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Short-range order in AgMn spin glass alloys : description from X-ray evidence
H. Bouchiat, E. Dartyge
To cite this version:
H. Bouchiat, E. Dartyge. Short-range order in AgMn spin glass alloys : description from X-ray evidence. Journal de Physique, 1982, 43 (11), pp.1699-1706. �10.1051/jphys:0198200430110169900�.
�jpa-00209552�
Short-range order in AgMn spin glass alloys : description from X-ray evidence
H. Bouchiat and E. Dartyge
Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France
(Reçu le 22 mars 1982, révisé le 10 juin, accepte le 28 juillet 1982)
Résumé. - Des expériences complémentaires de diffusion centrale aux rayons X effectuées sur des monocristaux
AgMn de concentration variant de 1,4 % à 24 % permettent de rejeter la description de l’ordre local basée sur
l’existence de microdomaines ordonnés. Nous pouvons ainsi affirmer que seule est correcte une description sta- tistique de l’ordre local en termes de paramètres d’ordre de Cowley, qui s’applique à une distribution homogène
de concentration dans l’alliage, comme nous pensons que c’est le cas dans AgMn ainsi que probablement CuMn.
Abstract. - Further small angle X-ray diffusion experiments carried out on AgMn crystals containing a concen-
tration of 1.4 at. % to 24 at. % Mn allow us to reject the description of S.R.O. based on the existence of ordered micro-domains. Instead, we carry out an analysis of the S.R.O. in term of Cowley parameters applicable to an
homogeneous distribution of concentration, which we claim is the case for AgMn and probably CuMn.
Classification Physics Abstracts
81.30
1. Introduction. - In metallic spin glasses such as CuMn, AgMn and AuFe, the random distribution of magnetic atoms in the metallic matrix is responsible
for the magnetic interaction disorder which is consi- dered to be the characteristic feature of spin glasses [1].
Such a position-randomness hypothesis is quite
reasonable for sufficiently dilute alloys (concentration
in magnetic impurities below 1 at. %) but becomes
more doubtful for higher concentrations. Even if
no long-range intermetallic ordered phase develops
in these alloys, chemical interactions between the different atoms in the alloy are responsible for the
existence of a short-range order. These atomic corre-
lations alter the distribution of magnetic interactions,
which becomes different from the one predicted by randomness, at least at distances equal to the atomic
correlation length. In order to provide information about the influence of this chemical non-randomness
on the short-range magnetic interactions, we have performed both diffuse X-ray scattering and magneti-
zation measurements (published separately [2]) on the
same AgMn single crystal samples and tried to
correlate the different results obtained with these two complementary means of investigation.
After recalling our early X-ray results published
in [2], we present in the following complementary X-ray small-angle scattering information. This enables
us to conclude in favour of a homogeneous purely
statistical description of the short-range order, using Cowley short-range order parameters and eliminat-
ing all microdomains descriptions.
2. Previous results : position of the problenl - In
reference [2] we present the diffuse X-ray scattering
results obtained with quenched AgMn single crystals alloys with concentrations ranging from 1 to
24 at. % Mn :
i) For concentrations c > 6 at. % Mn diffuse spots
were observed in the reciprocal space, centred at
(1 1 l2 0) reciprocal points (Fig. 1);
ii) Our small-angle scattering experiments showed
a lack of intensity scattered at low angles (with the length of the scattering vector I s I > 2 x 10 - 2 A -1 ) ;
iii) The absolute background Laue intensity mea-
sured was nearly independent of the concentration of
alloys and, in the case of 24 % alloy, was less by a
factor 2 than the theoretical intensity scattered by a perfect random alloy;
iv) The angular extension of the (1 1/2 0) spots lead to an estimate of the correlation length of $ 20 A
for the local order.
We initially proposed in reference [2] two possible, mutually exclusive, descriptions of the atomic corre-
lations in terms of microdomains which agree at least with the X-ray diffraction patterns obtained at large angles : [3]. These descriptions are summarized by :
- Model (1) : a heterogeneous model where the
alloy contains microdomains with 50 % Mn atoms
stoichiometric ratio based on 141 jamd symmetry.
- Model (2) : a homogeneous model where the
alloy presents sinusoidal composition fluctuations,
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198200430110169900
1700
Fig. 1. - a) Diffraction pattern of a AgMn 24 % single crystal. The radiation used is monochromatic MoKa, the
second harmonic being eliminated. The Buerger precession apparatus is set up for a reciprocal (h, k, 0) plane. b) Indexa-
tion of the Bragg spots and diffuse spots which are recorded in an undistorted shape. 1 Bragg spots. @ Diffuse spots.
with a wave vector perpendicular to 420 planes. This
model was rejected, as it was in contradiction with
our small-angle scattering results since it predicts a
scattered intensity nearly equal to the Laue back-
ground, which is indeed two times larger than what is
experimentally measured.
