Partial Antiferromagnetic Helical Order in Fe${}_3$PO${}_4$O${}_3$

Abstract

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.