Neutron diffraction studies of magnetic moments in
dilute transition metal alloys
M.F. Collins, G.G. Low
To cite this version:
M.F. Collins, G.G. Low.
Neutron diffraction studies of magnetic moments in dilute transition metal alloys.
Journal de Physique, 1964, 25 (5), pp.596-600.
<10.1051/jphys:01964002505059600>. <jpa-00205835>
HAL Id: jpa-00205835
https://hal.archives-ouvertes.fr/jpa-00205835
Submitted on 1 Jan 1964
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LE
JOURNAL DE
PHYSIQUE
-
TOME
25,
MAI
1964,
596.
NEUTRON DIFFRACTION STUDIES OF MAGNETIC MOMENTS
IN DILUTE TRANSITION METAL ALLOYS
By M.
F. COLLINS and G. G. LOW
Solid State Physics Division, U. K. A. E. A. Research Group,
Atomic Energy Research Establishment, Harwell.
Résumé. 2014 Des mesures de diffusion de neutrons par un désordre magnétique dans des alliages
ferromagnétiques dilués ont permis d’étudier les modifications de la distribution spatiale des
moments magnétiques autour de l’atome dissous. Les résultats sont présentés pour des alliages
dilués polycristallins dont la base est du fer en montrant la distribution magnétique autour des
atomes de manganèse, de chrome et de vanadium. La diffusion par les impuretés de manganèse
indique que leur présence n’a pas d’effet appréciable sur le moment des atomes de fer voisins. Dans
le cas des impuretés de chrome et de vanadium, les résultats ne peuvent s’interpréter que si l’on
admet un faible accroissement des moments des atomes de fer qui sont à une distance voisine de
4 Å des atomes dissous. Il semble y avoir un moment négatif sur les atomes d’impuretés euxmêmes.
Measurements of the magnetic disorder scattering of neutrons from dilute ferroAbstract.
magnetic alloys allow the spatial distribution of the magnetic moment disturbance around the
solute atoms to be investigated. Results are presented for dilute polycrystalline iron based alloys
showing the magnetic moment distribution around manganese, chromium and vanadium atoms.
The scattering from manganese impurities indicates that their presence has no appreciable effect
In the case of chromium and vanadium impurities, the
on the moment of nearby iron atoms.
data can only be interpreted in terms of a small increase of moment on iron atoms which are
roughly 4 Å distant from solute atoms. There appears to be a negative moment on the impurity
2014
atoms themselves.
Some rather direct information concerning the
electronic structure of magnetic transition metals
and their alloys is currently being produced by
the application of neutron diffraction techniques.
The usefulness of neutron scattering in this connection arises from the possibility of detecting
unpaired electron spins through their interaction
with the magnetic moment of the neutron. In an
ordered spin system two types of magnetic structure measurement
are
possible. Firstly, by
exa-
mination of the magnetic Bragg scattering an
average distribution of unpaired spin density over
A second type of
a unit cell may be plotted.
measurement, and the one with which we are
concerned in this paper, consists oi the observation
of the magnetic incoherent scattering from a
crystal containing magnetic defects. In this second case the experimental data enable the unpaired spin density disturbance surrounding the
defect to be derived.
Spin density disturbances are not necessarily
confined to the immediate vicinity of the defect
and in fact in a metal widespread disturbances
must certainly be envisaged. Results have previously been reported [1] in which extended disturbances are evident around dilute vanadium and
chromium impurities in nickel. In the present
work the effects of the addition of dilute impurities
into iron are investigated, the alloys studied being
those which form the Slater-Pauling diagram to
the left of iron. Thus, manganese, chromium and
vanadium are added as solutes and it is shown
that for manganese the magnetic disturbance is
confined to the impurity atom itself, whilst for
chromium and vanadium it is much more widespread, resulting in the transfer of moment on to
neighbouring iron atoms.
