Layered kagome spin ice

Spin ice materials provide a rare instance of emergent gauge symmetry and fractionalisation in three dimensions: the effective degrees of freedom of the system are emergent magnetic monopoles, and the extensively many `ice rule' ground states are those devoid of monopole excitations. Two-dimensional (kagome) analogues of spin ice have also been shown to display a similarly rich behaviour. In kagome ice however the ground-state `ice rule' condition implies the presence everywhere of magnetic charges. As temperature is lowered, an Ising transition occurs to a charge-ordered state, which can be mapped to a dimer covering of the dual honeycomb lattice. A second transition, of Kosterlitz-Thouless or three-state Potts type, occurs to a spin-ordered state at yet lower temperatures, due to small residual energy differences between charge-ordered states. Inspired by recent experimental capabilities in growing spin ice samples with selective (layered) substitution of non-magnetic ions, in this work we investigate the fate of the two ordering transitions when individual kagome layers are brought together to form a three-dimensional pyrochlore structure coupled by long range dipolar interactions. We also consider the response to substitutional disorder and applied magnetic fields.