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Submitted on 1 Jan 1964

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Neutron diffraction studies of magnetic moments indilute 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 metalalloys. Journal de Physique, 1964, 25 (5), pp.596-600. <10.1051/jphys:01964002505059600>. <jpa-00205835>

596.

NEUTRON DIFFRACTION STUDIES OF MAGNETIC MOMENTSIN DILUTE TRANSITION METAL ALLOYS

By M. F. COLLINS and G. G. LOWSolid 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 alliagesferromagnétiques dilués ont permis d’étudier les modifications de la distribution spatiale desmoments magnétiques autour de l’atome dissous. Les résultats sont présentés pour des alliagesdilués polycristallins dont la base est du fer en montrant la distribution magnétique autour desatomes de manganèse, de chrome et de vanadium. La diffusion par les impuretés de manganèseindique que leur présence n’a pas d’effet appréciable sur le moment des atomes de fer voisins. Dansle cas des impuretés de chrome et de vanadium, les résultats ne peuvent s’interpréter que si l’onadmet un faible accroissement des moments des atomes de fer qui sont à une distance voisine de4 Å des atomes dissous. Il semble y avoir un moment négatif sur les atomes d’impuretés eux-mêmes.

Abstract. 2014 Measurements of the magnetic disorder scattering of neutrons from dilute ferro-magnetic alloys allow the spatial distribution of the magnetic moment disturbance around thesolute atoms to be investigated. Results are presented for dilute polycrystalline iron based alloysshowing the magnetic moment distribution around manganese, chromium and vanadium atoms.The scattering from manganese impurities indicates that their presence has no appreciable effecton the moment of nearby iron atoms. In the case of chromium and vanadium impurities, thedata can only be interpreted in terms of a small increase of moment on iron atoms which areroughly 4 Å distant from solute atoms. There appears to be a negative moment on the impurityatoms themselves.

LE JOURNAL DE PHYSIQUE - TOME 25, MAI 1964,

Some rather direct information concerning theelectronic structure of magnetic transition metalsand their alloys is currently being produced bythe application of neutron diffraction techniques.The usefulness of neutron scattering in this con-nection arises from the possibility of detectingunpaired electron spins through their interactionwith the magnetic moment of the neutron. In anordered spin system two types of magnetic struc-ture measurement are possible. Firstly, by exa-mination of the magnetic Bragg scattering anaverage distribution of unpaired spin density overa unit cell may be plotted. A second type of

measurement, and the one with which we are

concerned in this paper, consists oi the observationof the magnetic incoherent scattering from a

crystal containing magnetic defects. In this se-

cond case the experimental data enable the un-paired spin density disturbance surrounding thedefect to be derived.

Spin density disturbances are not necessarilyconfined to the immediate vicinity of the defectand in fact in a metal widespread disturbancesmust certainly be envisaged. Results have pre-viously been reported [1] in which extended distur-bances are evident around dilute vanadium andchromium impurities in nickel. In the presentwork the effects of the addition of dilute impuritiesinto iron are investigated, the alloys studied being

those which form the Slater-Pauling diagram tothe left of iron. Thus, manganese, chromium andvanadium are added as solutes and it is shownthat for manganese the magnetic disturbance isconfined to the impurity atom itself, whilst forchromium and vanadium it is much more wide-spread, resulting in the transfer of moment on toneighbouring iron atoms.The existence of moment transfer effects leads

to the requirement for a suitable formalism inwhich to discuss the relevant neutron scattering.

In a simple magnetic crystal, be it ferromagnetic,ferrimagnetic or anti-f erromagnetic, in which theunpaired spins are all parallel or antiparallel toa particular direction z, the elastic magneticscattering of unpolarised neutrons is given by thedifferential cross section.

The integral is over the volume of the specimenVs and the first bracket has the numerical valueof 0 , 073 barn. x is the scattering vector of theneutrons and ot is the angle between x and thedirection z indicated above. represents themagnetic moment density arising from unpairedspins, a positive or negative sign being used accor-ding 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

or antiparallel to z. If orbital moment is present,the above cross section is in fact valid only atx = 0, but it still provides a fair approximationat other values of x. The diff use component ofthe scattering arises from the presence of defectsand is most conveniently expressed in terms of adensity p’(r - s) representing the deviation in

magnetic moment density at r caused by thepresence of a defect at lattice site s. The referencevalue against which the deviation is measured isthe moment density appropriate to the unper-turbed matrix. If it is assumed that the defectsare randomly distributed and sufficiently diluteto ensure that their effects superpose, the diffuse

