Multiple quantum phase transitions of different nature in the topological kagome magnet Co3Sn2−xInxS2

The exploration of topological electronic phases that result from strong correlations is a frontier in condensed matter physics. One class systems currently emerging as platform for such studies are so-called kagome magnets based on transition metals. Using muon spin-rotation, we explore magnetic the magnet Co$_{3}$Sn$_{2-x}$In$_{x}$S$_{2}$ function In-doping, providing putative evidence an intriguing incommensurate helimagnetic (HM) state. Our results show that, while undoped sample exhibits out-of-plane ferromagnetic (FM) ground state, at 5 ${\%}$ In-doping system enters state which FM and in-plane antiferromagnetic (AFM) coexist. At higher doping, HM emerges becomes dominant critical doping level only $x_{\rm cr,1}$ ${\simeq}$ 0.3. This indicates zero temperature first order quantum phase FM, through mixed to helical cr,1}$. In addition, cr,2}$ 1, second paramagnetic observed, evidencing point (QCP) diagram Co$_{3}$Sn$_{2-x}$In$_{x}$S$_{2}$. observed diversity interactions lattice drives non-monotonous variations Hall response this system.