Effect of lattice distortions on the competition between the double and superexchange mechanisms in LaMnO₃

Double exchange (DE), superexchange (SE), and higher-order contributions to the exchange interaction energy between Mn layers in LaMnO₃ are studied using the linear-muffin-tin-orbital method as generalized to treat noncollinear magnetic configurations. The degree of the internal lattice distortion (f) and the angle (θ) between ferromagnetically ordered Mn layers are considered as simulation parameters. We find that both global and internal lattice distortions dramatically influence the character of the exchange interactions: global distortions associated with variations of the apical Mn-O bond length promotes the DE contribution; the bending of the Mn-O bonds in the (a-b) plane suppresses the DE and promotes the antiferromagnetic SE contribution to the interlayer exchange energy. Overall, the character of exchange interactions is determined by SE contributions: in hypothetical ferromagnetic phases DE interactions mediated by itinerant electrons is present but still rather small compared with SE; in antiferromagnetic phases this DE is negligible and non-Heisenberg terms are small compared with SE. We find further that a metal-to-semiconductor transition (in the sense of a band-gap opening) occurs in the range of parameters of magnetic and lattice distortion variations given by θ≥120° and f≥ 0.7.