Topological Textures in Zr-Substituted Barium Titanate

Topological polarization textures in ferroelectrics offer pathways to dense memory, neuromorphic computing, and controlled probes of topology in solids. In rhombohedral barium titanate, theory has identified stable antiskyrmions of topological charge -2 that fractionalize into six -1/3 hotspots, termed topological quarks. Here we extend this landscape to Zr-substituted barium titanate (BZT) using a first-principles parameterized effective Hamiltonian framework. In an ordered 12.5% composition, the chemically doubled periodicity enforces an alternation along [111]: one half hosts the -2 antiskyrmion (six -1/3 quarks), the other a +4 skyrmion (six +2/3 quarks). The two share the same six-vortex scaffold (threefold motif) but differ in the core-level polarization texture, resulting in an integer +1 per vortex offset in the plane-integrated (slice) topological charge. In random BZT, nanodomains remain inducible and cryogenically stable, yet quenched disorder pins and distorts the vortices, producing a heterogeneous, skyrmion-glass-like state with fluctuations of the topological charge along the nanodomain axis. Thermal stability maps show that pure barium titanate retains -2 textures up to ~100 K, whereas in BZT the collapse temperature is nonmonotonic, with a minimum near 6-8% Zr, reflecting competition between ferroelectric softening and disorder pinning. Importantly, the 12.5% ordered arrangement remains rhombohedral above 300 K, enabling field-stabilized nanodomains at 293 K. Under a local [111] bias, the ordered system carries +4 slice charge, while the random composition fragments under the same conditions. These results establish BZT as a platform for chemically programmed, fractionalized ferroelectric topology from cryogenic to room temperature and suggest routes to multistate, reconfigurable devices.