  We discuss the phase diagram of the two-orbital model of half-doped
manganites by calculating self-consistently the Jahn-Teller (JT) distortion
patterns, charge, orbital and magnetic order at zero temperature. We analyse
the instabilities of these phases caused by electron or hole doping away from
half-doping, or by the application of a magnetic-field. For the CE insulating
phase of half-doped manganites, in the intermediate JT coupling regime, we show
that there is a competition between canting of spins (which promotes mobile
carriers) and polaronic self-trapping of carriers by JT defects. This results
in a marked particle-hole asymmetry, with canting winning only on the electron
doped side of half-doping. We also show that the CE phase undergoes a
first-order transition to a ferromagnetic metallic phase when a magnetic-field
is applied, with abrupt changes in the lattice distortion patterns. We discuss
the factors that govern the intriguingly small scale of the transition fields.
We argue that the ferromagnetic metallic phases involved have two types of
charge carriers, localised and band-like, leading to an effective two-fluid
model.

Materials Science