The existence of moment transfer effects leads
to the requirement for a suitable formalism in
which to discuss the relevant neutron scattering.
In a simple magnetic crystal, be it ferromagnetic,
ferrimagnetic or anti-f erromagnetic, in which the
unpaired spins are all parallel or antiparallel to
a particular direction z, the elastic magnetic
scattering of unpolarised neutrons is given by the
differential cross section.
The integral is over the volume of the specimen
Vs and the first bracket has the numerical value
of 0 , 073 barn. x is the scattering vector of the
neutrons and ot is the angle between x and the
direction z indicated above.
represents the
magnetic moment density arising from unpaired
spins, a positive or negative sign being used according as to whether the spins concerned lie parallel
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002505059600
597
If orbital moment is present,
or antiparallel to z.
the above cross section is in fact valid only at
x
0, but it still provides a fair approximation
at other values of x. The diff use component of
the scattering arises from the presence of defects
and is most conveniently expressed in terms of a
density p’(r - s) representing the deviation in
magnetic moment density at r caused by the
presence of a defect at lattice site s. The reference
value against which the deviation is measured is
the moment density appropriate to the unperturbed matrix. If it is assumed that the defects
are randomly distributed and sufficiently dilute
to ensure that their effects superpose, the diffuse
scattering may be written as [1]
=
c is the fractional concentration of defect sites in
the lattice and lV the total number of atoms.
From eq. (2) it is clear that the spatial distribution of the magnetic moment disturbance around
a defect may be obtained by Fourier inversion of
the diffuse scattering data. It may be noted that
in the forward direction (x
0) the cross section
is proportional to
The above
principles have recently been applied
investigation of magnetic defects
created when one transition metal is alloyed dilutely with another. This has required the development of a special apparatus employing long wavelength neutrons. A description of this instrument,
which enables the magnetic scattering of interest
to be accurately determined in the presence of
other competing forms of diffuse scattering, has
been given elsewhere [1].
at Harwell to the
The present work is concerned with three iron
based alloys, namely FeMn, FeCr and FeV. Polycrystalline samples of these alloys containing
roughly 1 % of solute atoms were prepared by
melting in an argon-arc furnace followed by
annealing to produce homogeneity. Measurements of the magnetic defect scattering as a
function of angle were carried out at a neutron
wavelength of about 5 Å. As in the previously
reported work care was taken to eliminate the
effects of multiple Bragg scattering from the
observations [1]. In the present experiments precautions in this connection are of great importance
because of the small magnetic disorder scattering
=
where
d~/dc represents the change of magnetic
sample per added defect. For
experiments carried out on polycrystals the cross
section has, of course, to be averaged over all
moment of the
directions of X relative to r. If we assume that
the magnetic moment disturbance may be expressed as fix) .ll~’~m), where /(x) is an atomic form
factor and lll’( m) represents the deviation from the
unperturbed value of the magnetic moment integrated over the unit cell surrounding lattice site m,
then this average may be written as
FIG. 1.
Magnetic impurity scattering of neutrons from
three dilute iron alloys. For Mn impurities the scattering follows the atomic 3d form factor shown, thus indicating that the magnetic disturbance in this case is
confined to the impurity atom sites. The scattering
f rom Cr or V alloys, on the other hand, shows a pronounced maximum at a scattering angle well removed
from the forward direction. The curves plotted for
these two alloys represent magnetic moment disturbances which are negative at the impurity atom sites and
on the nearest neighbour iron atoms and positive on
more distant neighbours (see text and figure 2).
-
The distance Rmn
and the form
factor is assumed to be spherically symmetric.
For large values of x, the second sum above, which
has an oscillatory nature, dies away rapidly so
that the intensity at high scattering angle is
==
roughly proportional
to
598
section of the iron alloys (i. e. the values
for these alloys are generally low). Moreover, the effects of multiple magnetic scattering
are large on account of the comparatively large
magnetic scattering length of iron. In fact measurements on the iron alloys were carried out at
a somewhat longer neutron wavelength than the
nickel alloy experiments [1]. This increased the
margin between the mean wavelength and the
cut-off for coherent scattering in the samples.
