Spontaneous electric polarization and electric field gradient in hybrid improper ferroelectrics: insights and correlations

An ab initio study of several hybrid improper ferroelectric (HIF) materials in the Ruddlesden-Popper phases and double perovskite structures is here presented. The focus is on the correlation between the electric field gradient at several nuclear sites (EFG) and the spontaneous electric polarization. As observed in some proper ferroelectrics, we found that the EFG tensor components, along possible switching paths to invert the polarization, are interchangeable between the ferroelectric and paraelectric phases in the HIF AA(2)'B2O7 and AA ` B2O6 (A, A ` = Ca, Cd and B = Mn, Ti) compounds. The results indicate that the relationship between the main continuous component of the EFG tensor and the electric polarization, even at sites without inversion symmetry, is primarily quadratic. Moreover, the claimed linear correlation was not observed. These results open a route to analyze the local octahedral distortions that underline HIF materials' functional multiferroic properties. (AU)