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.
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