Algebraic Loop Liquid in the Pyrochlore CsNiCrF_{6}

The β-pyrochlore CsNiCrF_{6} is a charge ice-each tetrahedron of the pyrochlore lattice is occupied by two Ni^{2+} and two Cr^{3+} 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. CsNiCrF_{6} 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.