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MAGNETIC EXCITATIONS IN
ANTIFERROMAGNETIC COBALTOUS OXIDE
V . Wagner
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, supplément au n" 8, Tome 39, août 1978, page C6-822
MAGNETIC EXCITATIONS IN ANTIFERROMAGNETIC COBALTOUS OXIDE
V. Wagner"Institut Laue-Langevtn, BP 156, 38042 Grenoble Cedex, France
Résumé.- Plusieurs excitations magnétiques au-dessus de la branche des ondes de spin ont été obser-vées par diffusion inêlastique des neutrons dans le composé antiferromagnétique CoO à 13 K. Les courbes de dispersion ont été déterminées selon les directions de haute symétrie. Un modèle basé sur les opérateurs pseudo-boson est en accord avec l'expérience pour trois des cinq excitations obser-vées.
Abstract.- At 13 K several magnetic excitations above the spin wave branch were observed in antifer-fomagnetic CoO by neutron inelastic scattering techniques and their dispersion was determined along the direction of high symmetry. A model set up in terms of pseudo-boson theory agrees satisfactorily for three of the five branches observed.
INTRODUCTION.- The interest in cobaltous oxide CoO is related to the degenerate electronic ground sta-te of the Co ion. In the cubic crystal field the orbital degeneracy is only partially lifted (l = 1, s = 3/2). Together with the fact that spin-orbit interaction and exchange interaction are of same size III, this gives rise to a complex excitation spectrum. Upon magnetic ordering CoO acquires a collinear antiferromagnetic spin arrangement of type II in a slightly deformed cubic lattice. Its magnetic space group is C 2/c as for NiO and MnO. The collinear spin arrangement has been recently confirmed /2/ as well as the preferred spin direc-tion close to ITl3_[.
The observation of magnetic excitations by neutron inelastic scattering was reported as early as 1967 /3/. However, well defined spin waves were observed only recently /4/. At present we report on magnetic excitations above the spin waves, which altogether arise from magnetic transitions within
2+
the multiplet ground state of Co m the crystal field. The experimental results are interpreted in terms of a pseudo-boson model as described in detail in the literature /5,6/.
EXPERIMENTAL RESULTS.- Dispersion curves of magne-tic excitations with frequencies up to 14 THz were measured by neutron inelastic scattering. The mea-surements were carried out with the triple axis crystal spectrometer INI at the hot source of the HFBR at the I.L.L.
" Guest scientist from Physik. Institut der Univer-sitat, 8700 Wurzburg Germany
How at Physik.-Technische Bundesanstalt, Bundesal-iee 100, 3300 Braunschweig, Germany.
The sample was a flame-grown single crystal of 2 cm3 volume at 13 K. The results are summarized in figure 1.
t I 1 1 1
1
-CTHz) . -;-_-_—-'' ~~-~—-. -.- r "X-—i —*Trx~S - •
o' 1 1 lo
(000) (ooJt^O) WOO) (^J,) WavevectorFig. 1 : Magnetic excitations in antiferromagnetic CoO at 13 K. The scattering intensity was observed in magnetic (•) or nuclear (A) zones. The spin wa-ve frequencies (0) were taken from reference / 4 / . The lines represent the model discussed in the text.
The wavevectors are reduced to a magnetic Brillouin zone, but given in units of a pseudo cubic unit cell. The sample was multi-domain with respect to the te-tragonal distortion as well as to the spin ordering. In most cases the magnetic character of the excita-tions could be inferred from the Q-dependence of the scattering intensity. Two modes at 6.9 THz and 9.2 THz were observed at the centre of a magnetic
1 1 3
zone fcrj) and two other modes at 7.8 THz and
13.9 THz at the centre of a nuclear zone (002). The three lower frequencies agree well with the values reported from optical work /6,8/. Therefore we con- clude that these frequencies are related to excita- tions with q = 0 and not to zone boundary modes, which might be simultaneously observed in a multi- domain sample. In figure 1 previous results for the spin wave branch /4/ have been included.
DISCUSSION.- In the following we give a prelimina- ry discussion of the experimental results in terms of a pseudo-boson model. Similar models were applied to COO /3,6/ and to KCoF3 151. The model is based on the energy levels and matrix elements of the spin operator calculated from the single ion Hamil- toninan which we take to
Where is the effective spin-orbit coupling and the molecular field term involves the exchange in- teraction J 'lietween n.n.n. spins only. The effecti-
2
ve anisotropy
-DsS~
is ref erred to the preferred di- rection of the spin, which deviates from a cubic axis by about 25'. The effects of the spin orienta- tion from the cubic axis is to reduced the symmetry to a monoclinic space group and causes a mixing of otherwise transverse and longitudinal excitons. As pointed out by Daniel and Cracknell 171 this results in a Davydov splitting of all magnetic excitons at ther
point.In view of the limited experimental evidence, which renders a correct assignment of the frequen- cies difficult, the values of the parameters in the single ion Hamiltonian (1) were taken from other experiments and only the exchange interaction J
2 has been determined by fitting the calculated dis- persion curves to the experimental results. Thus, with
X
= 6.0 THz from studies of Co2+ inMgO /9/ and D = 0.65 THz from the spin wave dispersion 141, one obtains J2 = 0.33 THz for J1 = 0. Satisfactory agreement is obtained for the lowest branch and the exciton at 14 THz, while discrepancies exist for the branches at 10THz (confer figure I). Allowing for an exchange interaction between n.n. spins (J1 # 0) vill slightly improve the agreement. Fur- thermore domain effects would arise, which have not yet been observed in the exciton dispersion. A more complete analysis will be undertaken after observa- tion of the dispersion curves along the@0g
with the aim to understand the density of magnetic sta- tes reported from a TOF experiment /lo/.CONCLUSIONS.- First results of an experimental de- termination of the dispersion have been reported for five branches of magnetic excitations in anti- ferromagnetic COO. The results do not confirm the dispersion curves, which were previously proposed on much less experimental evidence /3,6/. A pseudo- boson model accbunting for Heisenberg exchange and spin-orbit interaction gives a satisfactory overall description with a spin-orbit interaction, which is only moderately reduced from its free ion value in contrast to other models put forward /3,6/. Dis- crepancies observed at frequencies close to 10 THz demand a more complete experimental determination of the exciton dispersion.
References
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167
(1968) 510/4/ Wagner ,V. and Herrmann-Ronzaud ,D
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International Symposium on Neutron Inelastic Scattering, IAEA Vienna 1977, in press151 Buyers,W.J.L., Holden,T.M., Svensson,E.C., Cowley,R.A. and Hutchings,M.T.,J.Phys.$(l971)
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