The superexchange mechanism in crystalline compounds. The case of KMF3 (M = Mn, Fe, Co, Ni) perovskites

The ferromagnetic and antiferromagnetic wavefunctions of four KMF3 (M = Mn, Fe, Co and Ni) perovskites have been obtained quantum-mechanically with the CRYSTAL code, by using the Hartree-Fock (HF) Hamiltonian and three flavours of DF1' (PBE, B3LYP and PBE0) and an all-electron Gaussian type basis set. In the Fe and Co cases, with d(6) and d(7) occupation, the Jahn-Teller distortion of the cubic cell is as large as 0.12 angstrom. Various features of the superexchange interaction energies (SW), namely additivity, dependence on the M-M distance, on the (MFM) over cap angle, and on the adopted functional, are explored. The contribution to SIE, by the Coulomb, exchange and kinetic energy terms is analyzed. It is shown that, when using density functionals, SIE clearly correlates with the amount of exact (Hartree-Fock) exchange in the functional. The effect of SIE on the equilibrium geometry and volume of the unit cell is discussed, and it is shown that the key quantity is the spin polarization of the (closed shell) F ions along the M-F-M path. The effect of this magnetic pressure is evaluated quantitatively for the first time. The superexchange coupling constant J, evaluated at the HF level and through the Ising model, underestimates the experimental values by about 60%-70%. The more sophisticated Yamaguchi model (that takes into account the contamination of the FM and AFM spin states) does not reduce the discrepancy. The B3LYP hybrid functional overestimates the experiments. These last are bracketed by HF and PBE0. For PBE, the overestimation is huge. Finally, Mulliken population data, charge and spin density maps and density of states arc used to illustrate the electronic structure.