Modulation of the modulated magnetic structure of an Ho i-MAX phase described by a magnetic (3+2)-dimensional superspace group.

The magnetic structures of the Ho-based i-MAX phase (MoHo)GaC were studied with neutron powder diffraction at low temperature. (MoHo)GaC crystallizes in the orthorhombic space group Cmcm. The material undergoes two successive antiferromagnetic transitions at T = 10 K and T = 7.2 K. The magnetic structure below T is incommensurate with the propagation vector k = (0, k, 0) with k = 0.696 (1) at 9 K. For the analysis of the magnetic structure, a group-theoretical approach based on the space group of the nuclear structure and its subgroups was employed. A model in the (3+1)D superspace group Cmcm.1'(0β0)s0ss yielded the most accurate results in neutron powder diffraction refinements. The determined structure was found to be an incommensurate longitudinal amplitude-modulated magnetic structure. Below T, additional magnetic satellites develop. They could be indexed by a propagation vector k = (τ, 0, 0) with the τ value increasing below T until it stabilizes at approximately 3 K at 0.075. A magnetic structure determination considering two propagation vectors k and k was carried out using the superspace formalism by building the corresponding (3+2)D model. The determination was based on the observation that the additional magnetic peaks emerge exclusively in the vicinity of the incommensurate magnetic peaks with propagation vector k, and not in the vicinity of nuclear peaks. This indicates that only mixed-index reflections were observed, and not reflections purely related to k. The magnetic superspace group (MSSG) that was determined is Amma.1' (0,β,0)00s0 (0,0,γ)ss0s. The structure can be described as a longitudinal amplitude-modulated structure, which itself is amplitude-modulated in a perpendicular direction. This represents a very unusual case of a 2-k magnetic structure with no symmetry relation between the propagation vectors.