Coulomb phase diagnostics as function of temperature, interaction range and disorder

TL;DR

This paper develops a comprehensive theory of pinch points in spin ice, linking their shape to Coulomb interactions, and explains their experimental observation across various conditions including temperature, interaction range, and disorder.

Contribution

It provides a detailed theoretical framework for understanding the behavior of pinch points in spin ice under different physical conditions and disorder.

Findings

Pinch point shapes reveal Coulomb interaction strengths.

Pinch points persist at high temperature despite disorder.

The theory explains experimental observations in HoYTi2O7.

Abstract

The emergent gauge field characteristic of the Coulomb phase of spin ice betrays its existence via pinch points in the spin structure factor ${\cal{S}}$ in reciprocal space which takes the form of a transverse projector ${\cal{P}}$ at low temperature: ${\cal{S}} (q) \sim {\cal{P}} \sim q^2_\bot/q^2$. We develop a theory which establishes the fate of the pinch points at low and high temperature, for hard and soft spins, for short- and long-ranged (dipolar) interactions, as well as in the presence of disorder. We find that their detailed shape can be used to read off the relative sizes of entropic and magnetic Coulomb interactions of monopoles in spin ice, and we resolve the question why pinch points have been experimentally observed for Ho$_{1.7}$Y$_{0.3}$Ti$_2$O$_7$ even at high temperature in the presence of strong disorder.