A field trip through spin ice

TL;DR

This paper visualizes and analyzes the magnetic Coulomb field of emergent monopoles in spin ice, combining experimental NMR measurements with theoretical analysis to understand fractionalization phenomena in 3D magnetic materials.

Contribution

It provides the first direct visualization of monopole Coulomb fields in spin ice and compares experimental NMR data with theoretical models, revealing new insights into fractionalization.

Findings

Visualization of $1/r^2$ magnetic Coulomb field of monopoles

Excellent agreement between NMR lineshapes and calculations

Low-field site distribution decreases with weakening ferromagnetic correlations

Abstract

Fractionalisation -- 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 fractionalised magnetic compound in 3D: we directly visualise the $1/r^2$ magnetic Coulomb field of monopoles which emerge as the atomic magnetic dipoles fractionalise. We analyse the internal magnetic field distribution, relevant for local experimental probes. In particular, we present new zero-field NMR measurements which exhibit excellent agreement with the calculated lineshapes, 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 which exhibits a low density of low-field sites---in apparent disagreement with reported $\mu$SR results. Counterintuitively, the density of low-field locations decreases as the local ferromagnetic correlations imposed by the ice rules weaken.