Improper ferroelectricity in ultrathin hexagonal ferrites films

The suppression of ferroelectricity in ultrathin films improper ferroelectric hexagonal ferrites or manganites has been attributed to the effect interfacial clamping, however, quantitative understanding and related phenomenological model are still lacking. In this work, we report paraelectric-to-ferroelectric phase transition epitaxial h-ScFeO3 with different thickness through in-situ reflection high-energy electron diffraction (RHEED). Based on clamping Landau theory, show that thickness-dependence Curie temperature can be understood terms characteristic length layer bulk temperature. Furthermore, found critical is proportional layer. These results reveal essential role mechanical from interface manganites, could serve as guidance achieve robust films.