  A magnetic monopole in spin ice is a novel quasiparticle excitation in
condensed matter physics, and we found that the ac frequency dependent magnetic
susceptibility $\chi(\omega)$ in the two-dimensional (2D) spin ice (so-called
kagom\'{e} ice) of Dy$_2$Ti$_2$O$_7$ shows a single scaling form. This behavior
can be understood in terms of the dynamical scaling law for 2D Coulomb gas (CG)
systems [Phys. Rev. B 90, 144428 (2014)], characterized by the charge
correlation length $\xi (\propto1/\sqrt{\omega_1})$, where $\omega_{1}$ is a
characteristic frequency proportional to the peak position of the imaginary
part of $\chi(\omega)$. It is a generic behavior among a wide variety of models
such as the vortex dynamics of 2D superconductors, 2D superfluids, classical XY
magnets, and dynamics of melting of Wigner crystals.
