MAGNETIC PROPERTIES OF AuFe ALLOYS BELOW THE PERCOLATION LIMIT

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MAGNETIC PROPERTIES OF AuFe ALLOYS BELOW THE PERCOLATION LIMIT

A. Murani

To cite this version:

A. Murani. MAGNETIC PROPERTIES OF AuFe ALLOYS BELOW THE PERCOLATION LIMIT.

Journal de Physique Colloques, 1974, 35 (C4), pp.C4-181-C4-184. �10.1051/jphyscol:1974431�. �jpa-

00215622�

JOURNAL ^DE

Colloque C4, supplkment au no 5, tome 35, Mai 1974, page C4-181

MAGNETIC PROPERTIES

OF AuFe ALLOYS BELOW THE PERCOLATION LIMIT

A. P. M U R A N I

Physics Department, Imperial College, London SW7, U. K.

R6umC.

L'idee que l'alliage dilue Au-Fe serait ferromagnetique a des concentrations de Fe superieures a 12 at. % a kt6 gen6raleme~acceptee. On presente ici des mesures d'aimantation sur un alliage Au-15 % Fe qui sont en desaccord avec cette idke et revblent un gel

de type verre de spin

du degre de liberte magnetique des spins a une temperature proche de celle indiquee par les mesures d'effet Mossbauer. Alors que d'autres travaux ont cru mettre en Cvidence une temperature de Curie ferromagnktique superieure dans des alliages de cette concentration, nos mesures indiquent I'apparition d'un ordre ferromagnktique localisk cette tempkrature, qui persiste sous forme de superparamagnetisme geant a des temperatures inferieures, jusqu'a ce que le blocage des spins a l'echelle macroscopique s'etablisse A plus basse tempbature en accord avec les resultats Mossbauer. Remarquons que la limite de percolation pour le reseau cfc est proche de 20 at. % et que le ferromagnetisme, en supposant que l'interaction entre plus proches voisins soit ferromagnktique, ne devrait apparaitre qu'a cette concentration. En deqa, et plus particu- librement dans I'intervalle 12-20 at. %, la structure compliquee de spins gel& doit &tre attribuke

interactions oscillantes de type RKKY.

Abstract.

It has hitherto been commonly accepted that dilute &-Fe alloys exhibit long range ferromagnetism for Fe concentrations above about 12 at. %. We present magnetisation measure- ments on a Au-15 at. % Fe alloy which are in disagreement with this idea, and which reveal a spin glass type of magnetic freezing of spins occurring at a temperature close to the value expected from Mossbauer effect measurements. A higher ferromagnetic Curie temperature has been claimed for this concentration alloy by previous workers but present measurements reveal a cr ferromagnetic ordering >> occurring on a very localized scale at this temperature, accompanied by giant super- paramagnetic behaviour below it which persists until the magnetic freezing of spins on a long range scale is established at the lower temperature, in agreement with the Mossbauer data. It should be noted that the percolation limit for the f.c.c. lattice is close to 20 at. % and on the basis of the assumption that near neighbour interactions are ferromagnetic, long range ferromagnetism is expected to be delayed until this concentration is reached below which, and especially in the range 12-20 at. %, the more complicated magnetic freezing of spins must be attributed to the oscillatory RKKY interactions.

I t is well known that solute spins even in very dilute Au-Fe

-

alloys (-- 0.1 at. % Fe) [2] freeze magnetically a t low temperatures in almost random orientations giving rise t o a complex magnetic system which has been variously described as a Spin Glass [3] or a Mictomagnet [4]. The former term has been suggested t o be rather appropriate [5], because of the similarity of some of the properties of such systems with real glasses, and may in general be applied t o any binary solid solution alloy, consisting of moment bearing atoms dissolved in a non-magnetic metallic matrix, which is neither simple ferromagnetic nor antiferro- magnetic but which exhibits properties which are the result of a mixture of both such types of interac- tions. In magnetisation measurements the spin glass behaviour manifests itself as a broad maximum in the static ((susceptibility

and the observation of iso- thermal remanance and field cooling effects below the temperature of the maximum.

