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

The magnetic structures of the Ho-based i-MAX phase (Mo_2/3Ho_1/3)₂GaC were studied with neutron powder diffraction at low temperature. (Mo_2/3Ho_1/3)₂GaC crystallizes in the orthorhombic space group Cmcm. The material undergoes two successive antiferromagnetic transitions at T_N1 = 10 K and T_N2 = 7.2 K. The magnetic structure below T_N1 is incommensurate with the propagation vector k₁ = (0, k_y, 0) with k_y = 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_N2, additional magnetic satellites develop. They could be indexed by a propagation vector k₂ = (τ_x, 0, 0) with the τ_x value increasing below T_N2 until it stabilizes at approximately 3 K at 0.075. A magnetic structure determination considering two propagation vectors k₁ and k₂ 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 k₁, and not in the vicinity of nuclear peaks. This indicates that only mixed-index reflections were observed, and not reflections purely related to k₂. 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.