Figure 3: Spin ice correlations and quantum dynamics probed with elastic and inelastic neutron scattering.
(a) Inelastic Q-map with energy transfer of 0.25 meV obtained after subtracting the corresponding data at 15 K as background. The broad diffuse scattering pattern carries the symmetry of the crystal but cannot be associated with phonon scattering, which is concentrated around strong nuclear Bragg peaks at low energies. Instead we associate it with inelastic magnetic scattering. The fact that the scattering is wave vector dependent further links it to inter-site quantum spin dynamics. (b) Elastic Q-map with pinch points at (002), (111), and (
). By subtracting 22 K data from 0.1 K data to cancel elastic nuclear scattering processes at Bragg peaks, we obtain quasi-static spin correlations on the time scale of τ=/δE=2 ps. The black ellipses at (002) in (a) and (b) indicate the full width at half maximum instrumental resolution. (c) Temperature-dependence of the spin ice correlation length ξice (left) and the relaxation rate Γ (right). The black solid line denotes 
with the activation energy fixed at the value of Δχ=1.62(3) K. The red solid line shows 
, where C=1.4(2). The black horizontal dashed line indicates the mean distance between 1% of the Pr sites, which according to synchrotron X-ray analysis are occupied by Zr (Supplementary Figure S2 and Supplementary Note 1). (d) Inelastic neutron scattering (INS) spectra at Q=(003) and T=0.1 K (solid circle) and 2.0 K (open circle) after subtraction of INS data obtained at the same Q but at the elevated temperature of 15 K. A correction to the monitor rate was applied to account for order contamination in the unfiltered incident beam. The fitting curve and the corresponding background resulting from subtraction of magnetic scattering at T=15 K to derive Γ are shown by red solid and blue dashed curves, respectively. The details of the analysis are described in Supplementary Note 3. The error bars reflect one s.d. counting statistics. When error bars are not visible they are smaller than the symbol size.
