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Chiral patterns of tilting of oxygen octahedra in zero-dimensional ferroelectrics and multiferroics: a first principle-based study.

First-principles-based Monte Carlo approaches are developed to investigate finite-temperature properties of stress-free nanodots made of the ferroelectric Pb(Zr,Ti)O3 system and of the multiferroic BiFeO3 compound. These zero-dimensional materials both exhibit various, novel chiral patterns for the tilting of the oxygen octahedra. Such exotic patterns originate from the coupling between the tiltings of the oxygen octahedra and the electric dipole vortices, and require original order parameters to quantify them.