In order to further test the heterogeneous model (1)
we had concluded that it would be necessary to make
small-angle scattering measurements for a scattering
vector less than 2 x 10 - 2 Å -1 (which was the limit
of our previous measurements) [2] : in the case of the heterogeneous model (1) the microdomains must contribute to a large intensity in this part of the reci-
procal space.
In the following we present (under 3) additional
data concerning the small-angle scattering on AgMn,
and (under 4) an evaluation of the short-range order
parameters derived from the shape of the diffuse (1 1/2 0) spots and not presented in reference [2].
It is important to note at this point that the results obtained for the S.R.O. parameters are derived enti-
rely from the intensities of the diffuse spots and that the S.R.O. itself contributes very little to the small-
angle scattering. Indeed, it is because we observe very
little, if any, intensity scattered at small angles that
we may proceed to our analysis in terms of a homoge-
neous alloy (with S.R.O. present), rather than in terms of an inhomogeneous situation. This quantita-
tive analysis of course suffers from the defects inherent in the photographic technique and should be further
supported by absolute intensity determinations. Never- theless we believe that the subsequent S.R.O. deter- mination is meaningful, since :
i) the contribution from lattice-distortion effects does not need to be taken into account in AgMn
for Mn concentration less than 30 % [4], since the
lattice parameter remains constant to within better than 10 - 4 in relative units;
ii) the contribution from thermal scattering can be
observed in pure Ag or very dilute AgMn alloys (see Fig. 5a of [2]) and does not interfere with our measurement near the (1 1 /2 0) spots ; .
iii) the background thermal contribution, together
with Compton scattering and fluorescence, is slowly changing near the (1 1/2 0) spots and has been simply
subtracted from the wings of the assumed Lorentzian-
shape (1 1/2 0) diffuse spot in the densitometric results. This admittedly crude way to proceed is not a major source of error, as long as the intensity of the (1 1/2 0) spots is an order of magnitude above this
featureless background.
3. Small-angle results. - Figure 2 gives the varia-
tion of small-angle scattered intensity by a 20 at. % Mn alloy for scattering vectors in the range 7.13 x
10 - 3 A -1 s 1.66 x 10 - 2 A-I. Only a weak, cons-
tant intensity is observable in this part of the reci-
procal space. The scattered intensity is given in arbitrary units because of our lack of absolute cali- bration of the transmitted beam of the (monochro- matic) synchroton radiation used. We have measured
Fig. 2. - Intensity scattered at small angles by an Ag-20 %
Mn single crystal. The intensity diffracted by a pure Ag crystal has been subtracted. This data has been obtained
at the L. U. R. E. facility.
in reference [2] the absolute scattering power of our
samples and of pure Ag with the technique described
in references [5] and [6], which is especially designed
for high sensitivity at low scattering power.
We remark that since the high-angle side of this measurement is 1.66 x 10 - 2 Å -1, and the lowest
angle used in reference [2] corresponds to 2 x
Fig. 3. - Absolute scattering power measured in electrons/
atoms at small angles for AgMn alloys from 1.4 at. % to
24.3 at. % Mn. s is the length of the scattering vector,
The results for pure Ag and 20 % alloy are presented in
reference [3].
10-2 A-1, it is quite feasible to extrapolate the data of reference [2] in order to obtain an absolute value for the present measurement. We give in figure 3 the data corresponding to the absolute value of the scattered power in el/atom of the alloys not presented in refe-
rence [2] in the range 4 x 10 - 2 Å - 1 s 8 x 10 - 2 A -1. If heterogeneous microdomains (with high
Mn concentration and sizes > 20 A) had been pre- sent in the crystal we should have observed a strong
intensity, decreasing towards higher angles. It is thus possible to conclude that the crystals do not contain heterogeneous microdomains of sizes > 20 A. It should be noted that the slight upwards trend observed for the most dilute alloys can be safely attributed to
multiple scattering [6].
By means of electron microscopy on the same samples it has been demonstrated [7] that the diffuse
scattering is qualitatively similar to that found by X-
rays. Furthermore, using dark-field imaging tech- niques with the short-range order diffuse scatter-
ing [8], we have found that there were no locally
ordered regions of size larger than = 5 A. These observations, together with the small-angle scatter- ing results, essentially eliminate the possibility of the
existence of microdomains.
In complete contrast with the type of local order present in AuFe alloys [9], we must admit here that the only acceptable description of the local order is a purely statistical one, concerning only the average
composition in each neighbour shell around a Mn atom rather than their mutual positions. This des- cription uses the short-range order Cowley para- meters [10, 11] defined as a(Ri) = 1 - p(Ri)l(l - c)
where p(Ri) is the probability of the presence of
an Ag atom at the point Ri for a Mn concentration
equal to c, assuming the presence of a Mn atom at the origin.
