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Submitted on 1 Jan 1971
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INELASTIC NEUTRON SCATTERING INVESTIGATION OF SPIN WAVES AND MAGNETIC INTERACTIONS IN α-Fe2O3
E. Samuelsen, G. Shirane
To cite this version:
E. Samuelsen, G. Shirane. INELASTIC NEUTRON SCATTERING INVESTIGATION OF SPIN WAVES AND MAGNETIC INTERACTIONS INα-Fe2O3. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-1064-C1-1065. �10.1051/jphyscol:19711382�. �jpa-00214421�
ONDES DE SPIN (2' partie)
INELASTIC NEUTRON SCATTERING INVESTIGATION
OF SPIN WAVES AND MAGNETIC INTERACTIONS IN a - F e 2 0 3 (*) by E. J. SAMUELSEN
Institute for Atomenergi, Kjeller, Norway (**) and Brookhaven National Laboratory, Upton, N. Y., U. S. A.
and G. SHIRANE
Brookhaven National Laboratory, Upton, N. Y., U. S. A.
Rksum6. - Nous avons 6tudi6 les ondes de spin dans a-Fez03 antiferromagnktique a des temperatures de 240 OK et 290 OK par la diffusion inklastique de neutrons. Nous reportons ici la premikre dktermination de la branche acoustique dans toute la zone de Brillouin et la premikre observation de la branche optique. La relation de dispersion ne change pas au passage de la transition de renversement de spin a 260 OK. Des rksultats expkrimentaux, nous dkduisons les valeurs des paramktres d'interaction d'kchange proches voisins que nous trouvons trks diffkrents des paramktres correspondants dans ( 3 2 0 3 .
Abstract. - We have studied spin waves in antiferromagnetic a-Fez03 at temperatures of 240 OK and 290 OK by means of inelastic neutron scattering, and we report here the first determination of the acoustical branch throughout the entire Brillouin zone and the first observation of the optical branch. No effect on the dispersion relation was seen in crossing the spin flip transition at 260 OK. The data were used to deduce the values of the nearest neighbour exchange interaction parameters, and they were found to be very different from the corresponding parameters for CrzO3.
Hematite or a-Fe20, has represented a challenge to physicists for the last two decades. The main puzzle has been to understand the spin flip transition at TM = 260 OK and the associated occurrence of weak ferromagnetism above TM [I], but also the question of what the exchange interaction pattern in the mate- rial is, has attracted some interest. In this respect the comparison with the chemically isomorphous Cr203 is interesting, and theoretical predictions have been for- warded on the pair exchange interaction parameters for the two compounds based on superexchange theories [2]. Although the two materials both have the corundum chemical structure, their spin ordering structures are different. The rhombohedral corundum unit cell contains four cations, two with up-spins and two with down-spins in the antiferromagnetic state, but the sequence of + - is different for the two cases.
In fact for Cr203 a unit cell containing only two Cr3+-ions can be chosen, and for isotropic Heisenberg interactions the spin wave spectrum may be described in a Brillouin zone containing only one continuous branch. For a-Fe203 this is not possible, and a true optical branch must exist in addition to the acoustical one.
The spin wave spectrum of Cr203 has previously been obtained by inelastic neutron scattering measurements [3], and a continuous branch throughout the extended zone was in fact observed. Here we report on similar measurements for a-Fe203. They were carried out at the Brookhaven High Flwr Beam Reactor using triple axis techniques on a large natural single crystal sample.
Incident neutron energies up to 165 meV were used for studying the high energy end of the spectrum, and regions of the reciprocal space of the highest
(*) Work supported by the United States Atomic Energy Commission.
(**) Permanent address.
dynamical structure factors were selected out, in order to cope with the inherent loss of intensities at such high energy transfers. The observed dispersion relations at 240 OK for three principal directions are shown in figure 1. The slope of the linear parts of the acoustical
-z r D r A- z r
WAVEVECTOR q. 1.'
FIG. 1. - Observed and calculated spin wave dispersion rela- tions for a-Fez03 at 240 OK in three principal rhombohedral directions. Along [ I l l ] is the calculated curve shown all to the next zone centre to compare with the dispersion relation for Cr203 at 78 OK 131, shown as a dashed curve. A sketch of the Brillouin zone is shown inserted in the upper right corner,
together with that used for Cr203 (dashed).
branch is in good agreement with previous determina- tions [4]. The optical branch has not been previously observed. It is seen to be quite flat, except at the zone boundary near the Z-point, where it dips down <(to meet >> with the acoustical branch.
