Strain-induced two-step phase transition and polar-antipolar mode coupling stabilize robust ferroelectricity in thin-film hafnia

Hafnia attracts considerable research interest due to its compatibility with current silicon technologies and its robust ferroelectricity in the thinnest film, which make it a promising candidate for next generation devices to overcome many issues of devices based on perovskite ferroelectrics. However, the origin of this robust ferroelectricity and the ferroelectric phase transition mechanism is still elusive. Here, we prove that the robust ferroelectricity arises from a unique two-step antipolar-ferroelectric phase transition, which is induced by tensile strain and strong polar-antipolar mode coupling. The antipolar mode instability could be induced by tensile strain and thus the first-step phase transition to an antipolar phase could be activated. When the amplitude of antipolar mode is above a threshold, the secondary ferroelectric phase transition occurs due to the cooperative coupling between antipolar and polar mode. Since the antipolar mode is not susceptible to depolarization, the spontaneous antipolar displacement, through the cooperative polar-antipolar mode coupling, could stabilizes the polarization against depolarization effect. We demonstrate that this polar-antipolar coupling is strong enough to offset even the unscreened depolarization field and stabilize the polarization even in the thinnest film. Our results demonstrate that the strain and polar-antipolar coupling are the origins of robust ferroelectricity in hafnia. This finding of strain induced phase transition could also explain the reverse size effect in hafnia and the cooperative mode coupling effect provides a new mechanism against depolarization other than conventional improper ferroelectricity.