Theory of Manganites Exhibiting Colossal Magnetoresistance

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The electronic properties of many transition metal oxide systems require new ideas concerning the behaviour of electrons in solids for their explanation. A recent example, subsequent to that of cuprate superconductors, is of rare earth manganites doped with alkaline earths, namely Re₁₋ₓAₓ MnO₃, which exhibit colossal magnetoresistance, metal insulator transition and many other poorly understood phenomena. Here we show that the strong Jahn Teller coupling between the twofold degenerate (dₓ₂ ₋y₂ and d₃z₂ ₋ᵣ₂) eg orbitals of Mn and lattice modes of vibration (of the oxygen octahedra surrounding the Mn ions) dynamically reorganizes the former into a set of states (which we label ℓ) which are localized with large local lattice distortion and exponentially small intersite overlap, and another set (labelled b) which form a broad band. This hitherto unsuspected but microscopically inevitable coexistence of radically different ℓ and b states, and their relative energies and occupation as influenced by doping x, temperature T, local Coulomb repulsion U etc., underlies the unique effects seen in manganites. We present results from strong correlation calculations using the dynamical mean-field theory which accord with a variety of observations in the orbital liquid regime (say, for 0.2< x < 0.5).We outline extensions to include intersite ℓ coherence and spatial correlations/long range order.