Topology and geometry of spin origami

Abstract

Kagome antiferromagnets are known to be highly frustrated and degenerate when they possess simple, isotropic interactions. We consider the entire class of these magnets when their interactions are spatially anisotropic. We do so by identifying a certain class of systems whose degenerate ground states can be mapped onto the folding motions of a generalized "spin origami" two-dimensional mechanical sheet. Some such anisotropic spin systems, including Cs2ZrCu3F12, map onto flat origami sheets, possessing extensive degeneracy similar to isotropic systems. Others, such as Cs2CeCu3F12, can be mapped onto sheets with non-zero Gaussian curvature, leading to more mechanically stable corrugated surfaces. Remarkably, even such distortions do not always lift the entire degeneracy, instead permitting a large but sub-extensive space of zero-energy modes. We show that for Cs2CeCu3F12, due to an additional point group symmetry associated with structure, these modes are 'Dirac' line nodes with a double degeneracy protected by a topological invariant. The existence of mechanical analogs thus serves to identify and explicate the robust degeneracy of the spin systems.

5 pages, 4 figures

References in corpus (12)

• Dirac Line Nodes in Inversion Symmetric Crystals
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Nonlinear conduction via solitons in a topological mechanical insulator
• Selective buckling via states of self-stress in topological metamaterials
• Topological mechanics of origami and kirigami
• Transformable topological mechanical metamaterials
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials
• A classification of magnetic frustration and metamaterials from topology
• Uniaxial stress tuning of geometrical frustration in a Kondo lattice
• Supersymmetry "protected" topological phases of isostatic lattices and kagome antiferromagnets
• Structural phase transitions in the kagome lattice based materials Cs2-xRbxSnCu3F12 (x = 0, 0.5, 1.0, 1.5)

Cited by in corpus (8)

• Symmetry and Topology in Non-Hermitian Physics
• Disordered flat bands on the kagome lattice
• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Topology in non-linear mechanical systems
• Hidden symmetries generate rigid folding mechanisms in periodic origami
• Dynamics and energy landscape of the jammed spin-liquid
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Strain tuning of highly frustrated magnets: Order and disorder in the distorted kagome Heisenberg antiferromagnet