  Magnetic topological phases of quantum matter are an emerging frontier in
physics and material science. Along these lines, several kagome magnets have
appeared as the most promising platforms. Here, we explore magnetic
correlations in the transition-metal-based kagome magnet TbMn$_{6}$Sn$_{6}$.
Our results show that the system exhibits an out-of-plane ferrimagnetic
structure $P6/mm'm'$ (comprised by Tb and Mn moments) with slow magnetic
fluctuations in a wide temperature range. These fluctuations exhibit a slowing
down below $T_{\rm C1}^{*}$ ${\simeq}$ 120 K and a slightly modified
quasi-static magnetic state is established below $T_{\rm C1}$ ${\simeq}$ 20 K.
A canted variation of the $P6/mm'm'$ structure is possible, where all moments
contribute to a net $c$-axis ferrimagnetic state which exhibits zero net
in-plane components. Alternatively, a small incommensurate $k$-vector could
arise below $T_{\rm C1}$. We further show that the temperature evolution of the
anomalous Hall conductivity (AHC) is strongly influenced by the low temperature
magnetic crossover. More importantly, the here identified magnetic state seems
to be responsible for the large quasi-linear magnetoresistance as well as for
the appearance of quantum oscillations, which are related to the quantized
Landau fan structure featuring a spin-polarized Dirac dispersion with a large
Chern gap. Therefore the exciting perspective of a magnetic system arises in
which the topological response can be controlled, and thus explored, over a
wide range of parameters.
