Sub-nm² Ferroelectric Domains via Charged 180° Walls in ZrO₂

Flat phonon bands in fluorite ferroelectrics ( ${\mathrm{HfO}}_2$ or ${\mathrm{ZrO}}_2$ ) shrink polar domains laterally to an irreducible half-unit-cell width ( $\sim$ 0.27 nm) within which the vertical arrangement of dipoles is expected to remain uniform. Here, we report on the direct observation of nonuniform and nearly discrete vertical arrangements of dipoles in ${\mathrm{ZrO}}_2$ thin films consisting of closely spaced head-to-head (HH) and tail-to-tail (TT) charged 180 ${}^{\circ }$ walls, each exhibiting a distinct bulk-like structure. These charged domain walls (CDWs) further compress the irreducibly narrow, laterally stacked domains vertically to a thickness of $\sim$ 1-2.75 nm, yielding in-plane domains with sub- ${\mathrm{nm}}^2$ footprints-among the smallest ever reported for any ferroelectric material. The HH and TT walls form due to their flat longitudinal optical (LO) polar bands, and the former are electrostatically stabilized by bound-charge compensation via interstitial oxygen atoms, which act as natural structural defects at the HH walls. Moreover, these walls are predicted to be conducting and to exhibit ultralow propagation barriers, with HH walls (1.6 meV) being far more mobile than TT walls (22.3 meV), indicating strong potential for low-voltage, domain-wall-based nanoelectronics.