4. Evaluation of short-range order parameters. - Our last small-angle experiments show that the
diffuse intensity scattered by AgMn alloys is mainly
concentrated around the (1 1720) diffuse spots. (No important scattering occurs at 0 angles.) We then
choose to describe all the diffuse intensity as a product
of Lorentzian functions centred at si = 1 1/2 0 and equivalent points of the reciprocal space [11] ]
si are the different (1 1 /2 0) vectors of the reciprocal
space and Asix Asiy LBsi= are the experimental widths of
the diffuse spots. The
factor - 2
3n C(I - c) ( fAg - V fMn)2comes from the fact that the integrated intensity
over one reciprocal cell V* is :
with c being the atomic concentration of Mn atoms,
fAg fMn the atomic scattering factors of Ag and Mn respectively, and V the volume of one unit cell.
1702
With expression (1) for the scattered intensity, it is possible to evaluate the Cowley short-range order
parameters [12, 13]
For each point Ri of the crystal we get :
with
When applied to an alloy of given concentration c this expression is physically meaningless unless :
Then one can note that it is possible to have long-
range (1 1 /2 0) correlations (which implies : As’1,2 = L’BSl/2 = Asz, /2 = Oand(x([l, 1, 1 ]) = - 1), only when c
is equal to 50 at. %.
We have measured on microdensitometer profiles
the width of the diffuse spots with an uncertainty of
15 %. Their values for the different concentrations are
given in table I. Asm is the width of a diffuse spot
along the double period axis, As. is the width along
the two other directions. The eight first-neighbour
parameters deduced from (4) are given in table II a.
Table I. - Measured values of the 1 1/2 0 diffuse
spots width, a is the cubic lattice parameter for the four concentrations of Mn.
The observed increase in the width of the diffuse spots with decreasing concentration gives physically
consistent values for the local order parameters
(except concerning the parameter a 1 for the 10.6 at. % Mn sample [8]).
5. Discussion. - In reference [2] we quoted values
for al and a2, obtained assuming a concentration
(1 1/2 0) waves description (model 2), which agree in sign but which are much lower in magnitude than
Table II a. - Computed values for the 8 first nearest-neighbour short-range order parameters.
Short-range order parameters cxi calculated assuming for the diffuse scattering a product of Lorentzian-
shape functions centred on [1, 1/2, 0]* reciprocal point (expression (4)).
Table II b. - c = 24.3 %.
Short-range order parameters ai calculated assuming a juxtaposition of two Lorentzian functions centred
on [1, 1/4, 0]* and [1, 3/4, 0] reciprocal points (expression (5)). In both cases the widths have been taken experi- mentally as reported in table I.
Fig. 4. - Microdensitometer profile of intensity of a (1 1/2 0) diffuse spot for a single crystal Ag-24 % Mn taken parallel to [0 1 0] direction. See figure 1 for the original
data.
those obtained with exp. (4) in this work. In contrast with the concentration-modulation models the des-
cription given here has the merit of being in agreement with the fact that no scattered intensity is observed
at low angles : near s = 0 the intensity is mainly
due to the 24 Lorentzian functions centred at (1 1 /2 0)
and other equivalent points. As a partial coherence
test of the S.R.O. parameters that we have determined, assuming that the intensity in the low-angle range is
spherically distributed, we calculated their contribu- tion at small angles and we found that the agreement between the theoretical and experimental small-angle
results is excellent (See Fig. (5)). We note that the
agreement observed is not a stringent test of the S.R.O.
parameters but only shows that our model is consis- tent with the small-angle scattering power that we
were able to measure directly in el/atom units as explained in (I-a). It is important to note that this quantitative agreement was obtained without adjus-
table parameters, but by using expression (1) for the
diffuse intensity and adding to it the experimental
results obtained for pure silver crystals.
However, it is important to note that another
reasonable choice for the mathematical fit of diffuse
Fig. 5. - Variation of the absolute small-angle scattering
power expressed in el/atom units of AgMn crystals versus
concentration. Dotted line : theoretical intensity obtained
for disordered crystals. Continuous line : theoretical inten-
sity obtained with the expression (5) for the diffuse scattering
after adding the experimental scattering power of pure Ag crystal.
spots given in expression (1) may yield different values for oci, especially for i > 3. The set of ai given in table I
represents a possible choice to describe the short- range order in the AgMn alloy. These parameters are in agreement with--the experimental distribution of
intensity in the reciprocal space but they are not uniquely determined because of the lack of precise quantitative knowledge concerning this diffuse scatter- ing.
For the highest concentration studied, as shown
in figure 4, one observes a splitting of the diffuse spots.
This observation is not in agreement with the conclu- sions of Wemer et al. in their work on CuMn alloy -
see note [15].
