Pathways towards ferroelectricity in hafnia

The question of whether one can systematically identify (previously unknown) ferroelectric phases of a given material is addressed, taking hafnia $({\mathrm{HfO}}_{2})$ as an example. Low free energy phases at various pressures and temperatures are identified using a first-principles based structure search algorithm. Ferroelectric phases are then recognized by exploiting group theoretical principles for the symmetry-allowed displacive transitions between nonpolar and polar phases. Two orthorhombic polar phases occurring in space groups $Pca{2}_{1}$ and $Pmn{2}_{1}$ are singled out as the most viable ferroelectric phases of hafnia, as they display low free energies (relative to known nonpolar phases), and substantial switchable spontaneous electric polarization. These results provide an explanation for the recently observed surprising ferroelectric behavior of hafnia, and reveal pathways for stabilizing ferroelectric phases of hafnia as well as other compounds.