Supporting data for the paper "Algebraic loop liquid in the pyrochlore CsNiCrF6"

The 𝛽-pyrochlore is a charge ice – each tetrahedron of the pyrochlore lattice is occupied by two Ni2+ and two Cr3+ according to an ice rule, resulting in fully packed same-species loops with power-law length distribution. Using inelastic neutron scattering and numerical simulations, we show that the spin dynamics can be well described by a model with three antiferromagnetic interaction strengths, one for Ni-Ni, Cr-Ni, and Cr-Cr interactions. Because the strengths of the two intra-loop interactions are quite different, the fluctuations of each type of loop can be identified in the spectrum. therefore forms an algebraic loop liquid in which power-law cation correlations control the spin dynamics. Our parameters predict a transition to spin nematic order with associated arrest of dynamics at 𝑇𝑛≈0.55 K, while we observe a freezing transition at 𝑇𝑓=2.3K. Measurements of magnetisation, ac and non-linear susceptibility show that this is not a canonical spin glass transition so we associate it with the development of slow dynamics due to inter-loop nematic correlations.