  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.
