The bixbyite framework as a platform for frustrated noncollinear magnetism: resolving the magnetic ground state of $\beta$-Fe${}_2$O${}_3$

Abstract

Magnetic behavior across Fe${}_2$O${}_3$ polymorphs varies widely despite identical chemistry, highlighting crystal architecture as a key determinant of exchange topology, magnetic anisotropy, and ultimately magnetic order. Here, using neutron and synchrotron X-ray diffraction, we establish the magnetic ground state of the poorly understood bixbyite $\beta$-Fe${}_2$O${}_3$ polymorph and uncover the structural origin of its strong frustration. Below the Néel temperature, a noncollinear antiferromagnetic state emerges through activation of the $m{H}_1^{+}$ irrep at the H-point [$\mathbf{k}=(1,1,1)$] and the antitranslation $(1^{\prime }|\frac{1}{2},\frac{1}{2},\frac{1}{2})$, breaking the body centering and yielding two interpenetrating primitive cubic magnetic subcells with inverted moments and nonpolar type-IV symmetry. Under exclusively antiferromagnetic Fe${}^{3+}$-O-Fe${}^{3+}$ interactions, $\beta$-Fe${}_2$O${}_3$ exhibits a large frustration index ($f\approx 7.56$). This behavior originates from the intrinsic geometry of the bixbyite lattice: two magnetic sublattices with distinct point symmetries and anisotropy constraints are embedded in a three-dimensional exchange network containing interconnected triangular and hexagonal motifs. In $\{111\}$ planes, Fe2 ions form hexagonal rings interconnected by frustrated triangular units, while locally Ising-like Fe1 ions occupy the ring centers. Our results thus identify the bixbyite architecture as a promising general platform for frustrated noncollinear magnetism. Extending this structural framework to other magnetic transition-metal or 4$f$ ions opens a materials space for engineering competing exchange interactions and anisotropies, potentially stabilizing new noncollinear and field-tunable magnetic states.

32 pages, 14 figures, 6 Tables