Emergence of multiple quasi-ferromagnetic magnon modes induced by strong magnetoelastic coupling in $TmFeO_3$ single crystal

We investigate the magnetization dynamics of $TmFeO_3$ single crystals across the spin-reorientation phase transition using broadband microwave absorption spectroscopy up to 87.5 GHz. Temperature- and magnetic-field-dependent antiferromagnetic resonance measurements reveal the characteristic softening of the quasi-ferromagnetic (q-FM) resonance mode at the $Γ_2\rightarrowΓ_{24}$ and $Γ_{24}\rightarrowΓ_4$ transition points. The finite magnon gap observed at the transition points reflects the strong magnetoelastic coupling. In addition to the uniform q-FM mode, multiple magnon modes appear in the intermediate $Γ_{24}$ phase, separated by approximately 0.5–2 GHz and exhibiting similar field and temperature dependence. These additional modes are attributed to nonuniform spin-wave excitations arising from the periodic magnetic domain structure present in the intermediate phase and their hybridization with acoustic phonons mediated by strong magnetoelastic coupling. Our results demonstrate that the spin-reorientation transition in $TmFeO_3$ provides a natural platform for generating multiple hybridized magnon modes, offering new opportunities for tunable magnonic excitations in rare-earth orthoferrites.

💡 Research Summary

In this work the authors investigate the magnetization dynamics of TmFeO₃ single crystals across its spin‑reorientation phase transition (SRPT) using broadband microwave absorption spectroscopy up to 87.5 GHz. Two complementary measurement configurations were employed: a flip‑chip coplanar waveguide (CPW) for frequencies up to 40 GHz and a WR‑12 rectangular waveguide for the 70.5–87.5 GHz range. The external magnetic field was applied along the crystallographic c‑axis while the microwave magnetic field lay in the ab‑plane, ensuring efficient coupling to the quasi‑ferromagnetic (q‑FM) resonance mode. Temperature‑dependent measurements from 80 K to 100 K revealed the characteristic softening of the q‑FM mode at both the Γ₁→Γ₂₄ and Γ₂₄→Γ₄ transition points. Importantly, the mode does not collapse to zero frequency; instead a finite magnon gap of about 9 GHz remains, indicating strong magneto‑elastic coupling that prevents a true Goldstone mode. The critical field H_c for the field‑induced transition decreases linearly with temperature, consistent with theoretical expectations based on the free‑energy model that includes exchange, anisotropy, Dzyaloshinskii‑Moriya, and magneto‑elastic terms.

In the high‑frequency regime, several additional q‑FM resonances appear exclusively within the intermediate Γ₂₄ phase. These modes are spaced by roughly 0.5–2 GHz, share the same temperature and field dependence as the uniform q‑FM mode, and all soften near the SRPT. The authors attribute these extra resonances to non‑uniform spin‑wave excitations (finite‑k magnons) that arise from the periodic magnetic domain structure characteristic of the Γ₂₄ phase. The strong magneto‑elastic interaction hybridizes these magnons with acoustic phonons, producing magnon‑phonon hybrid modes (magnon‑polarons). Numerical simulations based on the Landau‑Lifshitz‑Gilbert equation with an added elastic free‑energy term reproduce the observed mode splitting and the persistence of a finite gap at the transition. The work thus demonstrates that the SRPT in TmFeO₃ provides a natural platform for generating multiple hybridized magnon modes, opening avenues for tunable magnonic excitations in rare‑earth orthoferrites through temperature and magnetic‑field control.