Example

An incommensurate case : AgCrSe₂

AgCrSe2 is another exampe of a layered compound with stacked triangular planes of Cr atoms. Magnetic ordering of the Cr spins is observed below T_N = 55 K, and is characterised by the propagation vector k = (0+ε, 0+ε, 3/2) (ε ~ 0.037(3)). The corresponding magnetic structure can be described as long wavelength antiferromagnetic cycloids running along [110] and stacked antiferromagnetically along c, with the Cr spins rotating within the ab plane :

In the magnetically ordered phase, a spin-wave dispersive magnetic signal is clearly visible in the excitation spectra : to quantitatively analyse the observations, spin wave modelling was carried out, using a simple spin Hamiltonian with nearest (J_ab), next-nearest (J_NN) neighbour interactions, and coupling between nearest neighbours in adjacent layers (J_C). J_ab, J_NN and J_C values were carefully chosen to stabilize the experimentally observed propagation vector k (ε = 0.037), at the mean field level, using the mean-field calculation option of spinwave with the chosen incommensurate propagation vector. The magnetic spectrum of AgCrSe₂ can be readily modelled within this approach, with a ferromagnetic J_ab ~ -2.1 meV, and two antiferromagnetic second neighbour J_NN ~ 0.71 meV and J_C ~ 0.09 meV. The commensurate case k=(0, 0, 3/2) is shown on the left panel of the figure below, and the incommensurate case on the right : in the incommensurate magnetic structures, additional branches are clearly visible, which modify the width and intensity of the dispersion, at low Q especially.

The input file corresponding to this case can be found in the download package.