Spin and lattice dynamics at the spin-reorientation transitions in the rare-earth orthoferrite Sm$_{0.55}$Tb$_{0.45}$FeO$_{3}$
Linear and non-linear couplings of magnetic and lattice excitations are at the heart of many fascinating magnetophononic phenomena observed in rare-earth orthoferrites, the distinctive feature of which is the tendency to spin-reorientation transitions. Here we report the results of the experimental study of the spin and lattice dynamics in the Brillouin zone center of the rare-earth orthoferrite Sm$_{0.55}$Tb$_{0.45}$FeO$_{3}$ by using polarized infrared reflectivity and Raman scattering spectroscopic techniques. The obtained results were supported by the first-principles calculations, which allowed us to reliably identify the parameters of most infrared- and Raman-active phonons. We reveal the spin-reorientation transitions $Γ_{4}(G_{a}F_{c}) \overset{T_{1}}\longleftrightarrow Γ_{24}(G_{ac}F_{ac}) \overset{T_{2}}\longleftrightarrow Γ_{2}(G_{c}F_{a})$ at $T_{1} \simeq 220$ K and $T_{2} \simeq 130$ K and carefully studied the following evolution of Raman scattering on magnetic excitations at these transitions. Notably, the intermediate magnetic structure $Γ_{24}$ displays an exceptionally broad temperature range $Δ{T} = T_{1} - T_{2} \simeq 90$ K in mixed Sm$_{0.55}$Tb$_{0.45}$FeO$_{3}$ compared to pure rare-earth orthoferrites. We attribute this broadening of the intermediate phase to the modification of the magnetocrystalline anisotropy as a result of the inhomogeneous magnetic structure caused by the random distribution of rare-earth $\mathrm{Sm}^{3+}$ and $\mathrm{Tb}^{3+}$ ions. We found neither change in the parameters of Raman-active $B_{1g}$ phonons nor the appearance of new phonons induced by spin-reorientation transitions, which have been reported in $\mathrm{SmFeO}_{3}$. We assume that our results provide a solid basis for more deeper understanding of magnetophononic phenomena in rare-earth orthoferrites.