Fig. 5.

DSSF of the KSL when including the DM interactions. (A) Phase diagram of the KAFM when including second nearest neighbor coupling $J_2$ and out-of-plane DM interaction $D^z$. The black square represents the KAFM with nearest neighbor couplings. The red star line shows the possible parameter regime for herbertsmithite (43, 44). (B) Spin gap for various $D^z$ under periodic (blue squares) and antiperiodic (purple circles) BC. The DSSF of the KSL phase at $J_2=0,D^z=0.06$ under (C) periodic BC and (D) antiperiodic BC for the longitudinal mode (purple dashed line) and the transverse mode (blue line).