  We introduce a new classical spin liquid on the pyrochlore lattice by
extending spin ice with further neighbour interactions. We find that this
disorder free spin model exhibits a form of dynamical heterogeneity with
extremely slow relaxation for some spins while others fluctuate quickly down to
zero temperature. We thus call this state "spin slush", in analogy to the
heterogeneous mixture of solid and liquid water. This behaviour is driven by
the structure of the ground state manifold which extends the celebrated the
two-in/two-out ice states to include branching structures built from
three-in/one-out, three-out/one-in and all-in/all-out tetrahedra defects.
Distinctive liquid-like patterns in the spin correlations serve as a signature
of this intermediate range order. Possible applications to materials as well
the effects of quantum tunneling are discussed.
