Size effect in metal/ferroelectric/metal heterostructures:Depolarizing effect vs. short-range coupling

Phase transitions in condensed matter are affected by a small volume and/or restricted geometry of the systems. The understanding of the relevant size effects is of practical importance when such systems are used as functional materials in the form of small particles and thin films. At the origin of these effects, one can distinguish two contributions. One is due to the fact that the atoms of the material close to its surface have an environment that is different form that of the bulk atoms. Here, short-range inter-atomic interactions are involved. The other contribution is related to the long-range macroscopic fields (electric, elastic, or magnetic) appearing in particles or films of the material due to its contact with other materials. Proper understanding of the size effect in solid-state systems implies separation of these contributions. In the present paper, we address the problem of this separation in the case of metal/ferroelectric/metal heterostructures, the systems where the long-range contribution is associated with the electrostatic depolarizing field. The problem is treated using an approach developed by the author [1], which combines first principles calculations with the phenomenological theory. The aforementioned contributions to the size effect are evaluated for SrRuO3/BaTiO3/SrRuO3 heterostructures with different (RuO2 orTiO2) terminations of the ferroelectric. It is shown that the relation between these contributions is controlled by the ??????polarization softness?????? of the metal.