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The forging of strong correlations on decreasing temperature can take placewithout the arousal of conventional order. If this happens, as in somegeometrically frustrated magnets, disorder can be a phenomenon more interestingthan order itself. A Coulomb phase, for example, has critical-like pair-spincorrelations, leading to neutron scattering \textit{pinch points} and emergentelectromagnetism. Here we present a new instance of disorder in an Isingpyrochlore lattice: the \textit{Polarized Monopole Liquid} (PML), a densemonopole fluid with pinch points in the \textit{magnetic charge}-paircorrelations. It is a phase of "monopole matter" never considered before which,in principle, can be stabilized in real materials using a magnetic field anduniaxial stress along the [100] direction. To explain how the monopolecorrelations arise, we show that the PML is a Coulomb phase in which spinfluctuations cannot be assigned either to monopoles or to internal magneticmoments, but necessarily comprehend both degrees of freedom. We develop asimple but nontrivial method to Helmholtz decompose the spin field into adivergenceless and a divergenceful part in magnetic charge disorderedpyrochlores that shows the appearance of pinch points associated to thedivergenceful component in places where Bragg peaks are observed for the"all-in/all-out" antiferromagnet.

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