Magnetic charge order in kagome spin ice with dipolar interactions

Dipolar interactions in spin ice are described most effectively in terms of magnetic charges residing on the dual lattice [1]. While spin ice on the pyrochlore lattice contains no magnetic monopoles at low temperatures, spin ice on kagome [2] contains a unit magnetic charge ($\pm 1$) on every triangle. With the aid of Monte-Carlo simulations, we show that long-range Coulomb interaction between the monopoles lifts the degeneracy of the spin-ice states and induces a phase transition into a state with ordered magnetic charges but no spin order. The residual entropy is reduced from the spin-ice value but remains extensive. The phase transition is continuous with critical exponents close to the two-dimensional Ising universality class. [1] C. Castelnovo, R. Moessner, and S. L. Sondhi, Nature {\bf 451,} 42 (2008). [2] A. S. Wills, R. Ballou, and C. Lacroix, Phys. Rev. B {\bf 66}, 144407 (2002).