  The orbital excitations of a series of transition-metal compounds are studied
by means of optical spectroscopy. Our aim was to identify signatures of
collective orbital excitations by comparison with experimental and theoretical
results for predominantly local crystal-field excitations. To this end, we have
studied TiOCl, RTiO3 (R=La, Sm, Y), LaMnO3, Y2BaNiO5, CaCu2O3, and K4Cu4OCl10,
ranging from early to late transition-metal ions, from t_2g to e_g systems, and
including systems in which the exchange coupling is predominantly
three-dimensional, one-dimensional or zero-dimensional. With the exception of
LaMnO3, we find orbital excitations in all compounds. We discuss the
competition between orbital fluctuations (for dominant exchange coupling) and
crystal-field splitting (for dominant coupling to the lattice). Comparison of
our experimental results with configuration-interaction cluster calculations in
general yield good agreement, demonstrating that the coupling to the lattice is
important for a quantitative description of the orbital excitations in these
compounds. However, detailed theoretical predictions for the contribution of
collective orbital modes to the optical conductivity (e.g., the line shape or
the polarization dependence) are required to decide on a possible contribution
of orbital fluctuations at low energies, in particular in case of the orbital
excitations at about 0.25 eV in RTiO3. Further calculations are called for
which take into account the exchange interactions between the orbitals and the
coupling to the lattice on an equal footing.
