Line-Graph Approach to Spiral Spin Liquids

TL;DR

This paper introduces a novel graph-theoretic approach to understanding spiral spin liquids on bipartite lattices, linking them to line-graph models, and validates the method with neutron scattering data from specific compounds.

Contribution

It proposes a new spectral graph theory method to approximate spiral spin liquids using line-graph models, expanding the range of potential materials supporting these phases.

Findings

Line-graph models can approximate spiral spin liquids on bipartite lattices.

Neutron scattering data from ZnCr₂Se₄ and CuInCr₄Se₈ support the approach.

The method reveals potential limitations in experimental realizations.

Abstract

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.