MÖSSBAUER STUDY OF MAGNETIC ORDERING IN AMORPHOUS Fe-Si ALLOYS

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MÖSSBAUER STUDY OF MAGNETIC ORDERING

IN AMORPHOUS Fe-Si ALLOYS

G. Marchal, Ph. Mangin, M. Piecuch, Chr. Janot

To cite this version:

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MOSSBAUER STUDY

OF MAGNETIC

ORDERING IN AMORPHOUS Fe-Si ALLOYS

G. MARCHAL, Ph. MANGIN, M. PIECUCH and Chr. JANOT Laboratoire de Physique du Solide (L. A. 155), Universitk de Nancy 1

-

C. 0. no 140,

54037 Nancy Cedex, France

Resume. - Des alliages amorphes du type Fe~Siloo-X (avec 30 G X G 75) ont et6 obtenus par coevaporation sur supports refroidis. Les propri6tes magnetiques de ces materiaux ont et6 Btudiees par spectrometrie Mossbauer sur le Fe55 par determination de la distribution de champ hyperfin en fonction de la tempkrature et de la concentration. La conclusion principale est que I'aimantation de ces materiaux resulte d'une competition entre effets a longue et a courte distance. Plus la concentration en fer est Blevie, ou plus la tempbrature est basse, plus il y a d'atomes de fer soumis h un champ hyperfin. Un modkle est propose ou, quelles que soient la concentration ou la temperature, ce champ hyperfin s'annule pour les atomes de fer ayant entre 6 et 7 fer en position de proches voisins.

Abstract.

-

Amorphous alloys of composition F e x S i l ~ ~ - x (30 G x 75) have been prepared by the vapour quenching technique. The Mossbauer effect in Fe57 has been used to study the magnetic properties of these materials. The hyperfine field distribution has been determined from these experiments as a -function of alloy composition and tempeature. The main conclusion is that the hyperfine field in these materials results from a competition between long range and short range effects ; the higher the iron concentration, or the lower the temperature, the more abundant are iron atoms experiencing an hyperfine magnetic field. On the other hand, a model is proposed

in which whatever X and T, the hyperfine field is zero for iron atoms having less than between

6 and 7 iron nearest neighbours.

1. Introduction.

-

The last decade has brought successful results in the study of metallic amorphous alloys, especially in the understanding of their structural nature in terms of a dense tetrahedral packing of hard spheres [l], which gives a fairly good description of the short range structural order in these systems. Although a great deal of attention has been devoted to their study, most of the physical properties of amorphous materials (magnetism, resistivity, optical behaviour, ...) are still far from being clarified. This is partly due to the fact that success in obtaining amorphous structure has often been limited to narrow composition range and that investigation have not been localized enough which could turn out to be a disadvantage in the study of short range ordered structure. In this respect, the Mossbauer spectroscopy can provide a wealth of information concerning the local electron density, the electric field gradient and, here the most interesting, the hyperfine magnetic field which gives a local investigation of the magnetic properties. Among such successful attempts, amorphous Fe-Pd-P alloys have been studied by Sharon et al. [2] whose main conclusion is the existence of a magnetic order with, however, a proportion of weakly coupled iron atoms. I t is clear that in such disordered systems, the large distribution of different environments (both chemical and structural) will result in a correspondingly large distribution of the hyperfine magnetic field. As a

consequence, the best that can be expected from a set of experimental data will be a good description of physical. parameter distributions with their mean values and standard deviations.

Let us remark that the usual description of amorphous systems through the radial distribution function (RDF) obtained from electron or X rays patterns [3] gives nothing but similar information

about the most probable nearest neighbouring atoms and the possible deviations, through peak intensity and width. However, while the RDF can be directly described in terms of nearest neighbour number, the hyperfine field distribution is far from being so easily interpreted but often leads to significant qualitative information, as it will be shown in this paper.

