Fig. 3: Anisotropy surfaces.

Angular dependence of the ferromagnetic resonance field, H_res, in the \((1\bar{1}0)\) plane is shown in a for Co₈Zn₈Mn₄ at 25 K and in b and c for Co₁₀Zn₁₀ at 25 and 250 K, respectively. Black dots are the experimental data points, representing the resonance fields as fitted from the individual spectra that were recorded in 5^∘ steps during a rotation of the magnetic field within the \((1\bar{1}0)\)-plane, as sketched in Fig. 6. Red lines show the fit of the magnetocrystalline anisotropy using Eqs. (4) and (5). The error of the resonance field (grey coloured area) was estimated to be 5% of the linewidth of the resonance peak. d–f display the anisotropy energy surface of the ferromagnetic state, \({\mathcal{E}}({\bf{m}})\), calculated based on the K₁, K₂ and K₃ values obtained from the fits in the corresponding panels above. g–i show the anisotropy energy of the helical state versus the orientation of the q-vector, \({\mathcal{E}}({\bf{q}})\), again calculated using the parameters obtained in the corresponding top panels. Arrows in panels d–i indicate the 〈100〉 axes. In the rotation plane of the magnetic field, the grey \((1\bar{1}0)\) plane, 〈111〉 and 〈110〉 axes are also shown.