  The quantum level interplay between geometry, topology, and correlation is at
the forefront of fundamental physics. Owing to the unusual lattice geometry and
breaking of time-reversal symmetry, kagome magnets are predicted to support
intrinsic Chern quantum phases. However, quantum materials hosting ideal
spin-orbit coupled kagome lattices with strong out-of-plane magnetization have
been lacking. Here we use scanning tunneling microscopy to discover a new
topological kagome magnet TbMn6Sn6, which is close to satisfying the above
criteria. We visualize its effectively defect-free purely Mn-based
ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic
state exhibits distinct Landau quantization upon the application of a magnetic
field, and the quantized Landau fan structure features spin-polarized Dirac
dispersion with a large Chern gap. We further demonstrate the bulk-boundary
correspondence between the Chern gap and topological edge state, as well as the
Berry curvature field correspondence of Chern gapped Dirac fermions. Our
results point to the realization of a quantum-limit Chern phase in TbMn6Sn6,
opening up an avenue for discovering topological quantum phenomena in the
RMn6Sn6 (R = rare earth element) family with a variety of magnetic structures.
Our visualization of the magnetic bulk-boundary-Berry correspondence covering
real and momentum space demonstrates a proof-of-principle method revealing
topological magnets.