In a previous paper [4] were reported preliminary Mossbauer results concerning two amorphous FexSiio0,, alloys with x = 70 and

x

= 65, studied at a few different temperatures. The spectra were analysed in terms of a continuous distribution of hyperfine magnetic field only, leading to characteristic P ( H ) probabilities exhibiting so-called low-field and high-

field components.

The first purpose of this paper is to report Mossbauer data extended to Fe,Si,,,-, amorphous alloys with

x

ranging from 30 to 75 and studied between 100 K

and 420 K. Secondly, we will see that the low-field

component corresponds in fact to iron atoms which do

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C6-764 G. MARCHAL, Ph. MANGIN, M. PIECUCH AND Chr. JANOT

not experience any hyperfine magnetic field. A careful analysis of the Mossbauer data as functions of both alloy composition and temperature will lead to significant conclusions concerning magnetic ordering in these materials.

2. Experimental procedures.

-

The amorphous Fe-Si alloys were obtained by vapour deposition onto liquid nitrogen cooled substrates, as described else- where [5] in detail. During the evaporation process, the pressure was less than 5 X 10-S torr while the

ultimate vacuum in the apparatus chamber was better than 10-' torr. The deposition rate was a few A/s with substrates being either glass plates, kapton foils or carbon covered grids according to their subsequent use as described in 141. Iron and silicon were evaporated from two separate electron gun crucibles [6] monitored by two distinct quartz regulating systems.

As described in [4], evidence of the amorphous structures were obtained from electrpn microscopy and diffraction observations. In particular, electron diffraction patterns give the interference function whose Fourier transform leads to the usual RDF i. e. the space probability of finding atoms around a given one. In the composition range x

>

50, the interference functions obtained were quite similar to those expected from a dense tetrahedral packing of hard spheres model, as long as both position and shape of the successive maxima in the diffraction patterns are concerned (a strong first maxima and then a weaker one with the characteristic shoulder) [4]. In this model, each metallic atom is surrounded by 12 nearest neighbours in a quasi-icosahedral environment.

A standard Mossbauer spectrometer operating in the constant acceleration mode and in absorption geometry was used to collect the data, along with a Co5' in Rh source. The specimens were many times folded kapton foils bearing an equivalent thickness of about 15 pm

of Fe,Si,,,-, alloys. The observation temperature was limited to 420 K to prevent structural transformation, since obvious irreversible changes occured at higher temperature.

3 Experimental results.

-

3.1 DATA ANALYSIS.

-

Typical Mossbauer spectra for the amorphous Fe,Si,,,-, alloys at room temperature are shown in figure 1.

For iron rich alloys (X

>

70) the Mossbauer patterns can be described as a broadened sextuplet and could certainly be roughly analysed in terms of a hyperfine field distribution only [S].

For relatively iron poor alloys (X 50) the Moss- bauer patterns appear as a broadened doublet which might be ascribed to a distribution of quadrupole effect in a non-magnetic material.

As described in a previous paper [8], it seems reaso- nable to 'assume that there are two kinds of iron atoms :

-

those experiencing a hyperfine magnetic field and which contribute to a sextuplet distribution with

Hi

2

100 kOe ;

-

those experiencing no hyperfine magnetic field but a quadrupole effect and which contribute to a doublet distribution.

I I I I I I

-6 -4 -2 0 2 4 6

Velocity (mm/s)

FIG. l.

-

Spectrum evolution with iron concentration at room temperature.

The patterns in figure 1 can then be analysed in terms of two distributions [S] : a quadrupole splitting distribution P(Q) (with a zero hyperfine field) and a true hyperfine magnetic field distribution P(Hi) with no quadrupole splitting as typically pictured in figqe 2.

The best fit was systematically obtained when the relative line intensities of the sextuplets were chosen so that their ratios were 3, 4, 1, meaning that the hyperfine magnetic field was lying in the film plane.

The total distribution has been normalized so that :

The later assumption of a zero quadrupole splitting in magnetically ordered material has been introduced for convenience in the fitting procedure of the spectra. This can be supported by both experimental and theoretical investigations [g] showing that' AEQ is much smaller when magnetic order occurs. Anyway, taking into account the material structural disorder [10], a quadrupole splitting would - only result in a distribu-

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FIG. 2.

