General Considerations

Abstract

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 MO ₃ array gives cooperative rotations of the MO _6/2 octahedra that bend the (180° - φ) M-O-M bonds by an angle φ. Ligand-field wavefunctions for d electrons at transition-metal M atoms are used to distinguish, for single-valent MO₃ arrays, where the M-O-M interactions should be treated by superexchange perturbation 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 electronic behavior due to a double-well potential for the equilibrium M-O bond length with (M-O) _loc > (M-O) _itin . Long-range and short-range cooperative Jahn-Teller distortions are contrasted with charge-density-wave instabilities; polarons and correlation bags are contrasted with strong-correlation fluctuations.