Dipolar effects on the behavior of magnetically diluted spin ice

In this paper, we explore the magnetic behavior of diluted spin-ice systems, where magnetic moments are randomly removed at various concentrations. We concentrate on features in which the effect of long-range dipolar interactions (usually masked by self-screening in these systems) is made visible by dilution. Our initial focus is on the configurations reached after cooling to low temperatures at zero field, sweeping the whole density range of impurities. We observe that the missing magnetic moments induce a certain type of local, magnetic charge order. Next, using Monte Carlo simulations, we examine the behavior of the magnetization under an applied magnetic field in the [111] crystallographic direction. The inclusion of dipolar interactions allows us to account for the main features observed in previous experimental results. Using the dumbbell model, where magnetic moments are represented as pairs of oppositely charged magnetic monopoles, we can understand the qualitative behavior of these curves as we increase doping. Additionally, we use this framework to calculate the critical fields corresponding to the phase transition observed in pure samples and the characteristic fields appearing at very low doping.