Single Ion Anisotropy of $Ln^{3+}$ (Ln = Tb, Dy, Ho) Controls Magnetic Excitations in $LnMn_{6}Sn_{6}$ Ferrimagnetic Kagome Metals

The $LnMn_{6}Sn_{6}$ family of materials, where $Ln^{3+}$ is a lanthanide trivalent cation, have attracted extensive interest due to the interplay of electronic structure, magnetism, and topology present in this family that gives rise to complex electronic and magnetic phenomena. Specifically, the crystal field effects on the lanthanide ion and crystal field splitting of otherwise degenerate energy levels causes dramatic changes in the orbital magnetic behavior and overall magnetic structure of these materials. The coupling of the highly anisotropic lanthanide ions’ spins (with large spin-orbit couplings) to the spins of the Mn atoms, which are arrayed in a kagome lattice, engenders exotic topological phenomena. This combination of magnetic anisotropy and electronic topology motivates investigation into the magnetic excitations of these materials, which unlike the ground state magnetic structures of this family, have not been extensively studied. Herein, we use Brillouin light scattering to measure the magnon spectra of $LnMn_{6}Sn_{6}$ (Ln = Tb, Dy, and Ho). This work represents the first detailed and comparative study on the magnetic dynamics in these materials and reveals that the identity of the lanthanide ion strongly influences the magnon frequency and demonstrates a direct correlation between the lanthanide’s magnetic anisotropy and the observed spin wave excitations. Quantitative analysis indicates that the lanthanide ion’s anisotropy controls the magnon frequency, while its total angular momentum influences the material’s gyromagnetic ratio. These findings suggest that lanthanide substitution provides a pathway for tuning magnon properties in this material family.

💡 Research Summary

This paper presents the first systematic investigation of magnon dynamics in the kagome‑based ferrimagnetic metals LnMn₆Sn₆ (Ln = Tb, Dy, Ho) using Brillouin light scattering (BLS). The authors motivate the study by highlighting the interplay between the highly anisotropic 4f‑derived single‑ion anisotropy (SIA) of the lanthanide ions and the two‑dimensional kagome Mn layers, which together give rise to exotic electronic topology (Dirac/Weyl points, topological surface states) and complex magnetic ground states (easy‑axis for Tb, easy‑cone for Dy and Ho).

Experimental methods: Flux‑grown single crystals of TbMn₆Sn₆, DyMn₆Sn₆, and HoMn₆Sn₆ were examined with a micro‑BLS setup (532 nm laser, 8 mW, ~3 µm spot). The incident and scattered beams were normal to the ab‑plane (parallel to the crystallographic c‑axis). An external magnetic field was applied in the ab‑plane while the BLS spectra were recorded at room temperature and over a temperature range of 253–373 K.

Key results:

1. Magnon frequencies – At zero field and room temperature, a single Stokes/anti‑Stokes magnon appears at ~17.6 GHz for TbMn₆Sn₆, ~22 GHz for DyMn₆Sn₆, and ~20 GHz for HoMn₆Sn₆. Increasing the in‑plane field up to ~200 mT raises the Tb magnon to ~27.9 GHz, following a Kittel‑type field dependence despite the field being orthogonal to the easy‑axis. The authors attribute this to a laser‑induced spin‑reorientation that temporarily aligns the magnetization within the plane during measurement.

2. Single‑ion anisotropy control – The systematic shift of magnon frequencies across the three lanthanides correlates directly with the magnitude of their SIA: Tb³⁺ (strong axial anisotropy) > Dy³⁺ (moderate) > Ho³⁺ (weaker). This demonstrates that SIA of the Ln³⁺ ion sets the magnon stiffness (exchange‑anisotropy term) in the effective spin‑wave Hamiltonian.

3. Gyromagnetic ratio dependence – The slope d f/d H extracted from the field‑dependent data scales with the total angular momentum J of the lanthanide ion (J_Tb = 6, J_Dy = 15/2, J_Ho = 8). The authors propose an effective gyromagnetic ratio γ_eff = γ · (1 + α J), indicating that the lanthanide’s spin‑orbit coupling contributes additively to the overall precessional dynamics.

4. Temperature evolution and spin‑reorientation – Variable‑temperature BLS at zero field shows a gradual red‑shift of the magnon frequency with heating, consistent with reduced saturation magnetization. Below ~263 K the magnon intensity drops sharply and disappears entirely at 253 K, a behavior the authors link to the spin‑reorientation transition (T_SR ≈ 312 K for Tb, 272 K for Dy, 185 K for Ho). They suggest that at low temperature the system reverts to its easy‑axis configuration, suppressing the in‑plane magnon mode, or that temperature‑dependent changes in the complex refractive index broaden the BLS peak beyond detection.

5. Implications for topological magnons – While the study does not directly resolve topological magnon bands, the demonstrated tunability of magnon frequencies via lanthanide substitution provides a practical route to engineer magnonic band gaps and edge modes in kagome‑derived systems. The combination of strong SIA and the intrinsic non‑trivial electronic structure of Mn kagome layers positions LnMn₆Sn₆ as a promising platform for future spintronic and magnonic devices operating in the GHz–THz regime.

The discussion acknowledges experimental limitations: the applied magnetic field never reaches the saturation field, laser heating may unintentionally trigger spin‑reorientation, and the BLS geometry does not resolve wave‑vector‑dependent dispersion. The authors recommend complementary techniques such as inelastic neutron scattering, THz time‑domain spectroscopy, and first‑principles spin‑wave calculations to map the full magnon band structure and confirm the presence of protected topological modes.

In summary, the paper establishes two fundamental relationships in LnMn₆Sn₆ ferrimagnets: (i) the lanthanide’s single‑ion anisotropy dictates the absolute magnon frequency, and (ii) the lanthanide’s total angular momentum governs the gyromagnetic response. These insights open a clear pathway for designing tunable magnonic materials by simple chemical substitution of the Ln³⁺ ion, with potential impact on high‑frequency spintronic technologies and the exploration of topological magnon phenomena.