Algebraic Loop Liquid in the Pyrochlore <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>CsNiCrF</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> </mml:msub> </mml:mrow>

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.