Short-range and long-range contributions to the size effect in metal-ferroelectric-metal heterostructures

The size-effect problem in metal-ferroelectric-metal heterostructures is analyzed in terms of the multiscale scheme---which combines phenomenology and first-principles calculations---recently developed by the authors. We demonstrate how this effect can be separated into two distinct contributions: a long-range electrostatic and a short-range ``chemical'' one. The formulated approach is applied to the description of SrRuO₃/BaTiO₃/SrRuO₃ heterostructures with different types of ferroelectric terminations (TiO₂-TiO₂ or RuO₂-RuO₂). It is shown that the balance between the long-range and the short-range contributions to the size effect can be essentially affected by the type of termination of the ferroelectric and by the polarization hardness of the electrode. The analysis presented demonstrates the leading role of the long-range contribution to the size effect in SrRuO₃/BaTiO₃/SrRuO₃ heterostructures.