Phase transitions in typical Pca2_1 ferroelectrics

While ferroelectric hafnia (HfO_2) has become a technically important material for microelectronics, the physical origin of its ferroelectricity remains poorly understood. The tetragonal P4_2/nmc phase is commonly assigned as its paraelectric mother phase, but it has no soft mode at the Brillouin zone center. In this work, we propose that the paraelectric-ferroelectric transition in hafnia-like Pca2_1 ferroelectric family can be described by a Pcca-Pca2_1 transition, where the Pcca mother phase will evolve into either the Pca2_1 ferroelectric phase or the centrosymmetric P2_1/c monoclinic phase, depending on the strain conditions. The Pcca phase is directly linked to both phases in the context of continuous phase transition. Hafnia is regarded as a special case of this family, in that it has accidental atomic degeneracy because all anions are oxygen. The theory is also correlated to the seven-coordination theory that explains the ferroelectricity in hafnia from a chemical perspective. In addition, the strain conditions to promote the ferroelectric phase in hafnia is discussed.