Stabilizing polar phases in binary metal oxides by hole doping

The recent observation of ferroelectricity in the metastable phases of binary metal oxides, such as ${\mathrm{HfO}}_{2},$ ${\mathrm{ZrO}}_{2},$ ${\mathrm{Hf}}_{0.5}{\mathrm{Zr}}_{0.5}{\mathrm{O}}_{2},$ and ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$, has garnered a lot of attention. These metastable ferroelectric phases are typically stabilized using epitaxial strain, alloying, or defect engineering. Here, we propose that hole doping plays a key role in the stabilization of polar phases in binary metal oxides. Using first-principles density-functional-theory calculations, we show that holes in these oxides mainly occupy one of the two oxygen sublattices. This hole localization, which is more pronounced in the polar phase than in the nonpolar phase, lowers the electrostatic energy of the system, and makes the polar phase more stable at sufficiently large concentrations. We demonstrate that this electrostatic mechanism is responsible for stabilization of the ferroelectric phase of ${\mathrm{HfO}}_{2}$ aliovalently doped with elements that introduce holes to the system, such as La and N. Finally, we show that spontaneous polarization in ${\mathrm{HfO}}_{2}$ is robust to hole doping, and a large polarization persists even under a high concentration of holes.