  Artificial spin-ices consist of lithographic arrays of single-domain magnetic
nanowires organised into frustrated lattices. These geometries are usually
two-dimensional, allowing a direct exploration of physics associated with
frustration, topology and emergence. Recently, three-dimensional geometries
have been realised, in which transport of emergent monopoles can be directly
visualised upon the surface. Here we carry out an exploration of the
three-dimensional artificial spin-ice phase diagram, whereby dipoles are placed
within a diamond-bond lattice geometry. We find a rich phase diagram,
consisting of a double-charged monopole crystal, a single-charged monopole
crystal and conventional spin-ice with pinch points associated with a Coulomb
phase. In our experimental demagnetised systems, broken symmetry forces
formation of ferromagnetic stripes upon the surface, a configuration that
forbids the formation of the lower energy double-charged monopole crystal.
Instead, we observe crystallites of single magnetic charge, superimposed upon
an ice background. The crystallites are found to form due to the intricate
distribution of magnetic charge around a three-dimensional nanostructured
vertex, which locally favours monopole formation. Our work suggests that
engineered surface energetics can be used to tune the ground state of
experimental three-dimensional ASI systems.
