Application of representation analysis to the magnetic structure of nickel chromite spinel

The magnetic structure of the tetragonal nickel chromite spinel (a₀ = 5.76; c = 8.50 Å) has been solved by representation analysis in space group I4₁amd. Magnetic reflexions decompose into two sets; (a) ferrimagnetic ones, produced by a Néel mode along the x-axis and belonging to the two-dimensional Γ_5g representation of wave vector k = [000]; (b) antiferromagnetic reflexions produced by non-colinear anticentered y and z modes belonging to a two-dimensional representation of wave vector k = [001]. The Shubnikov groups of the ferri- and antiferromagnetic modes considered separately are Imm′a′′ and I_p2′2′2₁ respectively. Their intersection has the very low symmetry P2′_y. The antiferromagnetic mode of Ni (in 000 and 0 ½ ¼) has only y components (S_y = 0.58). The chromium spins decompose into two sets: Cr₁ (in 0 ¼ 5/8 and ½ ¼ 1/8) has y and z components (S_y = + 0.73 for the former and −0.73 for the latter atom, S_z = −0.45): Cr_II (in ¼ ½ 7/8 and ¼ 0 3/8) has only z components (S_z = 0.86). The total spins are (Ni) = 1.0 and (Cr) = 1.11, and the moment values are μ(Ni) = 2.0 μ_B: μ(Cr) = 2.22μ_B. The figures are computed from neutron diffraction data given by Prince in 1961. An equivalent model (magnetic twin) has ferrimagnetism along Oy and antiferromagnetic x and z modes. Magnetic interactions are highly anisotropic.