Single impurities in insulators: Ab initio study of Fe-doped (formula presented)

We present a consistent approach to the study of single (isolated) defects in crystals. This has three stages: (i) band structure calculation of a perfect host crystal is used to define the shape and size of the supercell adequately modeling a perfect crystal, (ii) further supercell point defect calculation for unrelaxed lattice defines a proper cyclic cluster, (iii) the latter is used at the third, the most time-consuming stage for the lattice relaxation and defect property calculations. Using the unrestricted Hartree-Fock (HF) method in the linear combination of atomic orbitals approximation, the calculations of the defect energy level positions in the gap and atomic structure for a single (formula presented) impurity substituting for a host Ti atom in perovskite (formula presented) are performed. We study a convergence of results to the single defect limit and show that use of 160 atom cyclic clusters is necessary for the HF calculations and 320 atoms for the density functional theory PWGGA calculations. The high spin (formula presented) state is predicted to lie much lower in energy than the zero-spin state. The energy level positions strongly depend on the asymmetric displacement mode of the six nearest O ions which is a combination of the Jahn-Teller and breathing modes. A considerable covalent bonding between the Fe ion and four nearest O ions takes place.