Putative helimagnetic phase in the kagome metal Co₃Sn₂-xIn_xS₂

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