-

Changes in the [P(Q), P(H)] distribution with alloy composition at room temperature.

From such an analysis of the Mossbauer pattern we will extract in the following, the temperature and alloy composition dependence of :

-

the mean isomer shift as defined above ; - a mean hyperfine magnetic field

xi

defined as

Hi = Hi P(Hi) ; (1)

- the proportion of iron atoms exhibiting a magnetic behaviour inside the amorphous material, defined as

- a localized hyperfine field which will be obtained through a model described later on.

3.2 THE MEAN ISOMER SHIFT VALUES.

-

For each

alloy, the isomer shift has been obtained in all the temperature range, leading to typical changes of about 5.3 X 10-4 to 7.2 X l O W 4 mm/s/K which are not too

far from the theoretical value 3 kT/2 mc, within the

experimental errors.

Perhaps more meaningful are the data corresponding t o alloy composition dependence of the mean isomer shift at a given temperature. Examples of this depen- dence are pictured in figure 3 for room temperature measurements. The data from the present work have been complemented by results coming from crystalli- zed systems [ l l , 121. If the amorphous systems seem to behave as usual metallic solid solution in the rich iron region, certainly changes occur in the electronic structure of the alloys corresponding to X

Fe, Si, (Fe,)

0.3

D Fe SI

0 30 60 90

X

FIG. 3. - Variation of the isomer shift with alloy composition at room temperature. crystallized systems ; A solid solution

Si ; present work.

smaller than 50 where the isomer shift exhibits a maximum. This result could be compared with the material behaviour in electrical resistivity measurements (to be published in a next paper) : for X > 50,

p has a metallic behaviour with an almost linear temperature dependence, for X = 50, p is not temperature dependent and for x

< 50, p exhibits some semi-

conductor character such as exponential decrease

with T.

3.3 GENERAL DESCRIPTION OF THE DATA TEMPE- RATURE AND ALLOY COMPOSITION DEPENDENCE.

-

Looking directly at the Mossbauer spectra obtained from various alloy compositions and at different temperature allow us to point out some general features :

-

At a given temperature, the central part of the spectrum, i. e. the doublet, progressively grows with decreasing iron concentration and the total width of the magnetic component is reduced as well (Fig. 1). - A similar behaviour occurs when temperature increases. So the progressive dissappearance of the magnetic order might be achieved by simultaneously reducing the number of magnetic atoms and the mean hyperfine magnetic field. This is a new feature compared to the data reported by Sharon et al. [2] concerning Fe-Pd-P alloys where increasing temperature, or reducing iron concentration, seems to result in a progressive collapse of the hyperfine field without enhanc- ing the spectrum central part, which perhaps means that the magnetic properties of the two systems are quite different.

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C6-766 G. MARCHAL, Ph. MANGIN, M. PIECUCH AND Chr. JANOT and 5 respectively, as functions of the temperature for

each alloy studied.

FIG. 4.

-

Variation of the mean hyperfine field

z ( ~ )

with temperature, for different alloys : (a) Fe75Six ; (b) Fe-loSi30 ;

(C) Fe67.5Si32.5 ; ( d ) Fe65Si35 (e) Fe60Si40 ; (f) FessSi45.

FIG. 5.

-

Variation of the magnetic atom concentration

CE(T) (curve references are similar to that in figure 4).

Extrapolating the curves of figures 4 and 5 to = 0

or C, = 0, we can make an estimate of Curie tempera- tures which indicates that there is not any magnetic cluster left, all the atoms being decoupled. Table I

gives a few Tc values obtained in such a manner.

TABLE I

Tc value obtained from the C,(T) and %(T) curves

X 55 60 65

-

TC%) 300 360-400 500-550

The curves Bi(T) in figure 4 can be redrawn by plotting

(?Ji)'

versus T2. We obtained almost straight lines, at least for low temperature and (or) high iron concentration. The extrapolating procedure to

2;

= 0

is then made easier, and leads to a second set of Curie temperatures T& presented in table 11.

