Proposal to use neutron scattering to access scalar spin chirality fluctuations in kagome lattices

In the theory of quantum spin liquid, gauge fluctuation is an emergent excitation at low energy. The gauge magnetic field is proportional to the scalar spin chirality ${\mathit{S}}_1·{\mathit{S}}_2\times {\mathit{S}}_3$. It is therefore highly desirable to measure the fluctuation spectrum of the scalar spin chirality. We show that in the Kagome lattice with a Dzyaloshinskii-Moriya term, the fluctuation in $S_z$, which is readily measured by neutron scattering, contains a piece which is proportional to the chirality fluctuation.

Figure 1

DM vectors on the Kagome lattice for herbertsmithite. The arrow specifies the order of the operator ${\mathit{S}}_i\times {\mathit{S}}_{\mathbf{j}}$ (adapted from Ref. 11). $D_z$ is the $z$ component, while $D^{\prime }$ is the in-plane component.

Figure 2

Distortion of the Ir (solid) and oxygen (open) ions in the Ir-O plane of Sr${}_2$IrO${}_4$. Adapted from Ref. 24.