# Screening and the Pinch Point Paradox in Spin Ice

## TL;DR

This paper investigates the nature of pinch point singularities in spin ice, revealing a paradox between simulation/theory and experimental observations, and exploring potential explanations involving screening, disorder, or quantum effects.

## Contribution

It provides high-resolution simulations and new analytical theory of pinch points in dipolar spin ice, highlighting a paradox between theoretical predictions and experimental results.

## Key findings

- Simulations and existing theories predict infinitely sharp pinch points.
- Experiments show broadened pinch points, indicating screening effects.
- The paradox suggests possible roles for quantum fluctuations or fundamental theory corrections.

## Abstract

A pinch point singularity in the structure factor characterizes an important class of condensed matter that is a counterpoint to the paradigm of broken symmetry. This class includes water ice, charge ice and spin ice. Of these, dipolar spin ice affords the the pre-eminent model system because it has a well-established Hamiltonian, is simple enough to allow analytical theory and numerical simulation, and is well represented in experiment by Dy$_{2}$Ti$_{2}$O$_{7}$ and Ho$_{2}$Ti$_{2}$O$_{7}$. Nevertheless it is a considerable challenge to resolve the pinch points in simulation or experiment as they represent a very long range correlation. Here we present very high resolution simulations of the polarized neutron scattering structure factor of dipolar spin ice and new analytical theory of the pinch point profiles. We compare these with existing theory and experiment. We find that our simulations are consistent with theories that reveal the pinch points to be infinitely sharp, as a result of unscreened dipolar fields. However, neither simulation nor these theories are consistent with experiments, which instead is quantitatively captured by a theory that allows for screening of the dipolar fields and consequent strong broadening of the pinch points. This striking paradox is not easily resolved: broadening of the pinch points by random disorder seems to have been ruled out by existing theory, while deficiencies in the Hamiltonian description are not relevant. Intriguingly, we are left to consider the role of quantum fluctuations or the possibility of a fundamental correction to either the standard method of simulating dipolar systems, or the theory of polarized neutron scattering. More generally, our results may have relevance far beyond ice systems. For example, spin ice is a model Debye-H\"uckel (magnetic) electrolyte, so our basic observation that the screening length may diverge while...