  It has long been speculated that electronic flat band systems can be a
fertile ground for hosting novel emergent phenomena including unconventional
magnetism and superconductivity. Although flat bands are known to exist in a
few systems such as heavy fermion materials and twisted bilayer graphene, their
microscopic roles and underlying mechanisms in generating emergent behavior
remain elusive. Here we use scanning tunneling microscopy to elucidate the
atomically resolved electronic states and their magnetic response in the kagome
magnet Co3Sn2S2. We observe a pronounced peak at the Fermi level, which is
identified to arise from the kinetically frustrated kagome flat band.
Increasing magnetic field up to +-8T, this state exhibits an anomalous
magnetization-polarized Zeeman shift, dominated by an orbital moment in
opposite to the field direction. Such negative magnetism can be understood as
spin-orbit coupling induced quantum phase effects tied to non-trivial flat band
systems. We image the flat band peak, resolve the associated negative
magnetism, and provide its connection to the Berry curvature field, showing
that Co3Sn2S2 is a rare example of kagome magnet where the low energy physics
can be dominated by the spin-orbit coupled flat band. Our methodology of
probing band-resolved ordering phenomena such as spin-orbit magnetism can also
be applied in future experiments to elucidate other exotic phenomena including
flat band superconductivity and anomalous quantum transport.
