Impurity and boundary effects on magnetic monopole dynamics in spin ice

Using a SQUID magnetometer, we measure the time-dependent magnetic relaxation in Dy2Ti2O7 and find that it decays with a stretched exponential followed by a very slow long-time tail. In a Monte Carlo simulation governed by Metropolis dynamics we find that surface effects and a very low level of stuffed spins (0.30\%) - magnetic Dy ions substituted for non-magnetic Ti ions - can explain these signatures in the relaxation. We find that the additional spins trap the magnetic monopole excitations and provide the first example of how defects in a spin-ice material can obstruct the flow of monopoles.