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Pattern formation in spin systems with continuous-rotational symmetry (CRS) provides a powerful platform to study emergent complex magnetic phases and topological defects in condensed-matter physics. However, its understanding and correlation with unconventional magnetic order along with high-resolution nanoscale imaging are challenging. Here, we employ scanning nitrogen vacancy (NV) magnetometry to unveil the morphogenesis of spin cycloids at both the local and global scales within a single ferroelectric domain of (111)-oriented BiFeO₃, which is a noncollinear antiferromagnet, resulting in formation of a glassy labyrinthine pattern. We find that the domains of locally oriented cycloids are interconnected by an array of topological defects and exhibit isotropic energy landscape predicted by first-principles calculations. We propose that the CRS of spin-cycloid propagation directions within the (111) drives the formation of the labyrinthine pattern and the associated topological defects such as antiferromagnetic skyrmions. Unexpectedly, reversing the as-grown ferroelectric polarization from [ $\stackrel{ ¯}{1}$ $\overline{1}$ $\overline{1}$] to [111] produces a noncycloidal NV image contrast which could be attributed to either the emergence of a uniformly magnetized state or a reversal of the cycloid polarity. These findings highlight that (111)-oriented BiFeO₃is not only important for studying the fascinating subject of pattern formation but could also be utilized as an ideal platform for integrating novel topological defects in the field of antiferromagnetic spintronics. 

Engineering strain critically affects the properties of materials and has extensive applications in semiconductors and quantum systems. However, the deployment of strain-engineered nanocatalysts faces challenges, in particular in maintaining highly strained nanocrystals under reaction conditions. Here, we introduce a morphology-dependent effect that stabilizes surface strain even under harsh reaction conditions. Using four-dimensional scanning transmission electron microscopy (4D-STEM), we found that cube-shaped core-shell Au@Pd nanoparticles with sharp-edged morphologies sustain coherent heteroepitaxial interfaces with larger critical thicknesses than morphologies with rounded edges. This configuration inhibits dislocation nucleation due to reduced shear stress at corners, as indicated by molecular dynamics simulations. A Suzuki-type cross-coupling reaction shows that our approach achieves a fourfold increase in activity over conventional nanocatalysts, owing to the enhanced stability of surface strain. These findings contribute to advancing the development of advanced nanocatalysts and indicate broader applications for strain engineering in various fields.