The role of spin density for understanding the superexchange mechanism in transition metal ionic compounds. The case of KMF3 (M = Mn, Fe, Co, Ni, Cu) perovskites

Abstract

In many recent papers devoted to first row transition metal fluorides and oxides, not much attention is devoted to the spin density, a crucial quantity for the determination of the superexchange mechanism, and then for the ferro-antiferromagnetic energy difference. Usually, only the eigenvalues of the system are represented, in the form of band structures or, more frequently, of density of states (DOS). When discussing the orbital ordering and the Jahn-Teller effect, simple schemes with cubes and lobes are used to illustrate the shape of the d occupancy. But the eigenvectors, and the resulting spin density function, as obtained from the calculations, are rarely shown. When represented, only a fuzzy shape that recalls the d orbital shape can be observed. On the basis of these considerations, spin density maps for 5 compounds of the KMF₃ (M from Mn to Cu) family have been produced, which clearly illustrate which d orbital is singly or doubly occupied. At variance with respect to the near totality of the papers devoted to these systems, we use an all electron scheme, a Gaussian type basis set, and the Hartree-Fock Hamiltonian or the B3LYP hybrid functional (the resulting maps turn out to be very similar, in the scale used for our figures). The spin density in the five cases can easily be interpreted in terms of the shape of the d orbitals as appearing in textbooks.