SPIN WAVE DISPERSION RELATION IN ORDERED Fe3Al

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SPIN WAVE DISPERSION RELATION IN ORDERED Fe3Al

B. Antonini, F. Menzinger, A. Paoletti

To cite this version:

B. Antonini, F. Menzinger, A. Paoletti. SPIN WAVE DISPERSION RELATION IN ORDERED Fe3Al. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-1188-C1-1189.

�10.1051/jphyscol:19711426�. �jpa-00214469�

JOURNAL DE PHYSIQUE

Colloque C I , supple'ment au no 2-3, Tome 32, Pe'vrier-Mars 1971, page C 1 - 1188

SPIN WAVE DISPERSION RELATION IN ORDERED Fe ,A1

B. ANTONINI and F. MENZINGER

Laboratorio Fisica Nucleare Applicata, Centro Studi Nucleari della Casaccia del C. N. E. N., Roma, Italy A. PAOLETTI

Laboratorio Fisica NucIeare Applicata, Centro Studi NucIeari della Casaccia del C . N. E. N., Roma, Italy and Universita' dell'Aquila, Italy

R6sum6. -

La relation de dispersion des ondes de spin acoustiques dans FesAl ordonne a ete determinb par diffu- sion inClastique de neutrons polarisks. On a effectuB des mesures jusqu'8

A-

longueur d'ordre de magnon) et les points expkrimentaux ont Bte ajustCs griice

une loi de dispersion polynomiale. La loi qui rend le mieux compte des rksultats s'kcrit

avec

+

meV. A2 et

La diminution rapide de la constante de rigiditd par rapport

celle du fer pur ne s'explique pas uniquement par une simple dilution et suggkre que la variation de l'interaction d'echange dans la phase ordonnee doit jouer un r61e non negligeable. D'autre part, la loi de dispersion presque quadratique suggkre que l'interaction entre premiers voisins est prepondkrante.

Abstract. -

The dispersion relation of acoustical spin waves in ordered Fe3Al has been determined bu inelastic scattering of polarized neutrons. Measurements have been performed for values of magnon wavevectors

to

and the experimental points were fitted with a dispersion law of polynomial type. The best fit was found for the law

with

and B

The sharp decrease of the stiffness constant as compared with the one of pure Fe, can not be completely explained by simple dilution and suggests that the variation of the exchange interaction in the ordered phase should play an appreciable role. On the other hand the almost quadratic dispersion law suggests that the nearest neighbours interaction is predominant.

The Fe-A1 system undergoes an order-disorder TABLE I transition in the concentration range 20 at. % to

33 at. %

and two different values of the magnetic moment are associated to the unequivalent Fe atoms. At the stoichio- metric composition a magnetic moment

2.18

is associated with the iron atoms Fe,, surrounded by 8 Fe, nearest neighbours, while a moment ,uA

1 .SO

is associated with the FeA atoms surrounded by 4 Fe, and 4 A1 nearest neighbours [I].

The dispersion relation of the acoustical spin waves close to the [I101 direction has been measured at room temperature by the diffraction method with polarized neutrons [2]. The sample was a single crystal containing 26.5 at. % Al. The long range order para- meter was found to be the maximum allowed by this composition. The experimental results have been handled with the procedure described in ref. [3]. It consists in calculating directly from the scattering cross section the correct shape of the intensity profile instead of assuming a rectangular profile according to the procedure which has been generally followed until now. The angular width r of the magnon scatter- ing surface was measured for several missets from the (220) Bragg reflection. The results are shown in Table I.

The smallest crystal misset at which reliable measu- rements can be done is determined by overlapping of creation and annihilation processes, in this case 1.50.

The experimental data have been transferred from the space [(ki/kJ2, sin2(r/2)j to the space

q) following the procedure described in ref. 121. Here ki is the wavevector of the incoming neutron, k,, which is simply related to the misset angle, is given by ki + 2 nz, where z is the reciprocal lattice vector. A least squares fit has been performed assuming a dispersion law of the type hw

Dq2(1 -

Measured widths r of the scattering surfaces at various misset angles. ki and k, are defined in the text.

