Origin of Anomalous Size Effects in Ferroelectric Hafnia Thin Films

The persistence of ferroelectricity in ultrathin HfO$_2$ films challenges conventional theories, particularly given the paradoxical observation that the out-of-plane lattice spacing increases as the film thickness decreases, an anomalous size effect absent in perovskite ferroelectrics. Here, we resolve this puzzle by revealing that this lattice expansion is counterintuitively coupled to a suppressed out-of-plane polarization. First-principles calculations combined with analytical modeling identify two mechanisms behind this expansion: a negative longitudinal piezoelectric response to the residual depolarization field and a positive surface stress that becomes significant at reduced thickness. Their interplay quantitatively reproduces the experimentally observed lattice expansion. Furthermore, (111)-oriented HfO$_2$ films can support out-of-plane polarization even under open-circuit conditions, in contrast to (001) films that stabilize a nonpolar ground state. This behavior points to the emergence of orientation-induced hyperferroelectricity, an unrecognized mechanism that enables polarization persistence through orientation engineering without electrode screening. We further demonstrate that this principle generalizes to conventional perovskites such as PbTiO$_3$, offering a strategy to eliminate the critical thickness limit by choosing the appropriate film orientation. As a practical pathway to device integration, we also identify the two-dimensional electride Ca$_2$N as a near-ideal electrode that fully restores the ferroelectric properties of HfO$_2$ in ultrathin capacitors.