It is commonly believed that the spin glass magne- tism found in the lower concentration Au-Fe alloys gives way t o long range f e r r ~ m a ~ n e t i s r n w h e n the Fe concentration is increased above about 12 at. % [I].

The first observations of the transition to ferroma- gnetism in Au-Fe were made by Pan et al. [6], who have claimed t h a t t h e alloys with more than 10 at. % Fe were ferromagnetic, and were followed later by the work of Crangle and Scott 171 who measured the magnetisation of several Au-Fe alloys as a function of magnetic field and temperature and analysed their data with the help of Arrott plots of

H vs.M2 t o

M

obtain the ferromagnetic Curie temperatures T,.

They found that a n alloy containing 11.1 at. % Fe was not ferromagnetic according t o this criterion but another having 14.9 at. % Fe had a Curie tempe- rature of 110 K.

De Mayo [8] has reported magnetisation measu-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974431

C4-182

MURANI

rements on Au-Fe alloys with 5.10 and 13.8 at. % Fe and shows t h a t the magnetisation us. temperature behaviour of the alloys in a constant field of 12.6 kOe is strongly dependent on cold working and annealing heat treatments given to the samples as also are the ordering temperatures obtained from Arrott plots for the two higher concentration samples. The author also observes strong super-paramagnetic behaviour which is, again, affected by the metallurgical treatment of the samples and concludes that the properties of the alloys are due to clusters dispersed in what the author calls the ^spin glass matrix. However, the strong dependence of the magnetic properties on metallur- gical treatment is a general feature of most binary alloys. It has been shown in the case of concentrated Cu-Ni alloys, where the tendency towards atomic clustering is also pronounced, that high temperature annealing heat treatment can produce good random substitutional alloys whose properties are accountable in terms of purely statistical fluctuations of concen- tration [9]. As in all such systems the fact that non- random clustering can be induced does not mean that it cannot be avoided. We shall adopt this view point for the Au-Fe system. The present results show that the of the alloys, including the occur- rence of giant superparamagnetic behaviour, have a simple physical interpretation which does not depend upon atomic clustering effects.

The transition to ferromagnetism claimed by the magnetisation results mentioned earlier is, however, not corroborated by the Mossbauer effect measu- rements. Borg [lo] has found that the low tempe- rature Mossbauer spectra of Au-Fe alloys with up to 18 at. % Fe are essentiallysimilar and indicate spins frozen in random orientations which cannot be aligned parallel as a whole even with the appli- cation of magnetic fields of strengths up to 50 kOe.

Borg and Kitchens [Ill have measured magnetic properties of Au-Fe alloys with concentrations up to 12.5 at. % F e . ~ l t h o u g h no bulk magnetisation measurements beyond this concentration are reported the authors suggest that

the magnetic beha- viour of Au-Fe

in the concentration region

0.05 < Fe < 17 at. %

conforms to the standard definition of mictomagne- tism

which conclusion is based mainly (especially for concentrations above 12.5 at. %) on their earlier Mossbauer results [lo].

Another very important discrepancy between the magnetisation results and the Mossbauer effect measu- rements which has hitherto remained unexplained is the vast differences in the ordering temperatures obtained by the two types of measurements for Au-Fe alloys containing more than 12 at. % Fe (the concen- tration where ferromagnetism is thought to set in).

In contrast, the ordering temperatures deduced from the resistivity results (the temperatures of the maxima in dpldt) agree with those obtained from bulk magne-

tisation measurements over the whole concentration range [14]. The results are illustrated in figure 1 where we reproduce a diagram from a paper by Cannella and Mydosh [I].

FIG. 1. - Magnetic ordering temperatures To vs. concentration C for &Fe alloys as compiled by Cannella and Mydosh [I].

