Monopole ordered phases in dipolar and nearest-neighbours Ising pyrochlore: from spin ice to the "all-in--all-out" antiferromagnet

TL;DR

This study uses Monte Carlo simulations to explore phase diagrams of Ising pyrochlores, revealing complex monopole behaviors and phase transitions from spin ice to all-in--all-out antiferromagnetic order, influenced by magnetic charge interactions.

Contribution

It provides a comprehensive phase diagram of dipolar and nearest-neighbor Ising pyrochlores, highlighting monopole fluid phases and the effects of spin constraints on magnetic charge ordering.

Findings

Monopole fluid with charge order persists at high temperatures.

Phase diagram resembles ionic systems with charge interactions.

Construction constraints influence monopole phase behavior.

Abstract

We study Ising pyrochlores by means of Monte Carlo simulations. We cover a set of exchange constants ranging from the frustrated ferromagnetic case (spin-ice) to the fully-ordered "all-in--all-out" antiferromagnet in the dipolar model, reinterpreting the results --as in an ionic system-- in terms of a temperature vs. magnetic charge density phase diagram. In spite of its spin nature and the presence of both double and single non-conserved magnetic charges, the dipolar model gives place to a phase diagram which is quite comparable with those previously obtained for on-lattice systems of electric charges, and on spin ice models with conserved number of single magnetic charges. The contrast between these systems, to which we add results from the nearest-neighbours model, put forward other features of our phase diagram --notably, a monopole fluid with charge order at high monopole densities that persists up to arbitrarily high temperatures-- that can only be explained taking into account construction constraints forced by the underlying spin degrees of freedom.