Lanthanide Ion Electronic Structure Controls Magnetic Excitations in Topological Quantum Ferrimagnets LnMn₆Sn₆ (Ln = Tb, Dy, Ho)

The $LnMn_{6}Sn_{6}$ family of topological magnets is a promising platform for next-generation spintronic and magnonic technologies. However, the influence of the lanthanide ion ($Ln^{3+}$) on the excited-state spin dynamics, or magnons, remains a critical knowledge gap. Here, we present the first comparative study of the magnetic dynamics in $LnMn_{6}Sn_{6}$ materials (Ln = Tb, Dy, Ho) using Brillouin light scattering. Our findings reveal a direct correlation between the lanthanide ion's intrinsic properties and the magnon behavior. We demonstrate that the magnon frequency in the absence of an applied magnetic field is primarily dictated by the strength of the lanthanide exchange coupling, as modeled by its relationship with the de Gennes factor. The response of the magnon to an applied field is influenced by material's gyromagnetic ratio and the overall anisotropy of the material, which are dictated by total angular momentum and the anisotropy of the lanthanide sublattice, respectively. These results establish that simple lanthanide substitution provides a powerful and predictable method for tuning magnon properties, enabling the rational design of materials for advanced technological applications.