Partial Antiferromagnetic Helical Order in Fe\(_3\)PO\(_4\)O\(_3\)

Magnetic frustration in Fe\(_3\)PO\(_4\)O\(_3\) has been shown to produce to an unusual magnetic state below T\(_N = 163\) K, where incommensurate antiferromagnetic order is restricted to nanosized needle-like domains, as inferred from neutron powder diffraction. Here we show using single-crystal neutron diffraction that Fe\(_3\)PO\(_4\)O\(_3\) does not exhibit a preferred ordering wavevector direction in the \(ab\) plane despite having a well-defined ordering wavevector length. This results in the observation of continuous rings of scattering rather than satellite Bragg peaks. The lack of a preferred incommensurate ordering wavevector direction can be understood in terms of an antiferromagnetic Heisenberg model with nearest-neighbor (\(J_1\)) and second-neighbor (\(J_2\)) interactions, which produces a quasi-degenerate manifold of ordering wavevectors. This state appears to be similar to the partially ordered phase of MnSi, but in Fe\(_3\)PO\(_4\)O\(_3\) arises in a frustrated antiferromagnet rather than a chiral ferromagnet.