Differences between a-Fe20, and Cr203 originating from their different spin structures is illustrated on the left half of figure 1. The Brillouin zones for the two cases are indicated at the upper left corner, where in particular the larger dimension in the [I 111-direction of the Cr203-zone is shown. The acoustical branch for Cr203 in that zone scheme is shown as a dashed curve. For a-Fe203 the use of the same scheme would imply the acoustical branch of one zone continuing into the optical branch of the neighbouring zone.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711382
INELASTIC NEUTRON SCATTERING INVESTIGATION OF SPIN WAVES AND MAGNETIC INTERACTIONS C 1 - 1065
TABLE I
J1 Jz J3 J4 J5 J6 J7 Ref.
a-Fe203 J,,, 6.0 1.6 - 29.7 - 23.2 - 1 . 0 .5 - .1 This work
AJm 1.6 .6 2.0 1 .O 1 .O .4 .2
Cr203 Jm - 87.3 (*) - 37.8 .7 .2 (*) - 2.2 .6 - .1 Ref. [3]
AJm 23 (*) 1.5 2.0 2.3 (*) .8 .5 .5
(*) The fitting of Jl and J, was strongly correlated.
Exchange interaction constants J,,, between mth neighbours defined by X = - c J ( r , n j - rntjt) S n j . Sneje
nn' jj'
as determined from the spin wave dispersion relations for a-Fe,O, and Cr, O3 at temperatures of 2400K and 78 OK, respectively, in units of OK.
The gap at the Z-point then represents the different spin pattern of a-Fez03.
In Table I we give the values obtained for the nearest neighbour exchange interaction constants when fitting the data to theoretical expressions for the dispersion relation. The difference between the two compounds is striking. Whereas the two first nearest neighbour couplings are strongest and the two farther out are weak for Crz03, the situation is reversed for a-Fe203. In fact the two nearest neighbour couplings for a-Fez03 are ferromagnetic. - The observed diffe- rence is in fair qualitative agreement with theoretical predictions, in particular with that of Goodenough [2].
The primary reason for the different coupling para- meters in the two compounds is the difference in the d-orbital population, that allows different overlap patterns with the oxygen p-wave functions. Also direct d-d-orbital overlaps may play a role [2].
We shall give a few comments on the spin flip
transition. Qualitatively it may be described as being caused by a change of sign of the first order anisotropy constant K , at T M . For the spin wave spectrum this mechanism implies a softening of the acoustical mode at the zone centre when T approaches TM from below.
There are, however, some quantitative difficulties associated with this picture, and that led Herbert [5]
to propose a new mechanism, namely involving a softening of the optical mode instead. His point was that if the exchange part of the optical energy happened to be low by cancellation, interaction among spin waves might push the optical branch down to zero.
The present measurements of course show that this mechanism is impossible, since the optical spin wave energies are so high. In fact measurements at tempe- ratures on either side of TM showed only a minor (- 1 %) change of the spin wave energy on passing TM from 240 to 290 OK.
A full account of this work will appear elsewhere [6].
References
[I] See for instance OZHOGIN (V. I.) and SHAPIRO (V. G.), [4] DIMITRIJEVI~ (Z.), KRA~NICKI (S.), RZANY (H.), Zh. Eksp. Teoret. Fiz, 1968, 55, 1737. English TODOROVIC (J.), WANIC (A.), CURIEN (H.) and translation Sov. Phys. JETP, 1969, 28, 915. MILOJEVIC (A.), Phys. Stat. Sol., 1967,21, K 163.
[2] GOODENOUGH (J. B.), Phys. Rev., 1960, 117, 1442. [5] HERBERT (D. C.), J. Phys., C, 1970, 3 , 891.
[3] SAMUELSEN (E. J.), HUTCHINGS (M. T.) and SHIRANE [6] SAMUELSEN (E. J.) and SHIRANE (G.), Phys. Stat.
(G.), Solid State Comm., 1969, 7 , 1043 and Sol., 1970, 42, 240.
Physica, 1970, 48, 13.
