  We examine the effect of an FET geometry on the charge ordering phase diagram
of transition metal oxides using numerical simulations of a semiclassical model
including long-range Coulomb fields, resulting in nanoscale pattern formation.
We find that the phase diagram is unchanged for insulating layers thicker than
approximately twice the magnetic correlation length. For very thin insulating
layers, the onset of a charge clump phase is shifted to lower values of the
strength of the magnetic dipolar interaction, and intermediate diagonal stripe
and geometric phases can be suppressed. Our results indicate that, for
sufficiently thick insulating layers, charge injection in an FET geometry can
be used to experimentally probe the intrinsic charge ordering phases in these
materials.
