Polarized Neutron Scattering as a Probe of Emergent Gauge Structure in Classical Spin Ice

Spin ice compounds are exemplar frustrated magnetic systems that realize a classical spin liquid phase at low temperature described by an emergent gauge field with fractionalized magnetic monopole excitations. This emergent gauge structure manifests in polarized neutron scattering experiments as the characteristic pinch point singularities which have been clearly observed in the spin-flip (SF) channel. On the other hand, the non-spin-flip (NSF) channel generally lacks such striking features. In fact, within an extended model of spin ice, the NSF channel is found to be completely dispersionless, and we explore this utilizing both Monte Carlo and Large-N techniques. At the level of the Large-N approximation, this flatness is inherited directly from the flat bands of the adjacency matrix, and the temperature-dependent intensity of the featureless NSF channel is inversely proportional to the stiffness of the emergent gauge fields. We show how the SF and NSF channels can be understood as direct probes of the emergent gauge field correlations and explore the implications of this finding. This work lays the groundwork for a deeper understanding of NSF scattering in spin ice compounds, and could potentially lead to new experimental insights.