Tests on a pure iron specimen demonstrated that,
at this longer wavelength (1"’.1 5.3 A), the effects
of multiple magnetic scattering were reduced to
within the standard errors of the observations.
The results obtained for the three alloys concerned are shown in figure 1.
The scattering from Mn impurities is relatively
independent of angle over the range of x values
used for the present work. The curve in the figure
corresponds to a form factor appropriate to 3d
atomic wavefunctions and, as can be seen, this
represents the experimental data quite adequately.
This form factor is fitted at x
0 to a cross
section corresponding to the recently obtained
value [2] of dJ /dc = - 2.11 yB per solute atom
(see eq. (3)). It appears, therefore, that the effect
ot adding Mn atoms to iron may be simply described by saying that the solute atoms enter the
matrix in association with almost zero magnetic
moment and that the neighbouring Fe atoms are
largely unaffected by the presence of the impurities.
The scattering pattern from Cr and V solutes
is quite different. For these two alloys the values
are respectively
of
2 . 30 yB and
2 . 68 ~B
[2], so that it might have been expected that the
simple dilution mechanism found for FeMn would
also apply roughly in these cases. However, as
can be seen in the figure the scattering observed
actually increases as x departs from zero. Form
factors which behave in this manner can be accounted for only by a p’(r) distribution which has both
positive and negative values : in these circumstances a change of phase relating to a component
of the scattering can lead to an intensity increase.
In fact the scattering from these alloys may be
understood on the assumption that there is an
appreciable negative moment on each solute atom
and that the iron atoms which are nearest neighbours to an impurity carry moments which are
somewhat diminished from the value appropriate
to an unperturbed iron atom. More distant iron
neighbours require moments which are slightly
enhanced over the unperturbed magnitude. Thus,
the curves in the figure for the Cr and V solutes
represent calculations based on moments off
4 . 9 yB respectively for the impu- 0 . 7 yB and
atoms
concerned.
That a large difference in
rity
moment is required between an unperturbed iron
cross
d-ldc
=
’
-
-
and the impurities is apparent
atom (~ 2.22
from the comparatively large values of scattering
observed at high angles. In this region, as noted
above, the intensity is roughly proportional to
~m[M‘(m)]2. For any simple moment distribution
the values of [M’(m)]2 corresponding to the iron
atoms in the vicinity ot an impurity are too small
to account for the scattering at high angles and
so it follows that [M’(o)]2 must be large.
That
should be negative seems clear
the sign of
from the values of d-ldc.
Shull and Wilkinson [3] have measured magnetic disorder scattering from three concentrated
FeCr alloys and derived average moments for the
Fe and Cr atoms. Linear extrapolation of their
moments f or the Cr atoms to the low Cr concentration limit indicates a moment of about -1. 0
This would seem to be consistent with the value
used for our calculated curve to within the errors
involved.
The loss of moment suffered by nearest neighbour iron atoms is assumed in both cases to be
8 % of the unperturbed value, i. e. 8 % of 2.2
This is in agreement with shifts in the hyperfine
field found for both F_eCr and FeV alloys by Mossbauer effect experiments [4]. The calculations take
account of the first 112 neighbours of an impurity
-
FIG. 2.
Plot showing the magnetic moments for the
iron atom neighbours of an impurity site assumed in
calculating the form factors given in figure 1 for Fe Cr
and Fe V alloys. The moments on first and second
neighbours are not well determined (though the total
moment on these two shells is reasonably well defined)
and two fairly extreme cases are given ; (a) open circles
reduction in the moment of nearest
represent an 8
neighbours and (b) crosses represent equal moments on
first and second nearest neighbours.
