Extended Data Fig. 9: Solitonic spin states with a net magnetization from biquadratic magnetic interactions, following Supplementary Note 8.

To explain the observed distorted spin helix state with a weak net magnetization, we develop a simple 1D two-parameter model in Eq. (S8) in Supplementary Note 8. In this model, we introduce the exchange anisotropy Δ > 0 and \({\Delta }^{{\prime} } > 0\) to favour a spin helix with net magnetization along the z-axis; we also use the RKKY interaction J = 1, and the four spin interaction K. We optimize the energy to obtain the ground state of the model by simulated annealing. This figure shows the calculation results obtained for Δ = 0.1. Magnetic states with higher harmonics and spontaneous magnetization appear when the four-spin interaction is sufficiently large, K > 0.25.