Classical Fracton Spin Liquid and Exotic Phases in Ising-like Octochlore Magnets

For nearly three decades frustrated magnetism research in 3D has centered on the pyrochlore geometry of corner-sharing tetrahedra and the classical spin liquid (CSL) known as spin ice. In this talk I propose that a lattice of corner-sharing octahedra---appropriately dubbed the octochlore lattice---may provide the next-generation platform for 3D frustrated magnets, with realizations in anti-perovskite and certain potassium-flouride compounds. We study the phase diagram of Ising spins on the octochlore lattice with first- and second-neighbor interactions within each octahedron. In addition to a spin ice CSL, we identify a novel fracton CSL with excitations restricted to move on 1D lines, which is a classical U(1) analog of the celebrated X-cube model of fracton topological order. We characterize this fracton liquid from multiple perspectives---via its flat bands with nodal line touchings; as a condensate of spinon bound states; as a cage-net liquid; as a foliated fracton phase of intersecting spin vorticity models; and as a bionic spin liquid of intersecting square ice sheets---giving a comprehensive understanding of its excitations and connecting to many recent developments in the understanding of classical spin liquids. This works paves the way for the potential realization of fracton CSLs in real materials.