-
599
it being assumed that the magnetic moment
disturbances beyond first neighbours are distributed as shown in figure 2. Clearly at a 1 %
solute content these 112 neighbours include on the
average one or two impurity atoms and, as pointed
out above, the interpretation has been based on
the assumption that the effects of the overlapping
distributions superpose.
The magnetic moment disturbances around
chromium and vanadium impurity atoms used in
the above calculations are subject to the assumption that the moment loss suffered by nearest
neighbouring iron atoms is proportional to the
shift in hyperfine field observed in Mossbauer
measurements. If this assumption is not made we
find that it is still possible to fit our data only
with moment distributions of the same type as
shown in figure 2a. This is to be expected since,
as pointed out above, the main ieatures of the
distribution can be derived from quite general
arguments. The neutron data are however then
found to be fairly insensitive to the exact distribution of moment between first and second nearest
neighbours since these are at very similar distances
from the impurity atom ; it is only sensitive to the
total moment on these two sets of neighbours.
Thus it is not possible to derive very meaningful
values for the individual moments on these atoms
though the total moment disturbance over the
fourteen atoms must be about
1.2 =t 0.4 yB
to give satisfactory agreement with the experimental data. Figure 2b shows the case where
the moments on first and second neighbours are
assumed to be equal ; this gives only a slightly
worse fit to the experimental data than for the
distribution ot figure 2a.
It is apparent that the calculated curves reproduce the experimental observations with reasonable accuracy, at least out to scattering angles
where the intensity maxima are observed. At
high scattering angles a divergence between calculation and experiment is evident, especially in
the case of
However, it is felt that the
distributions of magnetic moment disturbance on
which the predicted curves are based almost certainly represent the correct general form for the
actual distributions in the samples.
In the case of the FeCr alloy the scattering in
the forward direction is in good agreement with
the value of dJ/dc cited above. For FeV similar
agreement was not found, however, and the curve
shown in figure 1 is actually the result of scaling
all the calculated intensities by a factor of 0 . 64.
The reason tor this discrepancy is not clear. It
may be the result simply of an error in the value
used for c, the solute concentration. This could
arise from inhomogeneities in the alloy, as analyses
were carried out only on small samples taken from
-
the
edges of the large specimens used in the neutron
If this possibility were the case,
the procedure described above in connection with
the calculated curve would be appropriate. There
are two other possibilities, however, firstly, a very
widespread magnetic disturbance would give rise
to scattering eff ects close to the forward direction
which would not be observed in the present experiments. Thus, the form factor for FeV may rise
to a value compatible with the observed value
of dJ /dc in the region where x
0.2 A-’. The
second possibility is that the FeV alloy was not
cornpletely disordered. In these circumstances
superlattice reflections would appear at the expense
of the diffusely scattered intensity. In fact measurements of the relative intensities of the shifted
and unshifted Mossbauer lines suggest that ordering
is difficult to eliminate from somewhat more concentrated FeV alloys [4]. However, examination,
of the nuclear scattering from our specimen over
the range of x values covered by the present experiments did not reveal any evidence of ordering at all.
From the above results it is clear that earlier
simple theories concerning the electronic structure
of the present 3d transition metal alloys are in
error.
Thus, it has been suggested that 3d elements of lower atomic number form dilute alloys
with iron in which the magnetic moment of the
iron matrix is unaffected by the solute atoms,
while the impurities themselves carry practically
zero moment.
This does indeed appear to be the
situation for FeMn. However, in the case of FeCr,
and with somewhat less certainty for FeV, it
seems that the impurities carry an appreciable
negative moment and that the neighbouring iron
atoms are significantly affected, first suffering a
loss of moment and then an enhancement with
increasing distance from the impurity. Clearly
a proper explanation of these phenomena calls for
a detailed analysis of the 3d and 4s electron states
concerned.
The authors wish to thank Drs. W. M. Lomer
and W. Marshall for their interest in this work.
