Fig. 3
Influence of the substrate-film interface on the improper ferroelectricity. a Averaged displacement |〈Q〉| for each atomic row in the first four unit cells of the HAADF-STEM image in Fig. 2a. The value of |〈Q〉| is reduced at the substrate interface and saturates at the bulk displacement value after two unit cells. The error bars are given by the standard error of the mean. b Trimerization amplitude Q calculated by density-functional theory (DFT) for a four-unit-cell YMnO3 film keeping the bulk-lattice parameters and assuming a clamped (Q = 0) unit cell toward the substrate interface and a free top surface. The amplitude displays a progressive build up over the thickness of the film and saturates after two-unit cells. The inset in b shows a schematic of the corresponding crystal structure with atomic positions as calculated by DFT.