The triangles are from the magnetisation data of Crangle and Scott [7] ; closed circles from the Mossbauer data [12 and 131 ; crosses represent the maxima in the susceptibility data of Lutes and Schmit [I91 ; and the open circles are the temperatures of the

maxima in dp/dT from Mydosh

al. 1141.

280-

2b0

In the following we present results of magnetisation measurements in low fields on a Au 15 at. % alloy which enable us to resolve this discrepancy and to show that both ordering temperatures have interesting physical significance. The present results also demons- trate unambiguously for the first time through bulk magnetisation measurements, the mictomagnetic or spin glass type of magnetic behaviour of a Au-Fe alloy in the concentration range above 12 at. %.

The alloy was prepared by argon arc melting appro- priate amounts of high purity Au (5N) and Fe (4N8) metals on a water cooled copper hearth. The melting was repeated a total of four times after turning over the alloy each time. The alloy was subsequently cold worked, homogenized for 72 hours at 900 OC, quenched in water and kept under liquid nitrogen until used.

Careful metallographic examination of a portion of the sample showed no traces of any second phase precipitation. The equilibrium solid solubility of Fe in Au is more than 50 at. % at 900 OC [15], so that at a concentration as low as 15 at. % Fe the above treatment should certainly yield a good random solid solution.

In figure 2 we present the magnetisation results for the Au-15 at. % Fe alloy measured in two different

I l I I I I I t I ' I UI

&Fe

- A CRANGLE

&

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- e MOSSBAUER SPECTRA lcornposite)

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1x1 '4

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MAGNETIC PROPERTIES OF AuFe ALLOYS BELOW THE PERCOLATION LIMIT C4-183

FIG. 2.

The magnetisation of the Au-15 at. % Fe alloy as a function of temperature in two constant fields. The curve marked a shows the magnetisation in 3.3 Oe with increasing temperature after cooling to 4.2 K in zero field. Curve b gives the measure- ments in the same field with decreasing temperature and curve

shows the magnetisation in 100 Oe, with increasing temperature,

after cooling in zero field.

fields. Curve a shows the magnetisation with increas- ing temperature in a constant external field of 3.3 Oe, the alloy having been initially cooled to 4.2 K in zero field (ensured by a mu-metal shield around the cryostat). Measurements made with decreasing tempe- rature in the same field are shown by curve b. Both curves indicate a decrease of magnetisation around 50 K marking the onset of the spin glass type of magnetic freezing of spins in the alloy. In addition, curve b demonstrates the field cooling effects common to spin glass systems. Measurements made with increas- ing temperature in a field at 100 Oe, after zero field cooling, are shown by curve c. Again a broad maxi- mum, characteristic of the behaviour found in spin glass systems, is observed around 50 K. It must be pointed out that the measurements are made in cons- tant external fields so, despite the fact that the sample is a thin cylinder, 1 mm in diameter and 14 mm long, with a demagnetisation factor of only about 0.01 along the axis [I61 (obtained by assuming the sample to be a prolate spheroid), the demagnetisation correction to the effective field within the sample is not negligible because of the large magnetisations and is most significant for the low field measurements. However, the general features of the curves will not be much affected by normalising the magnetisation to a constant effective field within the sample.

One very important respect in which the above magnetisation curves differ from those of a common spin glass is the rapid rise around 110 K to very large magnetisations as shown by the low field measu- rements curves a and b. Such behaviour, by itself, has been interpreted as indicating the onset of ferro- magnetism [I]. Isothermal magnetisation measu- rements at 78 K, however, show no detectable rema- nance after cycling the alloy in a field of 8 kOe. For a polycrystalline specimen this clearly implies the absence of long range ferromagnetic order. The magnetic isotherms between 50 and 110 K reveal the existence of giant super-paramagnetic momentsconsist- ing of several thousand Fe atoms [17]. We suggest that these are formed by the (predominantly) ferro- magnetic freezing of Fe spins (whether single or in statistical near neighbour clusters) on a localized microscopic scale which is marked by the sharp increase in the magnetisation around 110 K. The giant clusters so formed are, however, not large enough on a macroscopic scale to behave as ferromagnetic entities 1181 and will be free to rotate until they freeze relative to each other (with random orientations) over macroscopic dimensions, at some lower tempe- rature. If the thermal relaxation rate of the clusters is fast compared with the long life time of the Moss- bauer transition (- lo-' s) the latter measurements would not detect the short range order within them.

