EXPERIMENTAL DETERMINATION OF EXCHANGE INTEGRALS IN MAGNETITE

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EXPERIMENTAL DETERMINATION OF EXCHANGE INTEGRALS IN MAGNETITE

Gr. Diff. Inélastique Des Neutrons

To cite this version:

Gr. Diff. Inélastique Des Neutrons. EXPERIMENTAL DETERMINATION OF EXCHANGE IN- TEGRALS IN MAGNETITE. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-1182-C1-1183.

�10.1051/jphyscol:19711423�. �jpa-00214466�

JOURNAL DE PHYSIQUE Collogue C 1, suppl2ment au no 2-3, Tome 32, Fdvrier-Mars 1971, page C 1 - 1182

EXPERIMENTAL DETERMINATION OF EXCHANGE INTEGRALS IN MAGNETITE

GROUPE D E DIFFUSION INELASTIQUE DES NEUTRONS (*) Service de Physique du Solide et de RCsonance Magnttique Centre d'Etudes NuclCaires de SacIay, 91, Gif-sur-Yvette, France

R&um(?. - De nouvelles expkriences de diffusion inelastique de neutrons, au moyen d'un spectromktre a 3 axes, conduisent a une meilleure connaissance des intkgrales d'echange dans la magnetite. De nouvelles branches ont Btk obser- vkes. Leurs frkquences peuvent 6tre trks bien ajustkes dans le modkle d'Heisenberg, mais pas leurs intensites.

Abstract. - New experiments of inelastic neutron scattering, by means of a triple-axis spectrometer, lead to a better knowledge of the exchange integrals in magnetite. New optical branches have been observed. Their frequencies may very well be fitted in the Heisenberg model, but not their intensities.

Spin wave dispersion curves in magnetite (Fe,O,) have been studied by neutrons spectrometry in 1958 by Brockhouse and Watanabe [I], a t room tempera- ture, then by Torrie [2] at 77 OK in 1967. Brockhouse and Watanabe observed the whole acoustic branch and part of an optical one. These measurements gave JAB (exchange integrals between nearest-neighbor ions A and B) and suggested that JBB was about - 0.10 JAB, but gave no information about , J which was thought negligible.

Moglestue [3], analyzing a set of experimental results obtained by various methods, came to the conclusion that the three exchange integrals JAB, JAA, and JBB had to be taken into account, and he deter- mined a set of values in agreement with those already found by NCel [4], in 1948, in studying the parama- gnetic susceptibility (see Table).

JAB MeV JAB MeV JAB MeV

-

-

NCel - 2. - 1.5 0.04

Glasser and Mil-

ford - 2-4 0 0.24

Moglestue - 2.42 - 1.52 0.3 1

This work - 2.38 - ^1.56 0.26

Our work was lead on a triple-axis spectrometer, in Saclay, with a natural crystal (4 x 4 x 1.3 em3), aligned with a vertical [I101 axis, a n electromagnet being able to produce a vertical field of some 2 000 Gauss a t the sample. Measurements were made a t room temperature, along the [001] direction, most of them around the reciprocal lattice point (W), some ones being made or confirmed around other points.

We could improve the optical branch observed by Brockhouse and Watanabe and disclosed two other

FIG. 1. - Experimental results, without corrections. Solid lines are calculated curves with ^JAB

- 2.38 MeV,

JAA = - 1.56 MeV, JBB

0.26 MeV, JAS

0.11 MeV.

(*) The Group of Diffusion Inelastic of the Neutrons is optical branches (w, and w, in Glasser and Milford [ 5 ] composed by : Mr. H. Bourdonna~, A. Bousquet, ^J- P- Cotton, notations) (see Fig. 1). The magnetic origin of these D. Cribier, B. Farnoux, R. Feuillatre, B. Hennion, J. Jacquier,

Ci. Jannink, R. Kahn, D. Mons, J. Mom, G. Parette, G. Perpy, branches was ascertained by the a magnetic L. Rouleau, J. P. Trotin and Mrs. Moussa. field (see Fig. 2). Theoretical dispersion curves were

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711423

EXPERIMENTAL DETERMINATION OF EXCHANGE INTEGRALS I N MAGNETITE C 1 - 1183

acoustic msgnon

Intensity i n .4 ^(branch

₃ ^{h0.1.3 [001] direction}

= Z.LZ~IO'~~AE = T O mev)

890

field off

acoustic phonon + field on 600

'\

FIG. 2. - Neutron groups, with and without magnetic field.

Q-constant method for the acoustic magnon. v-constant method for the optical magnon.

I

, ,

4.1 L.2 43 4.L

Intensity

calculated in the harmonic approximation from the Heisenberg hamiltonian, using the inverse spinel structure determined by Shull and al. [6]. The best fitting with experimental points is obtained by taking

600 500

400

300

JAB = - 2.38 M e V , JAA ⁼ - 1.56 MeV,

-

h0=0.81A

-

-

field off

+ f ~ e l d on

-

JBB = 0.26 MeV,

values in fair agreement with those proposed by Moglestue. It seems that the fitting is improved by adding an exchange integral between second-neighbor ions A(JAs) of about - 0.10 JAA.

The diagonalization of the hamiltonian gives the eigenvectors and the scattering cross-section may then be calculated for each mode. In the Heisenberg model, the structure factor of the spin wave mode ^o,, in the [OOl] direction, is zero in the whole (004) Brillouin zone, therefore the o, branch should not be seen there.

But it was actually observed in the (004) zone and the observed intensity was comparable with that of the o, branch. An interaction between o2 and a4 branches has an effect too localized near the crossing of the branches as to explain such a fact.

As indeed it is the hamiltonian symmetry which causes the cancellation of the structure factor, it seems that the symmetry must be broken by introducing magnetic interaction of another type than S i . S j Hei- senberg term. Calculus are now pursued.

We are very grateful to Mrs. Nauciel, Mr. Herpin, Mr. Sarma and Mr. Winter for very constructive discussions.

References

[I] BROCKHOUSE (B. N.) and WATANABE (H.), Physics [41 N ~ E L (L.), Ann. Ph~s., 1948, 3, 137.

Letters, 1962, 1, 189. [5] GLASSER (M. L.) and MILFORD (F. J.), Phys. Rev., [2] TORRIE (B. H.), Solid State Communications, 1967, ^1963, 130, 1783.

5, 715. [6] SHULL (C. G.), WOLLAN (E. 0.) and KOEHLER (W. C.), [3] MOGLESTUE (K. T.), I. A. E. A. Congress of Copen- Phys. Rev., 1951, ^84, 912.

hagen, 1968, 2, 117.