T& value obtained from the H:(T2) curves

X 60 65 67,5 70 75

-

--

-

(K) 235 420 550 670 760

However, as a linear behaviour of %;(T') can be connected to homogeneous effects, T& certainly indi-

cates the disappearance of only the long range magnetic interactions, which explains that T& is smaller than Tc in as much as short range magnetic coupling can survive to long range effects.

3.4 TEMPERATURE AND CONCENTRATION DEPENDENCE OF THE LOCALIZED HYPERFINE FIELD.

-

The mean hyperfine field

Pi

and the concentration of magnetic atoms CH as obtained through an averaging process

over the whole distribution, are not dependent on the details of the spectrum analysis and do not need any assumption about structural model. Though giving unquestionable information,

6

and CH have no localiz- ed significance.

Now, we are going to define a localized contribution to the hyperfine field within a dense tetrahedral packing of hard spheres model. In this model iron and silicon atoms are randomly distributed over a shell of about 12 nearest neighbours around a given iron atom. The discussion will be restricted to alloys with X between 60 and 75 for which this model appears to be valid from electronic diffraction experiments [4].

On the other hand, the usual additivity rule will be considered valid to calculate the localized contribution to the hyperfine field, which is supposed to be influenc- ed by the chemical disorder only and directly connected only to the number of nn iron atoms (for a given temperature and a given composition) whatever their positions and the atomic distances.

This localized contribution to the hyperfine magnetic field H?) acting on the iron atoms having n iron atoms

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H?) is the limit of the area in the

P(Q)

+

P ( H )

n

distribution whose value is

ZP,,

where P, is the pro-

k = O

bability of finding k iron atoms in the nearest neigh- bourhood.

Such an analysis is basically similar to that made by Stearns [l11 and Haggstrom et al. [l31 in the case of Fe-Si crystallized alloys, but modified to be applied to continuous distribution.

Figure 6 shows the

H?)

variations at room temperature for various Fe-Si amorphous alloys.

FIG. 6.

-

Variations of H,(") at room temperature (ref. as in figure 4).

H?) exhibits an approximate linear behaviour for n

ranging from 8 to 10 (if we skip out the Fe,,Si,, alloy whose amorphous structure we are suspicious about) with the following typical numerical characteristics :

g

z 25 k ~ e . at-' whatever x

An

'

3

1 7 kOe/% Fe whatever n

.

Ax

For the n values larger than 10 (i. e. 11 and 12) H?) cannot be easily calculated because of the tiny probability PI1 and P,, of finding more than 10 iron nn and the occasional oscillations occuring in the tails of the [P(&), P ( H ) ] distribution.

From this data it is clear that the H?) changes result

from a competition between short range and long range effects. If the short range effect, connected to the iron nn dependence of H?), is natural and more or less a part of the model, the long range effect results in an iron concentration dependence connected to influence of distant iron atoms.

For the n values smaller than 8, and more precisely between 6 and 7, Hi(") falls steply to zero. So we can define a so-called critical number n, (between 6 and 7)

of iron atoms nearest neighbours of a given iron atom, under which this atom does not experience any more an hyperfine field and may be considered as non magnetic.

4. Discussion.

-

The main characteristic of the amorphous Fe-Si alloys, as reported in this paper, is their inhomogeneous magnetic behaviour, with however long range interactions in the rich iron alloys region. This results have to be compared to the data collected by Endoh et al. [l41 through magnetization

measurements, carried out on Fe-Ge alloys and to Mossbauer experiments from Sharon et al. [2] on Fe- Pd-P alloys where homogeneous effects seems t o be the prominent ones.

