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

For nearly three decades frustrated magnetism research in three dimensions (3D) has centered on the pyrochlore geometry of corner-sharing tetrahedra and the classical spin liquid (CSL) known as spin ice. In this work, we propose that a lattice of corner-sharing octahedra -- appropriately dubbed the octochlore lattice -- may provide a next-generation platform for the study of 3D frustrated magnetism, with realizations in anti-perovskite and certain potassium-fluoride compounds. We study the phase diagram of Ising spins on the octochlore lattice with first- and second-neighbor interactions within each octahedron, which displays a rich variety of frustrated phases, including CSLs with extensive ground state degeneracies, as well as phases with subextensive ground state degeneracies intermediate between spin liquids and long-range order. In addition to a spin ice CSL, we identify a novel fracton CSL with excitations restricted to move along one-dimensional (1D) lines, which is a classical U(1) analog of the celebrated X-cube model, a paradigmatic realization of fracton topological order. The existence of these two CSLs is rationalized as condensation of 1D ferro-spinons bound states from a parent phase with subextensive degeneracy due to frustration of ferromagnetically polarized chains. We also find a spin nematic phase exhibiting two-stage dimensional reduction from cubic to tetragonal (uniaxial) and finally orthorhombic (biaxial) symmetry, driven by strong fluctuations arising from deconfined 1D antiferro-spinons. This work paves the way for the potential realization of fracton CSLs and the exploration of other exotic frustrated states in real materials.