Inertial effects in systems with magnetic charge

This short article sets out some of the basic considerations that go into detecting the mass of quasiparticles with effective magnetic charge in solids. Effective magnetic charges may be appear as defects in particular magnetic textures. A magnetic monopole is a defect in this texture and as such these are not monopoles in the actual magnetic field B, but instead in the auxiliary field H. They may have particular properties expected for such quasiparticles such as magnetic charge and mass. This effective mass may-in principle-be detected in the same fashion that the mass is detected of other particles classically e.g. through their inertial response to time-dependent electromagnetic fields. I discuss this physics in the context of the “simple” case of the quantum spin ices, but aspects are broadly applicable. Based on extensions to Ryzkhin's model for classical spin ice, a hydrodynamic formulation can be given that takes into account inertial and entropic forces. Ultimately, a form for the susceptibility is obtained that is equivalent to the Rocard equation, which is a classic form used to account for inertial effects in the context of Debye-like relaxation.