In this case, a better fit of the diffuse spot shapes
can be obtained by the juxtaposition of two Lorent-
zian peaks centred on the (1 1/4 0) and (1 3/4 0) posi-
tions and both having identical widths in the three cubic directions equal to As., instead of the unique
Lorentzian peak described above
The computed values of short-range order para- meters are given in table II b for c = 24 % and can be compared to the values obtained using equation (4).
The difference between the two sets of values appears
especially for ai with i > 3 (one can see for example
that the sign a3 is changed). We emphasize that ai and a2 are almost independent of the choice of the
mathematical representation of the diffuse spots,
as long as the diffuse intensity remains concentrated around ( 11 /2 0) and equivalent points in the reciprocal
space and gives only a minor contribution in the
small-angle range.
We first remark that if the local order consists of ordered microdomains in the alloy, the existence of well-defined periodic positions of the magnetic atoms
within the microdomains implies the existence of a
magnetic order whose correlation is of the order of the atomic correlation length [3-16]. But the statistical
description of the local order (which we now think is
the only coherent one concerning AgMn and probably
also CuMn alloys) does not give a determination of the relative positions of atoms even on distances equal
to the local-order correlation length. Thus one cannot
attribute a priori any magnetic correlation length to
such a type of local order. However the distribution of
magnetic interactions is not the one predicted by
randomness. Let us consider in particular the case of
first- and second-neighbour interactions which are
respectively antiferromagnetic and ferromagnetic.
The average numbers of first and second Mn neigh-
bours near a Mn atom are respectively given by :
1704
Table III. - Evaluation of the numbers of Mn first-
and second-neighbours according to the short-range
order parameters (XI and a2 given in table II a. N1 (random) and N2 (random) are the expectation for a
disordered alloy.
(*) The non physical value of N1 for 10.6 at. % concen-
tration is due to the fact that the 1 1 /2 0 and 1 3/2 0 peaks
are poorly resolved in this case.
(**) One obtains N2 = 3 when the splitting of the diffuse spots is taken into account.
These values are obtained from the a parameters given in table II a. The variations of N and N2 versus
concentration show that :
- N 1 is close to zero for c 15 % and increases
rapidly for higher concentrations but remains lower than its statistical value in a random alloy.
- N2 is larger than its statistical value in a random
alloy and increases more slowly than N1 for c > 15 %.
As we cannot measure quantitatively the width of the diffuse spots for less than 10.6 at. % Mn concen-
trated samples, we do not have direct information
concerning N1 and N2 in this low concentration range. However we know that there is no sudden
disapearance of the local order below a certain con-
centration as diffuse spots are still visible for c - 5.4 %.
Thus it looks reasonable to interpolate the values of
N1 and N2 linearly towards zero in the low concen-
tration range. This extrapolation is expressed by :
and is depicted by dotted lines in figure 6.
These results can be compared (see Figs. 7a and b)
with room temperature susceptibility measurements
performed on the same samples [17]. (These measure-
ments added to the one performed in the spin glass
low temperature range will be presented in detail separately.)
These susceptibility measurements are in good agreement with those obtained by Scheil and Wach-
tel [18] who performed experiments in the range of concentration 10-30 % Mn. It can be observed in
figure 7b that the susceptibility per Mn atom versus the concentration has a weak maximum at c - 15 %.
Figure 6 shows that 15 at. % Mn is the concentration above which the number of first neighbours around
a Mn atom (with antiferromagnetic interactions) is no negligible compared to the number of second neigh-
bours (with ferromagnetic interactions). This indicates
a qualitative agreement between the variation of the
susceptibility and the 1 st and 2nd Mn neighbours
with the concentration of the samples.
Fig. 6. - Variation of N1 (squares) (first neighbours) and N2 (circles) (second neighbours) versus concentration deduc- ed from our X-ray scattering data given in table III as a
function of concentration of Mn. Dotted lines : what seems
to be the reasonable extrapolation of these quantities in the
low concentration range. Continuous lines : variation of
N1 and N2 with concentration expected in a random alloy.
Finally, we wish to emphasize the essentially diffe-
rent nature of short-range order existing in AgMn (and most certainly CuMn as well) on one hanl7and
AuFe [9] on the other hand. Whereas in the former system the distribution of Mn corresponds every- where to the average concentration, but with a ten- dency of Mn first neighbours to repel each other to the benefit of second and third nearest-neighbours, on the contrary the AuFe system unambiguously shows a tendency towards segregation of Fe-rich microdo- mains which we have described by our platelet
model [9].
6. Conclusion. - The lack of intensity scattered
at low angles makes us eliminate any heteregeneous-
microdomain descriptions of the local order in the
AgMn system.
The alloy remains homogeneous on a scale equal
to the correlation length (20 A) of the short-range order, which is of the anticlustering type. We propose
a description of this local order which is a purely
statistical one, using Cowley parameters and giving
