Nanosized helical magnetic domains in strongly frustrated Fe$_3$PO$_4$O$_3$

Non-centrosymmetric Fe$_3$PO$_4$O$_3$ (space group $R3m$) contains triangular motifs of Fe$^{3+}$ ions coupled by strong antiferromagnetic interactions ($|\Theta_{CW}| > 900$ K). Neutron powder diffraction below $T_N = 163$ K reveals the formation of an ordered helical incommensurate magnetic structure, with helical axis in the hexagonal $ab$ plane and modulation length of $\sim$ 100 Å. The magnetic structure forms needle-like correlation volumes perpendicular to the $ab$ plane that extend at least to 900 Å along the $c$-axis, but are confined to $\sim$ 70 Å in the $ab$ plane. The refined magnetic moment, supported by magnetization measurements of a magnetically diluted series (Fe$_{3-x}$Ga$_x$PO$_4$O$_3$), indicates a reduced Fe$^{3+}$ moment, suggesting metal-ligand charge transfer. High-resolution synchrotron X-ray diffraction reveals no lattice symmetry change below $T_N$. Absence of long-range in-plane order below $T_N$ signifies the formation of a high density of defects in the magnetic structure. The defect-rich helical magnetic phase in Fe$_3$PO$_4$O$_3$ offers insight into the stabilization of topological spin textures in antiferromagnets.