Theory of Manganites Exhibiting Colossal Magnetoresistance

Abstract

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 $R{e}_{1-x}{A}_{x}Mn{O}_3$, 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 ($d_{x^2-y^2}$ and $d_{3z^2-r^2}$) $e_g$ 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 $\ell$) 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 $\ell$ 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 $0.2\stackrel{<}{\sim }x\stackrel{<}{\sim }0.5$).We outline extensions to include intersite $\ell$ coherence and spatial correlations/long range order.

26pages, 4 figures, to appear as a chapter in "Colossal Magnetoresistive Manganites", ed. T. Chatterji, Kluwer Academic Publishers, Dordrecht, Netherlands (2003)