# The Polarized Monopole Liquid: a Coulomb phase in a fluid of magnetic charges

## TL;DR

This paper introduces the Polarized Monopole Liquid, a new Coulomb phase in an Ising pyrochlore lattice featuring a dense monopole fluid with characteristic pinch points, expanding understanding of disorder in magnetic systems.

## Contribution

It presents the first theoretical description of the Polarized Monopole Liquid as a Coulomb phase with unique monopole correlations in a pyrochlore lattice.

## Key findings

- Discovery of pinch points in magnetic charge correlations
- Identification of a monopole fluid phase without conventional order
- Development of a Helmholtz decomposition method for spin fields

## Abstract

The forging of strong correlations on decreasing temperature can take place without the arousal of conventional order. If this happens, as in some geometrically frustrated magnets, disorder can be a phenomenon more interesting than order itself. A Coulomb phase, for example, has critical-like pair-spin correlations, leading to neutron scattering \textit{pinch points} and emergent electromagnetism. Here we present a new instance of disorder in an Ising pyrochlore lattice: the \textit{Polarized Monopole Liquid} (PML), a dense monopole fluid with pinch points in the \textit{magnetic charge}-pair correlations. It is a phase of "monopole matter" never considered before which, in principle, can be stabilized in real materials using a magnetic field and uniaxial stress along the [100] direction. To explain how the monopole correlations arise, we show that the PML is a Coulomb phase in which spin fluctuations cannot be assigned either to monopoles or to internal magnetic moments, but necessarily comprehend both degrees of freedom. We develop a simple but nontrivial method to Helmholtz decompose the spin field into a divergenceless and a divergenceful part in magnetic charge disordered pyrochlores that shows the appearance of pinch points associated to the divergenceful component in places where Bragg peaks are observed for the "all-in/all-out" antiferromagnet.