Dipolar Hyperkagome Spin Ice

Non-magnetic doping of the Pyrochlore spin ices Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ has been shown\footnote{X. Ke {\it et al}., Phys. Rev. Lett. {\bf 99}, 137203} to exhibit a nonmonotonic residual entropy per spin as a function of doping, with an increase near one quarter doping. Hyperkagome corresponds to a disorder-free one quarter doping of the Pyrochlore lattice with a large residual Pauling entropy $S/N = 1/3\ln(9/2)$. In this talk we discuss the physics of local Ising spins coupled through antiferromagnetic nearest neighbour exchange and a long range dipolar interaction. We generalize the phase diagram\footnote{B.C. den Hertog {\it et al}., Phys. Rev. Lett. {\bf 84}, 3430-3433 (2000)} of dipolar Pyrochlore spin ice to the Hyperkagome case, finding a crossover to a spin ice state followed by a transition to a charge ordered state and finally a transition to an ordered ground state, as first seen on the Kagome lattice\footnote{Gia-Wei Chern {\it et al}., Phys. Rev. Lett. {\bf 106}, 207202 (2011)}. We show that our hybrid single spin flip/loop algorithm Monte Carlo simulations agree with analytical results for small sizes, and present results for systems as large as $12*L^3$ spins with $L=4$.