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

TL;DR

This paper explores a new 3D frustrated magnet lattice called octochlore, revealing diverse spin liquid phases including a fracton spin liquid with restricted excitations, and discusses potential material realizations.

Contribution

It introduces the octochlore lattice as a platform for 3D frustrated magnetism and identifies novel spin liquid phases, including a fracton CSL, expanding understanding of exotic magnetic states.

Findings

Discovery of a fracton spin liquid with 1D restricted excitations.

Identification of a spin nematic phase with dimensional reduction.

Rich phase diagram with classical spin liquids and exotic phases.

Abstract

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.