Improper ferroelectricity in ultrathin hexagonal ferrites film

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