  If spin liquids have been famously defined by what they are not, i.e.
ordered, the past years have seen the frontier between order and spin liquid
starting to fade, with a growing number of materials whose low-temperature
physics cannot be explained without co-existence of (partial) magnetic order
and spin fluctuations. Here we study an example of such co-existence in the
presence of magnetic dipolar interactions, related to spin ice, where the order
is long range and the fluctuations support a Coulomb gauge field. Topological
defects are effectively coupled via energetic and entropic Coulomb
interactions, the latter one being stronger than for the spin-ice ground state.
Depending on whether these defects break the divergence-free condition of the
Coulomb gauge field or the long-range order, they are respectively categorized
as monopoles - as in spin ice - or monopole holes, in analogy with electron
holes in semiconductors. The long-range order plays the role of a
fully-occupied valence band, while the Coulomb spin liquid can be seen as an
empty conducting band. These results are discussed in the context of other
lattices and models which support a similar co-existence of Coulomb gauge field
and long-range order. We conclude this work by explaining how dipolar
interactions lift the spin liquid degeneracy at very low energy scale by
maximizing the number of flippable plaquettes, in light of the equivalent
quantum dimer model.
