High-Pressure Synthesis and Structural Instability of A-Site-Ordered Quadruple Perovskite LaHg ₃ Ti ₄ O _{12 <b>+</b> δ}

PbHg₃Ti₄O₁₂ (PHTO) represents the first example of ferroelectricity in quadruple A-site-ordered perovskites AA'₃B₄O₁₂, which features Hg²⁺ ions in an unusual 8-fold coordination at the A'-site, forming a structural bridge between simple perovskites and conventional A-site-ordered perovskites. Here, we engineer the A-site charge and lone-pair activity by substituting La³⁺ for Pb²⁺, and synthesize a new A-site-ordered perovskite LaHg₃Ti₄O_12+δ (LHTO) under high-pressure and high-temperature conditions. LHTO crystallizes in the centrosymmetric <i>Im</i>3̅ structure at room temperature and is isostructural with PHTO, retaining the 8-fold coordination of the Hg²⁺ ions. Structural and dielectric characterizations, and first-principles calculations, show a structural instability around 90 K driven by phonon soft modes dominated by Ti-O vibration and the weakening of lone pair, which prevents the development of long-range ferroelectric order. Our results establish a dual A-site design strategy─tuning both lone-pair activity and electron doping─for controlling ferroelectricity in A-site-ordered quadruple perovskites and uncover a competing instability characteristic of this intermediate-coordination regime.