Fig. 2.

DSSF of different quantum phases on the KAFM. (A–C) Contour plots of the DSSF as a function of energy and momentum for (A) $q=\left(\mathrm{0,0}\right)$ phase at $J_2=0.25,J_3=0.0$; (B) CSL at $J_2=0.5,J_3=0.5$; and (C) KSL at $J_2=J_3=0$. The white (black) dashed line in C shows the constant-energy values at the low-frequency (high-frequency) region, which are compared with the INS observations in herbertsmithite (Fig. 4 has details). (D–F) The energy scans of the DSSF with the momentum along the path $\mathrm{\Gamma }\to M_1\to K_1\to M_2$ in the extended BZ. The intensity scales differ among the different panels. D, Inset shows the extended BZ with denoted high-symmetry momentum points and reciprocal vectors (${\overrightarrow{b}}_{\mathrm{1,2}}$).