  TbMn6Sn6 is a metallic ferrimagnet displaying signatures of both topological
electrons and topological magnons arising from ferromagnetism and spin-orbit
coupling within its Mn kagome layers. Inelastic neutron scattering measurements
find strong ferromagnetic (FM) interactions within the Mn kagome layer and
reveal a magnetic bandwidth of ~230 meV. The low-energy magnetic excitations
are characterized by strong FM Mn-Mn and antiferromagnetic (AFM) Mn-Tb
interlayer magnetic couplings. We observe weaker, competing long-range FM and
AFM Mn-Mn interlayer interactions similar to those driving helical magnetism in
the YMn6Sn6 system. Combined with density-functional theory calculations, we
find that competing Mn-Mn interlayer magnetic interactions occur in all RMn6Sn6
compounds with R= Y, Gd-Lu, resulting in magnetic instabilities and tunability
when Mn-R interactions are weak. In the case of TbMn6Sn6, strong AFM Mn-Tb
coupling ensures a highly stable three-dimensional ferrimagnetic network.
