Spin and lattice dynamics at the spin-reorientation transitions in the rare-earth orthoferrite Sm$_{0.55}$Tb$_{0.45}$FeO$_{3}$

TL;DR

This study investigates spin and lattice dynamics at spin-reorientation transitions in the mixed rare-earth orthoferrite Sm$_{0.55}$Tb$_{0.45}$FeO$_3$ using polarized infrared reflectivity and Raman spectroscopy, complemented by first-principles lattice-dynamics calculations. It identifies two spin-reorientation temperatures, $T_{1} \approx 220$ K and $T_{2} \approx 130$ K, between Γ$_4$, Γ$_{24}$, and Γ$_2$ magnetic structures, with an unusually wide intermediate Γ$_{24}$ phase ($\Delta T \approx 90$ K) attributed to inhomogeneous magnetocrystalline anisotropy from Sm/Tb disorder. Raman measurements reveal two magnon modes, qFM ≈ 7 cm$^{-1}$ and qAFM ≈ 18 cm$^{-1}$, whose intensities and frequencies evolve with temperature and magnetic structure; the qFM mode softens but retains a magnetoelastic gap (~6 cm$^{-1}$), while no new Raman-active phonons appear across the transitions. Infrared-active phonons and Raman-active phonons largely follow calculated predictions, with no evidence for spin-phonon coupling or defect-induced phonons at the transitions. The results advance understanding of magnetophononic phenomena in rare-earth orthoferrites and show how compositional disorder can tune spin-reorientation temperatures, informing potential temperature-controlled magnetic devices.

Abstract

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.

Figures (8)

• Figure 1: The crystal and magnetic structures of $\mathrm{Sm}_{0.55}\mathrm{Tb}_{0.45}\mathrm{FeO}_{3}$ in the $Pbnm$ setting in the (a) $\Gamma_{2}$ and (b) $\Gamma_{4}$ magnetic configurations. (c) The precession of weak ferromagnetic moment $\mathbf{M} = \mathbf{M}_{1} + \mathbf{M}_{2}$ for quasi-ferromagnetic (qFM) mode and (d) amplitude oscillation of $\mathbf{M}$ for quasi-antiferromagnetic (qAFM) mode in orthoferrites.
• Figure 2: The infrared reflectivity spectra with the electric field $\mathbf{E}$ of radiation polarized along the (a) $a$, (b) $b$ and $c$ (c) axes of the $\mathrm{Sm}_{0.55}\mathrm{Tb}_{0.45}\mathrm{FeO}_{3}$ at room temperature in the $Pbnm$ setting. The solid black lines are fits using Eq. \ref{['eq:reflectivity']} with a complex dielectric permittivity $\varepsilon = \varepsilon_{1} - i\varepsilon_{2}$ from Eq. \ref{['eq:epsilon_TOLO']}. Spectra of the $\Im[\varepsilon(\omega)]$ and $-\Im[\varepsilon^{-1}(\omega)]$ from fits which correspond to the TO and LO infrared-active phonons with (d), (g) $B_{3u}$, (e), (h) $B_{2u}$, and (f), (i) $B_{1u}$ symmetries, respectively. Vertical dashed gray lines denote the experimental frequencies of infrared-active phonons. Color sticks at the bottom of plots represent the calculated phonon frequencies.
• Figure 3: The polarized Raman spectra of the (a) $A_{g}$, (b) $B_{3g}$, (c) $B_{2g}$, and (d) $B_{1g}$ phonons for $\mathrm{Sm}_{0.55}\mathrm{Tb}_{0.45}\mathrm{FeO}_{3}$ at ambient conditions. The polarization configurations are given in Porto's notation as described in the text in the $Pbnm$ setting. The solid gray lines are fits of the phonons active in the corresponding polarization configuration as described in the text. The frequencies of these phonons are denoted by the vertical dashed lines. Purple sticks at the bottom of each plot represent the calculated phonon frequencies.
• Figure 4: The polarized Raman spectra of the quasi-ferromagnetic (qFM, $\simeq{\pm7}$ cm$^{-1}$) and quasi-antiferromagnetic (qAFM, $\simeq{\pm}18$ cm$^{-1}$) modes in $\mathrm{Sm}_{0.55}\mathrm{Tb}_{0.45}\mathrm{FeO}_{3}$ in $\Gamma_{2}$ (blue shaded area, $T = 78$ K) and $\Gamma_{4}$ (red shaded area, $T = 293$ K) magnetic structures. The polarization configurations are given in Porto's notation as described in the text in the $Pbnm$ setting. The anti-Stokes (AS) and Stokes (S) lines are denoted. The intensity of some spectra is multiplied by a factor denoted by the "$\times$" sign to highlight the weaker excitations.
• Figure 5: The temperature color map of the polarized Raman spectra of quasi-ferromagnetic (qFM, $\simeq{\pm7}$ cm$^{-1}$) and quasi-antiferromagnetic (qAFM, $\simeq{\pm}18$ cm$^{-1}$) modes in $\mathrm{Sm}_{0.55}\mathrm{Tb}_{0.45}\mathrm{FeO}_{3}$ in the $a(bc)\overline{a}$ (left panel) and $c(ab)\overline{c}$ (right panel) polarization configurations which are given in Porto's notation as described in the text in the $Pbnm$ setting. The $\Gamma_{4}$, $\Gamma_{24}$ and $\Gamma_{2}$ magnetic structures are separated by the white dashed lines. The intensity is given on a log scale.