Competing Magnetic Energy Scales in the Topological Ferrimagnet TbMn₆Sn₆

TbMn₆Sn₆ is a metallic ferrimagnet displaying signatures of topological electrons and topological magnons arising from ferromagnetism and spin-orbit coupling within the Mn kagome layers. We present inelastic neutron scattering data showing strong ferromagnetic (FM) interactions within a Mn 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 nearest-neighbor interlayer exchange, as well as weaker and competing longer range FM and AFM Mn-Mn interlayer exchange similar to those driving helical AFM order in YMn₆Sn₆. When these measurements are 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. This results in magnetic instabilities and tunability when Mn-R interactions are weak. In the case of TbMn₆Sn₆, the strong AFM Mn-Tb coupling ensures a highly stable three-dimensional ferrimagnet.