Hence it is not until the spin glass temperature of 50 K is reached and the clusters freeze that the Moss- bauer spectrum of Fe appears.

As pointed out above, the magnetisation of the alloy around 110 K and below is strongly field dependent and tends to saturation in fields above 20 Oe, hence an analysis of the magnetisation measured in moderate fields in terms of the Arrott plots would yield a ferro- magnetic ordering temperature near to where the cluster formation occurs and is the explanation for the results of Crangle and Scott [7].

It is also not difficult to understand why the maxi- mum in the first derivative of the resistivity of the alloy, suggesting the onset of magnetic freezing of spins, should coincide with the temperature of the formation of the clusters, for as far as the conduction electrons are concerned the latter event is the most significant one, if the size of the clusters greatly exceeds the mean free path of the electrons. This is certainly the case for the present alloy where the clusters span a region of about 105 atoms [17], and hence a cube of linear dimension around 50 lattice spacings, whereas the mean free path of the conduction electrons is only of the order of a few lattice spacings (since p - ^{150 pQ. cm).}

We are now in a position to understand a little more clearly the magnetic behaviour of the Au-Fe system.

It would appear that near neighbou~interactions

between Fe atoms in Au are ferromagnetic (as in

metallic Fe) but those between the next near neighbour

and beyond are of the oscillatory. R. K. K. Y. type.

C4-184

In such a situation long range ferromagnetism is established when the concentration of Fe atoms in the alloy is that given by the percolation limit, when the probability of having an infinite chain of near neighbour Fe atoms becomes finite. For the f. c. c.

lattice this occurs at a concentration of 19.5 at. % [20].

It would appear from the data in figure 1 that all three types of measurements - Mossbauer effect, magnetisation, and electrical resistivity

would yield the same ordering temperature for an alloy with concentration around 20 at. % Fe, which would then also show long range ferromagnetism. Below this concentration, however, as in the present case of the Au-15 at. % Fe alloy, any magnetic order can have only the spin glass character.

We conclude by saying that the above results are the first bulk magnetisation measurements which demonstrate unambiguously the spin glass type of magnetic behaviour of Au-Fe alloys in the controver- sial concentration region above 12 at. % Fe. The results also enable us to recognise clearly, for the first time, that the two vastly different ordering temperatures obtained by previous magnetisation and resistivity results, on the one hand, and the Mijssbauer effect measurements on the other, are both physically significant.

The author thanks Professor B. R. Coles for his interest and encouragement and with Mr. K. Mihill for helpful discussions. Financial support from the Science Research Council is also acknowledged.

References

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BUN. 5 (1970) 549.

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[ l l ] BORG, R. J. and KITCHENS, T. A,, J. Phys.

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and WIEDERSICH, H., J. Appl. Phys. 36 (1965) 2124.

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E. and BORG, R. J., Phys. Rev. 149 (1966) 540.

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[16] OSBORNE, J. A., Phys. Rev. 67 (1945) 351.

[17] The isothermal magnetisation of the alloy at 78 K suggests an extreme form of superparamagnetic behaviour with an average effective magnetic moment per Fe atom of about 900

hence an average cluster size of about 105 Fe atoms. Full results will be published shortly.

[I81 NEEL, L., C. R. Hebd. Sdan. Acad. Sci. 228 (1949) 664.

[19] LUTES, 0. S. and SCHMIT, J. S., Phys. Rev. 134 (1964) A 676.

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A 310.