Modelling colossal magnetoresistance manganites

Rare-earth (Re) manganites (with alkaline-earth (Ak) ions partially substituting them), i.e. Re_1−xAk_xMnO₃, have been intensively explored for the last decade or more because of the promise of magnetoelectronic applications as well as because of complex and unusual phenomena in which electronic, structural and magnetic effects are intertwined. A brief survey of these and a description of the three strong local interactions of the e_g electrons (in two different orbital states at each site), namely with Jahn–Teller phonon modes (strength g), with resident t_2g spins (ferromagnetic Hund's rule coupling J_H) and between each other (the Mott–Hubbard correlation U) form the background against which efforts at modelling manganite behaviour are described. A new two-fluid model of nearly localized (l) polarons and band (b) electrons for low-energy behaviour is hypothesized for large g; some of its applications are mentioned here. First I describe some results of large U, J_H calculations in single-site DMFT (dynamical mean field theory) which includes the effect of all the strong local correlations. These results are directly appropriate for the orbital liquid regime, found typically for 0.2<x<0.5, and not too low temperatures. I show that many characteristic manganite phenomena, such as an insulating ferromagnetic ground state, thermal insulator–metal transition (nearly coincident with the paramagnetic to ferromagnetic transition), colossal magnetoresistance (CMR), materials systematics dependent on the specific Re and Ak ions, and the observed low effective carrier density, can all be understood qualitatively as well as quantitatively. We also discuss the two-'phase' coexistence frequently found in these systems, and show that electrostatic Coulomb interactions mute lb phase separation into nanoscale electronic inhomogeneity with l regions and b puddles. Finally, some problems of current interest as well as general ones arising, e.g. polarons and the physics of large electron phonon coupling g in the adiabatic regime, are mentioned.