Fragmented Spin Ice and Multi-k Ordering in Rare-Earth Antiperovskites

We study near-neighbor and dipolar Ising models on a lattice of corner-sharing octahedra. In an extended parameter range of both models, frustration between antiferromagnetism and a spin-ice-like three-in-three-out rule stabilizes a Coulomb phase with correlated dipolar and quadrupolar spin textures, both yielding distinctive neutron-scattering signatures. Strong further-neighbor perturbations cause the two components to order independently, resulting in unusual multi-k orders. We propose experimental realizations of our model in rare-earth antiperovskites.