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Magnetic topological phases of quantum matter are an emerging frontier in physics and material science [1-6], of which kagome magnets appear as a highly promising platform. Here, we explore magnetic correlations in the recently identified topological kagome system TbMn$_{6}$Sn$_{6}$ using $\mu$SR, combined with local field analysis and neutron diffraction [1,4]. Our studies identify an out-of-plane ferrimagnetic structure with slow magnetic fluctuations which exhibit a critical slowing down below T$^{*}_{C1}\simeq$ 120 K and finally freeze into static patches with ideal out-of-plane order below T$_{C1}\simeq$ 20 K. The appearance of the static patches sets in at a similar temperature as the appearance of topological transport behaviors. We further show that a hydrostatic pressure of 2.1 GPa stabilizes the static out-of-plane topological ferrimagnetic ground state in the whole volume of the sample. Therefore the exciting perspective arises of a magnetically-induced topological system whose magnetism can be controlled through external control parameters. The present results [4] will stimulate theoretical investigations to obtain a microscopic understanding of the relation between the low-temperature volume-wise magnetic evolution of the static $c$-axis ferrimagnetic patches and the topological electronic properties in TbMn$_{6}$Sn$_{6}$.
[1] J.-X. Yin et al., Nature $\textbf{583}$, 533-536 (2020).
[2] Z. Guguchia et al., Nature Comm. $\textbf{11}$, 559 (2020).
[3] N.J. Ghimire and I.I. Mazin, Nature Materials $\textbf{19}$, 137-138 (2020).
[4] C. Mielke III et al., arXiv:2101.05763 (2021).
[5] C. Mielke III et al., Phys. Rev. Materials $\textbf{5}$, 034803 (2021).
[6] C. Mielke III et al. … Z. Guguchia, Nature $\textbf{602}$, 245-250 (2022).
