Depth-dependent study of time-reversal symmetry-breaking in the kagome superconductor AV₃Sb₅

The breaking of time-reversal symmetry (TRS) in the normal state of kagome superconductors AV₃Sb₅ stands out as a significant feature. Yet the extent to which this effect can be tuned remains uncertain, a crucial aspect to grasp in light of the varying details of TRS breaking observed through different techniques. Here, we employ the unique low-energy muon spin rotation technique combined with local field numerical analysis to study the TRS breaking response as a function of depth from the surface in single crystals of RbV₃Sb₅ with charge order and Cs(V0.86Ta0.14)₃Sb₅ without charge order. In the bulk (i.e., > 33 nm from the surface) of RbV₃Sb₅, we have detected a notable increase in the internal magnetic field width experienced by the muon ensemble. This increase occurs only within the charge ordered state. Intriguingly, the muon spin relaxation rate is significantly enhanced near the surface (i.e., < 33 nm from the surface) of RbV₃Sb₅, and this effect commences at temperatures significantly higher than the onset of charge order. Conversely, in Cs(V0.86Ta0.14)₃Sb₅, we do not observe a similar enhancement in the internal field width, neither in the bulk nor near the surface. These observations indicate a strong connection between charge order and TRS breaking on one hand, and on the other hand, suggest that TRS breaking can occur prior to long-range charge order. This research offers compelling evidence for depth-dependent magnetism in AV₃Sb₅ superconductors in the presence of charge order. Such findings are likely to elucidate the intricate microscopic mechanisms that underpin the TRS breaking phenomena in these materials.