Line-Graph Approach to Spiral Spin Liquids

Competition among exchange interactions is able to induce novel spin correlations on a bipartite lattice without geometrical frustration. A prototype example is the spiral spin liquid, which is a correlated paramagnetic state characterized by subdimensional degenerate propagation vectors. Here, using spectral graph theory, we show that spiral spin liquids on a bipartite lattice can be approximated by a further-neighbor model on the corresponding line-graph lattice that is nonbipartite, thus broadening the space of candidate materials that may support the spiral spin liquid phases. As illustrations, we examine neutron scattering experiments performed on two spinel compounds, ZnCr_{2}Se_{4} and CuInCr_{4}Se_{8}, to demonstrate the feasibility of this new approach and expose its possible limitations in experimental realizations.

Spiral Spin Liquid on a Honeycomb Lattice

Spiral spin liquids are correlated paramagnetic states with degenerate propagation vectors forming a continuous ring or surface in reciprocal space. On the honeycomb lattice, spiral spin liquids present a novel route to realize emergent fracton excitations, quantum spin liquids, and topological spin textures, yet experimental realizations remain elusive. Here, using neutron scattering, we show that a spiral spin liquid is realized in the van der Waals honeycomb magnet FeCl_{3}. A continuous ring of scattering is directly observed, which indicates the emergence of an approximate U(1) symmetry in momentum space. Our work demonstrates that spiral spin liquids can be achieved in two-dimensional systems and provides a promising platform to study the fracton physics in spiral spin liquids.