Fig. 2: Breaking the pure helix.

a, b Definition of the angle ϕ, magnetic exchange energies (\({J}_{1},{J}_{1}^{{\prime} }\) and J2), single-ion anisotropy G and in-plane thermal fluctuation (θi, i=1-6). c Energy landscape of six europium spins as a function of ϕ calculated from eqn (2) with parameters \({J}_{1}=-1.2|{J}_{2}|,{J}_{1}^{{\prime} }=0.5{J}_{1},G{S}^{4}=0.2|{J}_{2}|\), and J2 < 0. d Difference in free energy between the pure helix and the broken helix, where ΔF = FPH − FBH.