Microscopic modelling of doped manganites

Colossal magneto-resistance manganites are characterised by a complex interplay of charge, spin, orbital and lattice degrees of freedom. Formulating microscopic models for these compounds aims at meeting to conflicting objectives: sufficient simplification without excessive restrictions on the phase space. We give a detailed introduction to the electronic structure of manganites and derive a microscopic model for their low energy physics. Focussing on short range electron-lattice and spin-orbital correlations we supplement the modelling with numerical simulations.