Algebraic Loop Liquid in the Pyrochlore CsNiCrF₆

The β-pyrochlore CsNiCrF₆ 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 intraloop interactions are quite different, the fluctuations of each type of loop can be identified in the spectrum. CsNiCrF₆ 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 T_n ≈ 0.55 K, while we observe a freezing transition at T_f = 2.3 K. Measurements of magnetization, ac, and nonlinear susceptibility show that this is not a canonical spin glass transition so we associate it with the development of slow dynamics due to interloop nematic correlations.