Frustration in magnetic systems is fertile ground for complex behaviour, including unconventional ground states with emergent symmetries, topological properties, and exotic excitations. A canonical example is the emergence of magnetic-charge-carrying quasiparticles in spin-ice compounds. Despite extensive work, a reliable experimental indicator of the density of these magnetic monopoles in spin-ice systems is yet to be found. Here, using measurements on single crystals of Ho$_{2}$Ir$_{2}$O$_{7}$ in combination with dipolar Monte Carlo simulations, we show that the magnetoresistance is highly sensitive to the density of monopoles. Moreover, we find that for the orientations of magnetic field in which the monopole density is enhanced, a strong coupling emerges between the magnetic charges on the holmium sublattice and the antiferromagnetically ordered iridium ions, leading to an ability to manipulate the antiferromagnetic domains via a uniform external field. Our results pave the way to a quantitative experimental measure of monopole density and provide a powerful illustration of the interplay between the various magnetic and electronic degrees of freedom in the frustrated pyrochlore iridates. This interdependence holds promise for potential functional properties arising from the link between magnetic and electric charges, as well as for the control of antiferromagnetic domain walls, a key goal in the design of next-generation spintronic devices.
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