Misset angles -

2.0 2.5 3.0 3.5 4.0 4.5 5.0 - 2.0

- 3.0

- 4.0

(ki/k1>2 r,

degrees

-

-

1.038 4.61 , ^0.06

1.048 4.85

0.05 1.057 5.34 f 0.03 1.068 5.46

0.1 1 1.078 5.98

0.08 1.089 6.09 + ^0.09

1.099 6.39

0.08 0.966 4.26

0.13 0.951 5.16 + 0.06 0.935 5.56

0.12

the following results

D

(83 + ^{4) meV} . A2 and

(0.1

0.6) A2. The value of the stiffness constant is much reduced with respect to the one observed in pure Fe [4].

Previous experimental results on the Fe-A1 system [5]

have shown that the concentration dependence of the stiffness constant in the disordered phase, for A1 concentration up to 20 at. %, namely in the range of simple dilution, is in good agreement with the predic- tion of a localized electron model by Murray [6]. At higher A1 concentration two features were observed

the D value in the disordered phase undergoes a sharp fall which is not predicted by the Murray's model, and in the ordered phase the stiffness constant is even lower. According to Murray a D value of 155 meV.A should be expected for our composition in disordered phase if A1 entered the alloy as asimple diluent. However in this concentration range order

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711426

SPIN WAVE DISPERSION RELATION IN ORDERED Fe3AI C 1

-

IiIc. 1 . -Energy momentum dispersion relation. The line gives the best fit to the experimental points which were obtai- ned by transformation from the space [(kilkl)', sinZ(r/2)] to the space

(hw,

Energies are plotted against the square of the momentum in order to show the almost perfectly quadratic dispersion relation.

sets in and the magnetization decreases more rapidly than simple dilution, therefore a much smaller value of D could be expected. A more appropriate model must then take into account the structure of the alloy in the ordered state.

Leoni and Natoli [7] have calculated the relationship between the exchange integrals and the dispersion law in the Heisenberg model for the Fe,AI structure.

By means of a power expansion of their results we have derived, in the simplest case, when only the nearest neighbours exchange interaction JAD is operat- ing, the following relations

The spin of the atoms a t the sites A and D, SA and SD respectively, have been redetermined, for our composition, at room temperature, by polarized neu- trons. They are

SA

0.62 and SD

1.00. From these values we expect j3

0.33 A2, independent on the exchange integral, which is in good agreement with our experimental value. From the D value we obtain JAD

9.0

0.4 meV. Our results do not permit to rule out a longer range of the exchange interaction. In fact the presence of the next-nearest neighbours interaction JAA, either positive or negative, would give a value of /3 larger than 0.33 A2. However in pure Fe the most recent results [4] have shown only a small deviation from a nearest neighbours Heisenberg model which should be an indication that next-nearest neighbours interaction as already noted by Sato and ~ r r o t t [8] are not very important. Since in Fe3AI it happens that next-nearest neighbours have almost the same distance as in pure Fe, one expects that JAA is not large and not essential in establishing ferromagnetism also in Fe,Al. The nearest- neighbours exchange interaction is much reduced in this alloy with respect to pure Fe where, as it can be deduced from the measured stiffness constant

in the Heisenberg model it is 15.7 rneV at room tempe- rature.

It can be noted that the reduction of the nearest neighbours interaction JAD from pure Fe to Fe3A1 is 43 % i. e. the same as the reduction of the magnetic moment of the A site which goes from 2.18 to 1.24

The introduction of the exchange integrals and their comparison could be criticized

to be strictly correct, measurements at different temperatures and extrapolation of the D value at 0

should be done before introducing the J's. However we expect that the overall picture should not be affected very much.

This study provides an indication of the extension of the exchange interactions in Fe,Al and we think that the completion of the acoustic branch at higher q and the study of the optical branches with a triple axis spectrometer would be very valuable.

References

PICKART (S. J.) and NATHANS (R.), Phys. Rev., 1961,

123, 1163.

ALPERIN

A.), STEINSVOLL

NATHANS (R.) and SHIRANE (G.), Phys. Rev., 1967,

508.

ANTONINI (B.), MEDINA (R.) and MENZINGER

Nucl.

Meth., 1970, 87, 125.

[4] SHIRANE

MINKIEWICZ

and NATHANS

Phys., 1968, 39, 383.

El

ANTONINI (B.) and STRINGFELLOW (M.

Proc.

.-a - , ,

Phys. 'SOC., 1966, 89, 419.

[6] MURRAY (G.

PYOC. Phys. Soc., 1966, 89,

[7]

LEONI

and NATOLI

Physica, 1969,

181 SATO (H.)

and ARROTT (A.), Phys. Rev., 1959,114,1427.