Raman spectroscopy of rare-earth orthoferrites $R{\mathrm{FeO}}_3$ ($R$=La, Sm, Eu, Gd, Tb, Dy)

We report a Raman scattering study of six rare-earth orthoferrites $R{\mathrm{FeO}}_3$, with $R$ = La, Sm, Eu, Gd, Tb, Dy. The use of extensive polarized Raman scattering of ${\mathrm{SmFeO}}_3$ and first-principles calculations enable the assignment of the observed phonon modes to vibrational symmetries and atomic displacements. The assignment of the spectra and their comparison throughout the whole series allow correlating the phonon modes with the orthorhombic structural distortions of $R{\mathrm{FeO}}_3$ perovskites. In particular, the positions of two specific $A{}_g$ modes scale linearly with the two ${\mathrm{FeO}}_6$ octahedra tilt angles, allowing the distortion to be tracked throughout the series. At variance with literature, we find that the two octahedra tilt angles scale differently with the vibration frequencies of their respective $A{}_g$ modes. This behavior, as well as the general relations between the tilt angles, the frequencies of the associated modes, and the ionic radii are rationalized in a simple Landau model. The reported Raman spectra and associated phonon-mode assignment provide reference data for structural investigations of the whole series of orthoferrites.

Figure 1

Variation of the pseudocubic cell parameters and orthorhombic unit-cell volume as a function of the $R_{\mathrm{VIII}}^{3+}$ ionic radius [37]. The lattice parameters are taken from Refs. [38, 39].

Figure 2

Raman spectra at 80 K of six rare-earth orthoferrites $R{\mathrm{FeO}}_3$ ($R$ = La, Sm, Eu, Gd, Tb, Dy).

Figure 3

Polarized Raman spectra of ${\mathrm{SmFeO}}_3$ at ambient conditions. The measurement configurations are given in Porto's notation, in (a) for the vibration modes of $A_g$ symmetry and in (b) for the vibration modes of $B_{1g}$, $B_{2g}$, and $B_{3g}$ symmetries. $X, Y$, and $Z$ correspond to the orthorhombic axes in the Pnma space group.

Figure 4

Raman phonon wave numbers of $R{\mathrm{FeO}}_3$ as a function of the rare earth $R^{3+}$ ionic radius. All lines are guides to the eye only.

Figure 5

$R{\mathrm{FeO}}_3$ soft-mode wave numbers at ambient conditions as a function of octahedratilt angles for the $A_g$(3) and $A_g$(5) modes. Data from this work are complemented by literature data for ${\mathrm{NdFeO}}_3$ [50], ${\mathrm{HoFeO}}_3$ and ${\mathrm{TmFeO}}_3$ [48], ${\mathrm{ErFeO}}_3$ [49], and ${\mathrm{LuFeO}}_3$ [47]. The oval and the open symbols point out the mode mixing region of the $A_g$(2) and $A_g$(3) modes for ${\mathrm{LaFeO}}_3$, as discussed in the text.