Grateful acknowledgement is made to Drs. A.
Arrott and J. E. Noakes and to Drs. T. E. Cranshaw and M. S. Ridout for communication of
experimental results prior to publication. Thanks
are due also to L. J. Bunce, N. S. Clark, M. S.
Clarke and I. C. Walker for experimental assistance. Finally the authors are grateful to the
B. S. A. Research Centre for supplying the alloy
measurements.
samples.
Discussion
Pr RUNDLE. - Peut-on interpreter raugmentation du moment de Fe par un transfert d’61eetrons de Cr et ’1 vers Fe ?
600
Dr Lovi;. - Je dois rappeler que le moment sur
les atomes Fe proches voisins des impuretes apparait en fait diminu6, tandis que I’augmentation
semble s’appliquer seulement aux voisins plus
éloignés. Ainsi, toute explication théorique de ces
résultats doit tenir compte des deux perturbations
aussi bien positives que negatives de la distribution des moments magnétiques.
REFERENCES
[1] Low (G. G. E.) and COLLINS (M. F.), J. Appl. Physics,
1963, 34, 1195.
[2] ARROTT (A.) and NOAKES (J. E.), Iron and its dilute
solid solutions, Spencer C. W. and Werner F. E.
editors, Interscience Publishers, 1963.
LF;
JOURNAL DE
[3] SHULL (C. G.) and WILKINSON (M. K.), Phys. Rev.,
1955, 97, 304.
[4] CRANSHAW (T. E.) and RIDOUT (M. S.), Private communication.
TOME
PHYSIQUE
25,
MAII
1964,
THE MAGNETIC STRUCTURE OF CoPt
By B.
VAN LAAR
Reactor Centrum Nederland, Petten
Résumé. 2014 Les résultats
a
Å,
2,677
=
c
=
3,685 Å
en
(N. H.),
the Netherlands.
diffraction de rayons X montrent que CoPt est
quadratique,
(1/2, 1/2, 1/2)
pour l’échan-
avec
Co0,92Pt0,08
en
(000)
et
Co0,08Pt0,92
en
tillon étudié.
Les moments
magnétiques
sont
couplés ferromagnétiquement.
deux éléments constituants et
Abstract.
with,
X-ray
sample
2014
for the
dirigés suivant l’axe
under
Co
en
On montre que le moment
on estime la grandeur des moments localisés
diffraction data show that CoPt is
investigation, Co0.92Pt0.08
the c-axis.
at
(1/2, 1/2, 1/2)
(0 0 0) et Pt en
magnétique total se partage
c.
sur
2.677 Å,
tetragonal, a
(0 0 0) and Co0.08Pt0.92
=
The Co at
sont
entre les
Co et Pt.
c
=
3.685
Å,
at (1/2 1/2 1/2).
at (1/2 1/2 1/2)
and the Pt
magnetic
(0 0)
point along
coupled ferromagnetically. It is shown that the total magnetic moment is divided between the
constituent elements and an estimate is made of the magnitude of the moments localized on Co
The
moments
0
are
and Pt.
Introduction.
CoPt has a tetragonal unit cell.
The space group is P4 /mmm. From X-ray data,
taken on a Philips diffractometer, the cell dimensions were determined : a
c
2 . 677
3 . 685 ui.
In the ideal case there is one Co-atom at (0 0 0)
TABLE 1
-
=
and
one
Pt-atom at
I222
II
ui,
In the
=
over
POSITIONS
IN
UNIT
CELL
investigated
g
~0.076 ,T 0.008).
The distribution of the atoms
OF
=
sample, provided by Philips Research Laboratories, Eindhoven, some disorder was observed.
The disorder parameter, the probability of a Cosite being occupied by a Pt-atom is :
r
OCCUPANCY
the two sites
is given in table 1. At room temperature CoPt
has ferromagnetic properties. From measurement
of the saturation magnetization, carried out by