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 sub-dimensional 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 non-bipartite, 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.