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 O6 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.