Interstitial doping effect on ferroelectric rhombohedral HfO ₂ from <i>ab initio</i> simulations

The orthorhombic $Pca{2}_{1}$ phase of ${\mathrm{Hf}\mathrm{O}}_{2}$ exhibits exceptional ferroelectric stability at the nanoscale, yet its intrinsically high coercive field ${E}_{c}$ remains a significant obstacle to practical applications. The recent discovery of an interstitially doped ferroelectric rhombohedral R3m phase in ${\mathrm{Hf}\mathrm{O}}_{2}$ offers a promising route to reducing ${E}_{c}$. However, the atomic-scale mechanisms driving this behavior remain incompletely understood. Here, using phonon analysis combined with density functional theory simulations, we reveal that interstitial doping and compressive strain strengthen the weak trilinear couplings among the phonon modes that condense in the R3m phase and induced additional modes. These enhanced couplings dramatically increase the polarization, enabling switching at a remarkably low ${E}_{c}$. Our first-principles simulations show that the polarization response strongly depends on the interstitial dopant, as $\mathrm{Ti}$ induces large polarization under a slight compressive strain, while $\mathrm{Ce}$, $\mathrm{Hf}$, and $\mathrm{Zr}$ require a threshold strain to trigger a polarization jump. Interestingly, we further show that all group-IV interstitial dopants remarkably reduce the ${E}_{c}$ under compressive strain. These insights demonstrate that interstitial doping, combined with compressive strain, is a powerful strategy for tuning the ferroelectric properties of ${\mathrm{Hf}\mathrm{O}}_{2}$ and offers a promising pathway to enhanced polarization and reduced switching barriers in next-generation ferroelectric devices.