Electrostatic Control of Orbital Ordering in Noncubic Crystals

In noncubic insulating crystals where active orbitals are not degenerate the usual models to describe orbital ordering, Kugel-Khomskii and Jahn-Teller, are, in principle, not valid. For these materials we show, by means of first-principles calculations, that a key driving force behind orbital ordering is the electrostatic potential, V-R(r), created by the rest of lattice ions over the magnetic complex where active electrons are localized. In order to illustrate the key influence of V-R(r), often ignored in a true microscopic approach, we focus on K2CuF4 and La2CuO4 as model crystals since they have very similar electronic structure but, surprisingly, contrasting orbital orderings, antiferrodistortive and ferrodistortive, respectively. Considering the parent K2NiF4 structure (tetragonal space group 14/mmm) of both lattices, it is shown that in K2CuF4 the hole in a CuF64- complex is forced by the anisotropy of V-R(r) to be in a 3z(2) - r(2) orbital, while for La2CuO4 the shape of VR(r) forces the hole to be placed in the planar x(2) - y(2) orbital. As a salient feature, it is found that in the parent structure the orbitals of K2CuF4 are ferrodistortively ordered in contrast to the Kugel-Khomskii prediction. At the same time, it is also shown that in K2CuF4 this state is unstable and distorts to the experimental antiferrodistortive state where, despite the significant in-plane distortion, the hole is still found to be in a mainly 3z(2) - r(2) orbital, a fact in agreement with experimental magnetic resonance data. For this compound, it is found that V-R(r) induces changes on the energy of 3d levels, which are 2 orders of magnitude higher than those due to superexchange interactions. The present results stress that in insulating transition metal compounds with electrons localized on complexes the rest of the lattice ions play a key role for understanding the electronic and structural properties that is, in many cases, overlooked. The present ideas are also shown to account for the orbital ordering in other noncubic materials, like Na3MnF6, NaCrF4, or Sr2La2CuTi3O12, and thus open a window in the design of magnetic materials.