scattering may be written as [1]

c is the fractional concentration of defect sites inthe lattice and lV the total number of atoms.From eq. (2) it is clear that the spatial distri-

bution of the magnetic moment disturbance arounda defect may be obtained by Fourier inversion ofthe diffuse scattering data. It may be noted thatin the forward direction (x = 0) the cross sectionis proportional to

where d~/dc represents the change of magneticmoment of the sample per added defect. For

experiments carried out on polycrystals the crosssection has, of course, to be averaged over alldirections of X relative to r. If we assume thatthe magnetic moment disturbance may be expres-sed as fix) .ll~’~m), where /(x) is an atomic formfactor and lll’( m) represents the deviation from theunperturbed value of the magnetic moment inte-grated over the unit cell surrounding lattice site m,then this average may be written as

The distance Rmn == and the formfactor is assumed to be spherically symmetric.For large values of x, the second sum above, whichhas an oscillatory nature, dies away rapidly so

that the intensity at high scattering angle is

roughly proportional to

The above principles have recently been appliedat Harwell to the investigation of magnetic defectscreated when one transition metal is alloyed dilu-tely with another. This has required the develop-ment of a special apparatus employing long wave-length neutrons. A description of this instrument,which enables the magnetic scattering of interestto be accurately determined in the presence ofother competing forms of diffuse scattering, hasbeen given elsewhere [1].The present work is concerned with three iron

based alloys, namely FeMn, FeCr and FeV. Poly-crystalline samples of these alloys containingroughly 1 % of solute atoms were prepared bymelting in an argon-arc furnace followed byannealing to produce homogeneity. Measu-rements of the magnetic defect scattering as a

function of angle were carried out at a neutronwavelength of about 5 Å. As in the previouslyreported work care was taken to eliminate theeffects of multiple Bragg scattering from theobservations [1]. In the present experiments pre-cautions in this connection are of great importancebecause of the small magnetic disorder scattering

FIG. 1. - Magnetic impurity scattering of neutrons fromthree dilute iron alloys. For Mn impurities the scatte-ring follows the atomic 3d form factor shown, thus indi-cating that the magnetic disturbance in this case isconfined to the impurity atom sites. The scatteringf rom Cr or V alloys, on the other hand, shows a pro-nounced maximum at a scattering angle well removedfrom the forward direction. The curves plotted forthese two alloys represent magnetic moment distur-bances which are negative at the impurity atom sites andon the nearest neighbour iron atoms and positive onmore distant neighbours (see text and figure 2).

598

cross section of the iron alloys (i. e. the valuesd-ldc for these alloys are generally low). Mo-reover, the effects of multiple magnetic scatteringare large on account of the comparatively largemagnetic scattering length of iron. In fact mea-surements on the iron alloys were carried out ata somewhat longer neutron wavelength than thenickel alloy experiments [1]. This increased the

margin between the mean wavelength and thecut-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 effectsof multiple magnetic scattering were reduced towithin the standard errors of the observations.The results obtained for the three alloys concer-

ned are shown in figure 1.The scattering from Mn impurities is relatively

independent of angle over the range of x valuesused for the present work. The curve in the figurecorresponds to a form factor appropriate to 3datomic 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 obtainedvalue [2] of dJ /dc = - 2.11 yB per solute atom(see eq. (3)). It appears, therefore, that the effectot adding Mn atoms to iron may be simply des-cribed by saying that the solute atoms enter thematrix in association with almost zero magneticmoment and that the neighbouring Fe atoms arelargely unaffected by the presence of the impu-rities.The scattering pattern from Cr and V solutes

is quite different. For these two alloys the valuesof are respectively - 2 . 30 yB and - 2 . 68 ~B[2], so that it might have been expected that thesimple dilution mechanism found for FeMn wouldalso apply roughly in these cases. However, ascan be seen in the figure the scattering observedactually increases as x departs from zero. Formfactors which behave in this manner can be accoun-ted for only by a p’(r) distribution which has bothpositive and negative values : in these circums-tances a change of phase relating to a componentof the scattering can lead to an intensity increase.

