Real Structure of Perovskites Looked at From the Band Structure Point of View

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Although perovskites can be viewed as a dense packing of ionic spheres of three different sizes in a cubic structure, there are several deviations from this ideal. Most common is the tilting of the corner sharing octahedra like the SiO6 octahedra in MgSiO3. For transition metal complexes like CUF6 in KCuF3 Jahn-Teller distortions occur. With the symmetry lowered or the unit cell enlarged, gaps in the density of states grow or additional ones are opened. With local density band structure calculations (LDA) the tilting angle of the octahedra can be determined by minimizing the energy, in fair accord with the experimental values. With the same LDA Jahn-Teller distortions, however, cannot be calculated reliably. Since the d-density of states of the transition metal is placed above the p-density of O or F ions, a metal instead of an insulator is found. With the remedy of the LDA+U method one regains a proper description of the experimental facts. However, there are also cases for which the unmodified approach seems to be valid, for instance the perovskite SrRuO3 with 4d-electrons is correctly calculated as a ferromagnetic metal. In studying the restricted perovskite class we want to illustrate the quality of band structure calculations. The shortcomings are not so much linked to an improper description of the transition metal ion open shell structure but to the failure in estimating the potential differences between the ions correctly. This is probably due to the wrong accounting of the unwanted self-interaction of the electrons in the d-shells. We think that considering the real crystallographic structure is necessary to sort out what is left over to be accounted for by correlated electron physics and not to be misguided by some technical problems in the otherwise quite accurate LDA-methods.