Mass of magnetic monopoles and the magnetic susceptibility of spin ice

The effect of the finite mass of magnetic monopoles on the time and spatial dispersion of the magnetic susceptibility of spin ice is investigated. It is shown that the frequency dependence of the susceptibility in the low-frequency range follows the Debye law, while the susceptibility in the high-frequency range decreases more rapidly with an increase in the frequency. As a result, the sum rule violation typical of the Debye law is removed. The possibility of collective excitations, which are analogous to plasmons in systems with an electric charge, in a magnetic monopole system at high frequencies is also considered.