In fact the scattering from these alloys may beunderstood on the assumption that there is an

appreciable negative moment on each solute atomand that the iron atoms which are nearest neigh-bours to an impurity carry moments which aresomewhat diminished from the value appropriateto an unperturbed iron atom. More distant iron

neighbours require moments which are slightlyenhanced over the unperturbed magnitude. Thus,the curves in the figure for the Cr and V solutesrepresent calculations based on moments of f- 0 . 7 yB and - 4 . 9 yB respectively for the impu-rity atoms concerned. That a large difference inmoment is required between an unperturbed iron

atom (~ 2.22 and the impurities is apparentfrom the comparatively large values of scatteringobserved at high angles. In this region, as notedabove, the intensity is roughly proportional to~m[M‘(m)]2. For any simple moment distributionthe values of [M’(m)]2 corresponding to the ironatoms in the vicinity ot an impurity are too smallto account for the scattering at high angles andso it follows that [M’(o)]2 must be large. Thatthe sign of should be negative seems clearfrom the values of d-ldc.

Shull and Wilkinson [3] have measured magne-tic disorder scattering from three concentratedFeCr alloys and derived average moments for theFe and Cr atoms. Linear extrapolation of theirmoments f or the Cr atoms to the low Cr concen-tration limit indicates a moment of about -1. 0 This would seem to be consistent with the valueused for our calculated curve to within the errorsinvolved.The loss of moment suffered by nearest neigh-

bour 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 hyperfinefield found for both F_eCr and FeV alloys by Moss-bauer effect experiments [4]. The calculations takeaccount of the first 112 neighbours of an impurity

FIG. 2. - Plot showing the magnetic moments for theiron atom neighbours of an impurity site assumed incalculating the form factors given in figure 1 for Fe Crand Fe V alloys. The moments on first and second

neighbours are not well determined (though the totalmoment on these two shells is reasonably well defined)and two fairly extreme cases are given ; (a) open circlesrepresent an 8 reduction in the moment of nearestneighbours and (b) crosses represent equal moments onfirst and second nearest neighbours.

599

it being assumed that the magnetic momentdisturbances beyond first neighbours are distri-buted as shown in figure 2. Clearly at a 1 %solute content these 112 neighbours include on theaverage one or two impurity atoms and, as pointedout above, the interpretation has been based onthe assumption that the effects of the overlappingdistributions superpose.The magnetic moment disturbances around

chromium and vanadium impurity atoms used inthe above calculations are subject to the assump-tion that the moment loss suffered by nearestneighbouring iron atoms is proportional to theshift in hyperfine field observed in Mossbauermeasurements. If this assumption is not made wefind that it is still possible to fit our data onlywith moment distributions of the same type asshown in figure 2a. This is to be expected since,as pointed out above, the main ieatures of thedistribution can be derived from quite generalarguments. The neutron data are however thenfound to be fairly insensitive to the exact distri-bution of moment between first and second nearest

neighbours since these are at very similar distancesfrom the impurity atom ; it is only sensitive to thetotal moment on these two sets of neighbours.Thus it is not possible to derive very meaningfulvalues for the individual moments on these atoms

though the total moment disturbance over thefourteen atoms must be about - 1.2 =t 0.4 yBto give satisfactory agreement with the experi-mental data. Figure 2b shows the case wherethe moments on first and second neighbours areassumed to be equal ; this gives only a slightlyworse fit to the experimental data than for thedistribution ot figure 2a.

It is apparent that the calculated curves repro-duce the experimental observations with reaso-nable accuracy, at least out to scattering angleswhere the intensity maxima are observed. At

high scattering angles a divergence between calcu-lation and experiment is evident, especially inthe case of However, it is felt that the

distributions of magnetic moment disturbance onwhich the predicted curves are based almost cer-tainly represent the correct general form for theactual distributions in the samples.

In the case of the FeCr alloy the scattering inthe forward direction is in good agreement withthe value of dJ/dc cited above. For FeV similar

agreement was not found, however, and the curveshown in figure 1 is actually the result of scalingall 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 valueused for c, the solute concentration. This couldarise from inhomogeneities in the alloy, as analyseswere carried out only on small samples taken from

the edges of the large specimens used in the neutronmeasurements. If this possibility were the case,the procedure described above in connection withthe calculated curve would be appropriate. Thereare two other possibilities, however, firstly, a verywidespread magnetic disturbance would give riseto scattering eff ects close to the forward directionwhich would not be observed in the present expe-riments. Thus, the form factor for FeV may riseto a value compatible with the observed valueof dJ /dc in the region where x 0.2 A-’. Thesecond possibility is that the FeV alloy was notcornpletely disordered. In these circumstances

