  The standard way to find the orbital occupation of Jahn-Teller (JT) ions is
to use structural data, with the assumption of a one-to-one correspondence
between the orbital occupation and the associated JT distortion, e.g. in O6
octahedron. We show, however, that this approach in principle does not work for
layered systems. Specifically, using the layered manganite La0.5Sr1.5MnO4 as an
example, we found from our x-ray absorption measurements and theoretical
calculations, that the type of orbital ordering strongly contradicts the
standard local distortion approach for the Mn3+O6 octahedra, and that the
generally ignored long-range crystal field effect and anisotropic hopping
integrals are actually crucial to determine the orbital occupation. Our
findings may open a pathway to control of the orbital state in multilayer
systems and thus of their physical properties.
