First-Principles DFT+U Study of Orthorhombic Rivalry in Ferroelectric Hafnia-Zirconia

Ferroelectric Hf_1-xZr_xO₂ (HZO) is a leading candidate for silicon-technology-compatible non-volatile memory, yet the microscopic origin of its polarization remains under debate due to the near-degeneracy of polar orthorhombic phases. Here, we employ first-principles DFT+U calculations to systematically compare the structural, electronic, and ferroelectric properties of the Pca2₁ and Pmn2₁ polymorphs across a range of Hf/Zr stoichiometries. Equation-of-state analysis confirms mechanical stability for both phases, with Pmn2₁ exhibiting slightly larger lattice constants. Energetic trends reveal that phase stability is highly sensitive to Zr content, whereas the spontaneous polarization (∼56-60 μC cm^-2) and wide band gap (∼6 eV) remain remarkably robust. This resilience originates from the fact that substitutional Zr modifies orbital hybridization but preserves the underlying O-2p to Hf/Zr-d charge-transfer mechanism in both polymorphs. These findings show that stoichiometry dictates phase stability, while ferroelectric functionality remains robust against cation ratio and polymorphic competition, offering symmetry- and orbital-guided principles for designing hafnia-zirconia in future memory and logic devices.