The magnetic inhomogeneity of Fe-Si amorphous alloys appears in the fact that some iron atoms experience a hyperfine field, and then can be considered as magnetic, while some others are non magnetic. The magnetic atom concentration increases with iron concentration in alloys and (or) at low temperature within the model described in the previous section. The parameter determining which iron atoms are or are not magnetic is their number n of iron atom nearest neighbours ; for an atom to be magnetic, n has to be larger than n,, a so-called critical number, slightly temperature and composition dependent, which is near 6 for large iron concentration, and near 7 for iron poor alloys as pictured in figure 6 .

Then, in an attempt to describe the mechanism for the magnetic ordering in the Fe-Si amorphous alloys, it may be stated that the variations of the localized hyper- fine magnetic field Hi("' are mainly due to :

-

changes in the number of iron atoms out of the

12 nn of the given iron atom if n 2 n,,

-

the step decrease in the magnetic moment of the given iron atom if n _nc.

In this model, the temperature influence would be to initiate a transfer of atoms from the magnetic set to the non-magnetic one through fluctuation mechanism which would progressively affect the atom having a nearest neighbouring not too far from the critical one. So, the usual well defined Curie temperature must have to be turned into a fuzzy range of magnetic ordering temperature covering about 100 K.

If this model leads to a coherent interpretation of our experimental data, some questions, however, can be raised, whose answers are actually connected to basic problems.

First of all, it is not obvious that the so-called non- magnetic atoms are without magnetic moments. It is well known that relaxation effects can average the hyperfine field to zero, inside moment bearing clusters. In that case, the critical number n, would turn to be the minimum localized iron concentration to initiate magnetic coupling between neighbour clusters.

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C6-768 G. MARCHAL, Ph. MANGIN, M. PIECUCH AND Chr. JANOT

such a correlation effect is weaker in the Fe-Si system experimental approaches : Mossbauer spectroscopy than in the COP one since its consequence would be to with a large external applied field and at low tempera- limit the amorphous system existence to a concentra- ture, magnetization measurements, etc

...

Some of them tion range x

>

75. have been already completed in our laboratory and will

Answers to these questions need the support of other be the purpose of another paper.

References

[l] DIXMIER, J., J. Physique Colloq. 35 (1974) C 4-11.

121 SHARON, T. E. and TSUEI, C. C., Phys. Rev. B 5 (1972) 1047.

[3] FUJIME, S., Japan J. Appl. Phys. 5 (1966) 764.

[4] MARCHAL, G., MANGIN, Ph. and JANOT, Chr., Solid. State Commun. 18 (1976) 739.

[5] MARCHAL, G., MANGIN, Ph. and JANOT, Chr., Phil. Mag. 32 (1975) 1007.

[6] MARCHAL, G., MANGIN, Ph. and JANOT, Chr., J. Physique Colloq. 36 (1975) C 2-91.

[7] HESSE, J. and RUBARTSCH, A., J. Phys. E : Sci. Instrum. 7 (1974) 526.

[8] MANGIN, Ph., MARCHAL, G., PIECUCH, M. and JANOT, Chr., To be published in J. Phys. E : Sci. Instrum.

[g] RIDOUT, M. S., J. Phys. C : Solid. State Phys. 2 (1969) 1258.

PIECUCH, M. and JANOT, Chr., J. Phys. Chem. Solids 36(1975) 1135.

[l01 SHARON, T. E. and TSUEI, C. C., Solid State Commun. 9 (1971) 1923.

[l 1 ] STEARNS, M. B., Phys. Rev. 129 (1963) 1136.

[l21 SHINJO, T. and NAKAMURA, Y., J. Phys. Soc. Japan. 18 (1963) 797.

WANDJI, R., Thesis University Nancy, 1970.

[l31 ~ G G S T R O M , L., GRANAS, L., WAPPLING, R. and DEVA- NARAYANAN, S., Phys. Script. 7 (1973) 125.

[l41 ENDOH, Y., YAMADA, K., BEILLE, J., BLOCH, D., ENDOH. H.,

TAMURA, K. and FUKUSHIMA, J., Solid. State Cornrnun. l 8 (1976) 735.