an iron-alloy with a dilute nonmagne- tic component would have Heff(Fe) K NF,,~,". It is well known that Mossbauer-spectra obtained from such alloys show field components Ha, HI and Hz caused by 0, 1, and 2 nearest neighbour impurity atoms [lo], [ll]. Our formula gives for these cases
Experimental values exist for Al, Si, Ga, Sn, and Sb dissolved in Fe, which give h(') ranging from 6.0 to 8.0 % and h(2) -- 2 h('). For transition elements dis- solved in Fe, h(') is of a similar magnitude, from 4.3 to 8.6 %.
Another possible use of eq. (2) is given by FeS, which has not intermetallic binding, but each Fe is bound by superexchange to 6 other Fe atoms in the c-plane [12].
In FeS,,, one observes a disordered arrangement of vacancies among the Fe-atoms. When one neighbour vacancy gives H I , one finds experimentally
h'l' = (H, - Hl)/Ho = (9.0 + 0.5) %
while eq. (2) gives
Predictions. - On the basis of these syste- matic trends we are now able to make a couple of predictions. For Fe2As, which has typical intermetallic - bonding, the coordinations are NFeFe = 6 and zFe,, = 10.5, giving a calculated value 1 Be,, I = 222 kgauss. In the compound Fe,P the exact coordination numbers are difficult to specify, so the prediction is more uncertain - - : NFeFe S 10andNFe,P = 3, giving I He,, i Z 330kgauss.
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