The influence of orbital ordering on the electric and magnetic properties of strongly correlated 3d transition metal systems has attracted significant theoretical and experimental interest since the early 1960s. However it is only in the last few years, after the discovery of colossal magnetoresistance in perovskite-type manganites, that the physical phenomena related to charge, spin and orbital degrees of freedom have been recognised as a central issue in a broad range of materials, such that it has become one of the most popular topics in hard condensed matter physics. An important step forward in this field is represented by the very recent observation that resonant X-ray scattering can provide an accurate and direct experimental method to observe the long-range order for orbital occupancy. The orbital degeneracy is commonly lifted by the crystal field or by Jahn-Teller distortion. In both cases the orbital order can be deduced from the crystal structure, which is easily observable with standard scattering techniques. However, there are systems like V2O3 where orbital order is not accompanied by any cooperative Jahn-Teller phenomenon. In these cases, and if magnetism is involved, one can infer the existence and structure of orbital order only from the knowledge of the magnetic structure, which strongly depends on the occupied orbitals. Twenty years ago Castellani et al. [1] proposed an orbitally-ordered structure compatible with the observed magnetic structure determined by neutron diffraction (Figure 54). Taking into account both the spin and orbital degrees of freedom, this model can justify the breaking of trigonal symmetry in the honeycomb plane, in which the pseudo-spin associated with the orbital occupancy have the same sign as the in-plane exchange coupling, whereas it is the opposite between the vanadium sites along the hexagonal axis.

The experiments were carried out at ID20 (magnetic scattering beamline) on a Cr-doped V2O3 single crystal. The orbital Bragg peaks appear below the Néel temperature (TN = 180 K) at positions in reciprocal space which are forbidden for antiferromagnetic and charge reflections, and can be observed only by tuning the incident photon energy at the pre-edge of Vanadium K-photoabsorption. This resonance involves transitions from 1s core level to 3d electronic states via weak quadrupolar transitions. Crucial to these studies was the observation of a peculiar dependence of the diffracted intensity from the azimuthal rotation angle around the orbital reflection (Figure 55). Moreover, the analysis of the complex azimuthal dependence of scattered polarised photons provides information on the spatial symmetries of ordered orbitals.

These observations confirm the interplay between the orbital and magnetic order in V2O3 and illustrate a new experimental method to extract information on the electronic orbital occupancy in solids.

References
[1] C. Castellani, C.R. Natoli, J. Ranninger, Phys. Rev. B, 18, 4945 (1978).
[2] L. Paolasini, C. Vettier, F. De Bergevin, F. Yakhou, D. Mannix, A. Stunault, W. Neubeck, M. Altarelli, M. Fabrizio, P.A. Metcalf, J.M. Honig, Phys. Rev. Lett., 82, 4719 (1999).

Authors
L. Paolasini (a), C. Vettier (a, b), F. De Bergevin (c), F. Yakhou (a), W. Neubeck (a), A. Sollier (a), D. Mannix (a), A. Stunault (a), M. Fabrizio (d), M. Altarelli (e), P.A. Metcalf (f), J.M. Honig (f).

(a) ESRF
(b) Present address: ILL, Grenoble (France)
(c) Laboratoire de Cristallographie, CNRS, Grenoble (France)
(d) International School for Advanced Studies, SISSA, and International Center for Theoretical Physics, ICTP, Trieste (Italy)
(e) Sincrotrone Elettra, Trieste (Italy)
(f) Department of Chemistry, Purdue University (USA)