superlattice reflections would appear at the expenseof the diffusely scattered intensity. In fact measu-rements of the relative intensities of the shiftedand unshifted Mossbauer lines suggest that orderingis difficult to eliminate from somewhat more con-centrated FeV alloys [4]. However, examination,of the nuclear scattering from our specimen overthe range of x values covered by the present experi-ments did not reveal any evidence of ordering at all.From the above results it is clear that earlier

simple theories concerning the electronic structureof the present 3d transition metal alloys are inerror. Thus, it has been suggested that 3d ele-ments of lower atomic number form dilute alloyswith iron in which the magnetic moment of theiron matrix is unaffected by the solute atoms,while the impurities themselves carry practicallyzero moment. This does indeed appear to be thesituation for FeMn. However, in the case of FeCr,and with somewhat less certainty for FeV, it

seems that the impurities carry an appreciablenegative moment and that the neighbouring ironatoms are significantly affected, first suffering aloss of moment and then an enhancement with

increasing distance from the impurity. Clearlya proper explanation of these phenomena calls fora detailed analysis of the 3d and 4s electron statesconcerned.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. Crans-haw and M. S. Ridout for communication of

experimental results prior to publication. Thanksare due also to L. J. Bunce, N. S. Clark, M. S.Clarke and I. C. Walker for experimental assis-tance. Finally the authors are grateful to theB. S. A. Research Centre for supplying the alloysamples.

Discussion

Pr RUNDLE. - Peut-on interpreter raugmen-tation du moment de Fe par un transfert d’61ee-trons de Cr et ’1 vers Fe ?

600

Dr Lovi;. - Je dois rappeler que le moment surles atomes Fe proches voisins des impuretes appa-rait en fait diminu6, tandis que I’augmentationsemble s’appliquer seulement aux voisins plus

éloignés. Ainsi, toute explication théorique de cesrésultats doit tenir compte des deux perturbationsaussi bien positives que negatives de la distri-bution 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 dilutesolid solutions, Spencer C. W. and Werner F. E.editors, Interscience Publishers, 1963.

[3] SHULL (C. G.) and WILKINSON (M. K.), Phys. Rev.,1955, 97, 304.

[4] CRANSHAW (T. E.) and RIDOUT (M. S.), Private com-munication.

THE MAGNETIC STRUCTURE OF CoPt

By B. VAN LAARReactor Centrum Nederland, Petten (N. H.), the Netherlands.

Résumé. 2014 Les résultats en diffraction de rayons X montrent que CoPt est quadratique,a = 2,677 Å, c = 3,685 Å avec Co0,92Pt0,08 en (000) et Co0,08Pt0,92 en (1/2, 1/2, 1/2) pour l’échan-tillon étudié.

Les moments magnétiques sont dirigés suivant l’axe c. Co en (0 0 0) et Pt en (1/2, 1/2, 1/2) sontcouplés ferromagnétiquement. On montre que le moment magnétique total se partage entre lesdeux éléments constituants et on estime la grandeur des moments localisés sur Co et Pt.

Abstract. 2014 X-ray diffraction data show that CoPt is tetragonal, a = 2.677 Å, c = 3.685 Å,with, for the sample under investigation, Co0.92Pt0.08 at (0 0 0) and Co0.08Pt0.92 at (1/2 1/2 1/2).The magnetic moments point along the c-axis. The Co at (0 0 0) and the Pt at (1/2 1/2 1/2)

are coupled ferromagnetically. It is shown that the total magnetic moment is divided between theconstituent elements and an estimate is made of the magnitude of the moments localized on Coand Pt.

LF; JOURNAL DE PHYSIQUE TOME 25, MAI I 1964,

Introduction. - CoPt has a tetragonal unit cell.The space group is P4 /mmm. From X-ray data,taken on a Philips diffractometer, the cell dimen-sions were determined : a = 2 . 677 ui, c = 3 . 685 ui.In the ideal case there is one Co-atom at (0 0 0)and one Pt-atom at I I I In the investigated222 g

sample, provided by Philips Research Labora-tories, Eindhoven, some disorder was observed.The disorder parameter, the probability of a Co-site being occupied by a Pt-atom is :

r = ~0.076 ,T 0.008).The distribution of the atoms over the two sites

TABLE 1

OCCUPANCY OF POSITIONS IN UNIT CELL

is given in table 1. At room temperature CoPthas ferromagnetic properties. From measurementof the saturation magnetization, carried out by