Multiple symmetry sustaining phase transitions in spin ice

We present the full phase diagram of the dumbbell model of spin ice as a function of temperature, chemical potential and staggered chemical potential which breaks the point group symmetry of the underlying diamond lattice in favor of a magnetic charge crystal. We observe a double winged structure with five possible phases, monopole fluid (spin ice), fragmented single monopole crystal phases, and double monopole crystal, the zinc-blende structure. Our model provides a skeleton for liquid-liquid phase transitions and for the winged structures observed for itinerant magnets under pressure and external field. We relate our results to recent experiments on ${\mathrm{Ho}}₂{\mathrm{Ir}}₂{\mathrm{O}}₇$ and propose a wide ranging set of new experiments that exploit the phase diagram, including high-pressure protocols, dynamical scaling of Kibble-Zurek form, and universal violations of the fluctuation-dissipation theorem.