Competing magnetic energy scales in the topological flat-band ferrimagnet TbMn6Sn6

TbMn6Sn6 is a metallic ferrimagnet displaying signatures of Weyl-semimetallic behavior and topological magnons arising from flat-band magnetism 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 (AF) Mn-Tb interlayer magnetic couplings. We observe weaker, competing long-range FM and AF 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 AF Mn-Tb coupling ensures a highly stable three-dimensional ferrimagnetic network.