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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. 

Abstract Bismuth ferrite (BiFeO₃) is a multiferroic material that exhibits both ferroelectricity and canted antiferromagnetism at room temperature, making it a unique candidate in the development of electric-field controllable magnetic devices. The magnetic moments in BiFeO₃are arranged into a spin cycloid, resulting in unique magnetic properties which are tied to the ferroelectric order. Previous understanding of this coupling has relied on average, mesoscale measurements. Using nitrogen vacancy-based diamond magnetometry, we observe the magnetic spin cycloid structure of BiFeO₃in real space. This structure is magnetoelectrically coupled through symmetry to the ferroelectric polarization and this relationship is maintained through electric field switching. Through a combination of in-plane and out-of-plane electrical switching, coupled with ab initio studies, we have discovered that the epitaxy from the substrate imposes a magnetoelastic anisotropy on the spin cycloid, which establishes preferred cycloid propagation directions. The energy landscape of the cycloid is shaped by both the ferroelectric degree of freedom and strain-induced anisotropy, restricting the spin spiral propagation vector to changes to specific switching events. 

The AA′-stacked FCGT is a new class of room-temperature Néel-type skyrmion hosting material with C 6v symmetry.