Exchange coupling in ${\mathrm{CaMnO}}_3$ and ${\mathrm{LaMnO}}_3:$ Configuration interaction and the coupling mechanism

The equilibrium structure and exchange constants of ${\mathrm{CaMnO}}_3$ and ${\mathrm{LaMnO}}_3$ have been investigated using total-energy unrestricted Hartree-Fock (UHF) and localized orbital configuration interaction (CI) calculations on bulk compounds and ${\mathrm{Mn}}_2{\mathrm{O}}_{11}^{14-}$ and ${\mathrm{Mn}}_2{\mathrm{O}}_{11}^{16-}$ clusters. The predicted structure and exchange constants for ${\mathrm{CaMnO}}_3$ are in reasonable agreement with estimates based on its Néel temperature. A series of calculations on ${\mathrm{LaMnO}}_3$ in the cubic perovskite structure shows that a Hamiltonian with independent orbital ordering and exchange terms accounts for the total energies of cubic ${\mathrm{LaMnO}}_3$ with various spin and orbital orderings. Computed exchange constants depend on orbital ordering. Exchange contributions to the total energy vary between -20 and 20 meV per Mn ion, differences in orbital ordering energy vary between 3 and 100 meV, and a Jahn-Teller distortion results in an energy reduction of around 300 meV. The lattice constant of the lowest energy cubic perovskite structure (3.953 Å) is in good agreement with the lattice constant of the high-temperature “cubic” phase of ${\mathrm{LaMnO}}_3$ (3.947 Å). The total energy of Pnma ${\mathrm{LaMnO}}_3$ was minimized by varying lattice parameters and seven internal coordinates and a structure 194 meV per Mn ion below that of a structure determined by neutron diffraction was found. This optimized structure is nearly isoenergetic with a cubic perovskite structure, with a 5% Jahn-Teller distortion. UHF calculations tend to underestimate exchange constants in ${\mathrm{LaMnO}}_3,$ but have the correct sign when compared with values obtained by neutron scattering; exchange constants obtained from CI calculations are in good agreement with neutron-scattering data provided the Madelung potential of the cluster is appropriate. Cluster CI calculations reveal a strong dependence of exchange constants on Mn d $e_g$ orbital populations in both compounds. CI wave functions are analyzed in order to determine which exchange processes are important in exchange coupling in ${\mathrm{CaMnO}}_3$ and ${\mathrm{LaMnO}}_3.$