The antiferromagnetic transition in the frustrated bixbyite $\beta$-Fe${}_2$O${}_3$ magnet

Although Fe${}_2$O${}_3$ compounds are among the most extensively studied transition-metal oxides, the magnetic properties of $\beta$-Fe${}_2$O${}_3$ remain poorly characterized. Using neutron and synchrotron X-ray diffraction, we investigate the temperature-driven magnetic transition in $\beta$-Fe${}_2$O${}_3$. A noncollinear antiferromagnetic structure sets in abruptly via activation of irrep $m{H}_1^{+}$ at the H-point [$\mathbf{k}=(1,1,1)$] together with antitranslation $(1^{\mathrm{\prime }}\mathrm{\mid }\frac{1}{2},\frac{1}{2},\frac{1}{2})$. Below $T_{\mathrm{N}}$, the magnetic cell becomes primitive $(P_{I}a\bar{3})$, yielding two interpenetrating primitive cubic subcells with inverted moments and non-polar type-IV symmetry. All Fe${}^{3+}$-O-Fe${}^{3+}$ exchanges are antiferromagnetic, and the bixbyite structure promotes geometric frustration and noncollinear magnetism through coexisting magnetic sublattices with distinct symmetries and easy axes. Its frustration index $f\simeq 7.6$ is among the highest reported for binary magnetic oxides. In $\{111\}$ planes, distorted Fe2O${}_6$ octahedra form hexagonal rings interconnected by triangular units. Notably, hexagonal Fe2 rings host a central Fe1 ion with strong Ising-like anisotropy, which could act as a switching element for the rings’ magnetic state. These features point to routes for functional design.