Exchange coupling in CaMnO$_3$ and LaMnO$_3$: configuration interaction and the coupling mechanism

The equilibrium structure and exchange constants of CaMnO$_3$ and LaMnO$_3$ have been investigated using total energy unrestricted Hartree-Fock (UHF) and localised orbital configuration interaction (CI) calculations on the bulk compounds and Mn$_2$O$_{11}^{14-}$ and Mn$_2$O$_{11}^{16-}$ clusters. The predicted structure and exchange constants for CaMnO$_3$ are in reasonable agreement with estimates based on its N\'eel temperature. A series of calculations on 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 LaMnO$_3$ with various spin and orbital orderings. Computed exchange constants depend on orbital ordering. UHF calculations tend to underestimate exchange constants in 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 analysed in order to determine which exchange processes are important in exchange coupling in CaMnO$_3$ and LaMnO$_3$.