  A microscopic model Hamiltonian for the ferroelectric field effect is
introduced for the study of oxide heterostructures with ferroelectric
components. The long-range Coulomb interaction is incorporated as an
electrostatic potential, solved self-consistently together with the charge
distribution. A generic double-exchange system is used as the conducting
channel, epitaxially attached to the ferroelectric gate. The observed
ferroelectric screening effect, namely the charge accumulation/depletion near
the interface, is shown to drive interfacial phase transitions that give rise
to robust magnetoelectric responses and bipolar resistive switching, in
qualitative agreement with previous density functional theory calculations. The
model can be easily adapted to other materials by modifying the Hamiltonian of
the conducting channel, and it is useful in simulating ferroelectric field
effect devices particularly those involving strongly correlated electronic
components where ab-initio techniques are difficult to apply.
