Orbital order in La0.5Sr1.5MnO4: Beyond a common local Jahn-Teller picture

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 O-6 octahedron. We show, however, that this approach can be incorrect, e. g., for layered systems. Using the layered manganite La0.5Sr1.5MnO4 as an example, we found from our x-ray-absorption measurements and electronic structure calculations that the type of orbital ordering strongly contradicts the standard local distortion approach for the Mn3+O6 octahedra, and that the usually ignored long-range crystal-field effect and anisotropic hopping integrals are actually crucial for determining the orbital occupation