Symmetry-Guided Functional Pathways of Intercalation-Free Rhombohedral ( <i>R3</i> ) Hafnia Derived from the Fluorite Phase for Low-Coercive Ferroelectric Memory

Rhombohedral hafnia-based ferroelectrics promise low-coercive, scalable nonvolatile memories, yet their realization has traditionally relied on complex cation intercalation or external stress. Here, we demonstrate a possible intrinsic route to the rhombohedral (<i>R3</i>) phase in Hf_1-<i>x</i>Zr_<i>x</i>O₂ through symmetry breaking of the parent fluorite lattice. First-principles calculations under <i>R3</i> symmetry-constrained equation-of-state conditions show that the 12-atom fluorite-derived configuration, at equiatomic composition (<i>x</i> = 0.5), stabilizes an intrinsically polar <i>R3</i> ground state with spontaneous polarization <i>P</i>_<i>s</i> = 44.9 μC cm^-2, dielectric permittivity <i>ε</i>_<i>r</i> = 51.3, an ultralow switching barrier of 27.8 meV f.u^.-1, and a coercive field of 0.46 MV cm^-1. Distinct from orthorhombic <i>Pca2</i>_<i>1</i>, the <i>R3</i> structure shows nonmonotonic dielectric behavior, revealing a symmetry-renormalized polarization mechanism beyond conventional Vegard-type ferroelectricity. Moreover, the <i>R3</i> phase stabilizes at reduced thickness, with low built-in potential at proper electrodes preserving its low coercive field. Experiments using fast Fourier transform and geometric-phase analysis validate these predictions, and <i>R3</i>-phase-dominant Hf_1-<i>x</i>Zr_<i>x</i>O₂ capacitors exhibit comparably low coercive fields (0.65 MV cm^-1) and enhanced dielectric permittivity <i>ε</i>_<i>r</i> = 39.1.