General considerations

For reference, a few properties of AMO(3) perovskites are reviewed. Lattice distortions arising from the mismatch between equilibrium A-O and M-O bond lengths are discussed; a compressive stress on the MO3 array gives coopera tive rotations of the MO6/2 Octahedra that bend the (180 degrees - phi) M-O -M bonds by an angle phi. Ligand-field wavefunctions for d electrons at tra nsition-metal M atoms are used to distinguish, for single-valent MO3 arrays , where the M-O-M interactions should be treated by superexchange perturbat ion theory from where they should be described by tight-binding band theory . Double-exchange and indirect-exchange interactions are also reviewed. The possible symmetries of the spin configurations of magnetic perovskites are specified. The virial theorem is employed to demonstrate the existence of lattice instabilities at a cross-over from localized to itinerant electroni c behavior due to a double-well potential for the equilibrium M-O bond leng th with (M-O)(loc) > (M-O)(itin). Long-range and short-range cooperative Ja hn-Teller distortions are contrasted with charge-density-wave instabilities ; polarons and correlation bags are contrasted with strong-correlation fluc tuations.