Insulator-Metal Phase Diagram of the Optimally Doped Manganites from the Disordered Holstein-Double Exchange Model

We study the Holstein-Double Exchange model in three dimensions in the presence of substitutional disorder. Using a new Monte Carlo technique we establish the phase diagram of the clean model and then focus on the effect of varying electron-phonon coupling and disorder at fixed electron density. We demonstrate how extrinsic disorder controls the interplay of lattice polaron effects and spin fluctuations and leads to widely varying regimes in transport. Our results on the disorder dependence of the ferromagnetic T_c and metal-insulator transitions bear direct comparison to data on the `optimally doped', x=0.3-0.4, manganites. We highlight disorder induced polaron formation as a key effect in these materials, organise a wide variety of data into a simple `global phase diagram', and make several experimental predictions.