Sharp lines due to Cr³⁺ and Mn²⁺ impurities in insulators: going beyond the usual Tanabe-Sugano approach

This work is aimed at understanding the different behavior of optical sharp lines (corresponding to 10Dq-independent transitions) of Mn(2+) and Cr(3+) in normal and inverted perovskites that cannot be explained within the usual Tanabe-Sugano approach. In particular, we want to clarify why on passing from KMgF3:M to LiBaF3:M (M = Mn(2+), Cr(3+)) the energy, E((6)A1 → (4)A1), for Mn(2+) decreases by Δ = 1100 cm(-1), while Δ < 100 cm(-1) for the energy E((2)E →( 4)A2) corresponding to Cr(3+). The origin of this surprising difference in these model systems is clarified by writing the transition energies of MF6 complexes through the ten Coulomb and exchange integrals consistent with the cubic symmetry and not considered in the usual Tanabe-Sugano approach. It is shown that E((6)A1 → (4)A1) depends on exchange integrals K(3z(2) - r(2), xy) and K(x(2) - y(2), xy), while E((2)E → (4)A2) depends on K(xz, yz) where the two involved electrons display a π character. These exchange integrals have been calculated just considering a MF6 unit subject to the internal electric field due to the rest of the lattice ions. In addition to a reasonably reproduction of the main trends observed experimentally for the model systems, the present calculations prove that the exchange integrals are not related in a simple way to the covalency of involved orbitals. Particular attention is also paid to explain why the transitions, which are 10Dq-independent are less sensitive to the host lattice change than those which do depend on 10Dq. The present work shows that K(xz, yz) for Cr(3+) is particularly insensitive to the host lattice change and thus sheds light on the origin of the near independence of E((2)E → (4)A2) along the series of oxides doped with such an impurity .