Magnetic Coulomb fields of monopoles in spin ice and their signatures in the internal field distribution.

Fractionalization-the breaking up of an apparently indivisible microscopic degree of freedom-is one of the most counterintuitive phenomena in many-body physics. Here we study its most fundamental manifestation in spin ice, the only known fractionalized magnetic compound in 3D: we directly visualize the 1/r(2) magnetic Coulomb field of monopoles that emerge as the atomic magnetic dipoles fractionalize. We analyze the internal magnetic field distribution, relevant for local experimental probes. In particular, we present new zero-field NMR measurements that exhibit excellent agreement with the calculated line shapes, noting that this experimental technique can in principle measure directly the monopole density in spin ice. The distribution of field strengths is captured by a simple analytical form that exhibits a low density of low-field sites-in apparent disagreement with reported muon spin rotation results. Counterintuitively, the density of low-field locations decreases as the local ferromagnetic correlations imposed by the ice rules weaken.