  The possibilities of combining several degrees of freedom inside a unique
material have recently been highlighted in their dynamics and proposed as
information carriers in quantum devices where their cross-manipulation by
external parameters such as electric and magnetic fields could enhance their
functionalities. An emblematic example is that of electromagnons, spin-waves
dressed with electric dipoles, that are fingerprints of multiferroics.
Point-like objects have also been identified, which may take the form of
excited quasiparticles. This is the case for magnetic monopoles, the exotic
excitations of spin ices, that have been recently proposed to carry an electric
dipole although experimental evidences remain elusive. Presently, we
investigate the electrical signature of a classical spin ice and a related
compound that supports quantum fluctuations. Our in-depth study clearly
attributes magnetoelectricity to the correlated spin ice phase distinguishing
it from extrinsic and single-ion effects. Our calculations show that the
proposed model conferring magnetoelectricity to monopoles is not sufficient,
calling for higher order contributions.
