Monopole ordered phases in dipolar and nearest-neighbors Ising pyrochlore: From spin ice to the all-in–all-out antiferromagnet

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 nonconserved 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 a conserved number of single magnetic charges. The contrast between these systems, to which we add results from the nearest-neighbors 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.