Fig. 6.

(A and B) Normalized goodness of fit χ ² for the field dependence of the Γ−point mode for the $\mathrm{JK}\mathrm{\Gamma }{\mathrm{\Gamma }}^{\prime }$ and XXZ $\text{-}{J}_1\text{-}{J}_3$ models. (C and E) Classical phase diagram around the only regions where incommensurate order was observed for the restricted parameter space that reproduces the field-dependent Γ−point mode energies. (C and D) correspond to the constraints Γ + 2Γ′=3.0 meV and 3J + K = −12.1 meV, whereas (E) corresponds to $J_{\mathit{xy}}^{(1)}+J_{\mathit{xy}}^{(3)}=-5.0$ meV and $J_z^{(1)}+J_z^{(3)}=-2.0$ meV. The red dashed lines enclose the regions where the Luttinger–Tisza approximation fails, and the ground state is instead determined by a combination of simulated annealing and a variational single-Q Ansatz. The contour lines in the spiral phase of (E) represent the magnitude of the ordering wavevector. The black stars in panels (C) and (E) are the representative points used for both models (see Eqs. 14 and 13 ). (F–I) Representative spin configurations for the reported classical commensurate phases with the corresponding color in the phase diagrams.