Franck-Condon higher order lattice excitations in the $\mathrm{La}{\mathrm{Fe}}_{1-x}{\mathrm{Cr}}_x{\mathrm{O}}_3$ ($x=0$, 0.1, 0.5, 0.9, 1.0) perovskites due to Fe-Cr charge transfer effects

First and higher order lattice excitations in the $B$-site disordered perovskites $\mathrm{La}{\mathrm{Fe}}_{1-x}{\mathrm{Cr}}_x{\mathrm{O}}_3$ ($x=0$, 0.1, 0.5, 0.9, and 1) and ${\mathrm{La}}_{0.835}{\mathrm{Sr}}_{0.165}{\mathrm{Fe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_{3-\delta }$ are investigated using temperature dependent and polarized inelastic light scattering [$\lambda =515\mathrm{nm}$ $\left(2.41\mathrm{eV}\right)$ and $676\mathrm{nm}$ $\left(1.83\mathrm{eV}\right)$] on oriented crystallites. A peak at approximately $2.4\mathrm{eV}$ in the imaginary part of the dielectric function of $\mathrm{La}{\mathrm{Fe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ is assigned to a charge transfer from ${\mathrm{Fe}}^{3+}$ $\left(d^5\right)$ to ${\mathrm{Cr}}^{3+}$ $\left(d^3\right)$ ions, coupled with the appearance of an intense $A_g$-like mode at approximately $700{\mathrm{cm}}^{-1}$ in the Raman data. This excitation is identified as a symmetric oxygen breathing mode activated by the Fe-Cr charge transfer through an orbital coupling mechanism. Higher order scattering (up to seventh order) of the intrinsic Raman active symmetric breathing mode is also explained by an orbital-mediated electron-phonon coupling, similar to the Franck-Condon effect observed in the Jahn-Teller active-perovskite-structured manganite $\mathrm{La}\mathrm{Ma}{\mathrm{O}}_3$. These results show that the Franck-Condon mechanism is a more common mechanism for resonant higher order scattering in solids than previously believed and propose the $\mathrm{La}{\mathrm{Fe}}_{1-x}{\mathrm{Cr}}_x{\mathrm{O}}_3$ system as a model system for electron-phonon coupling and higher order Raman scattering in solids.

Figure 1

Crystal axes and polarization directions of an oriented ideal perovskite $ac$ plane. Straight edges in as-grown samples run along the $a$ and $c$ crystal axes due to strong $B–\mathrm{O}$ bonds and are used for orientation. The white areas represent the oxygen octahedra in the $ac$ planes. (Note that the $A$ sites are not in the same plane as the $B$ and O sites).

Figure 2

The dielectric function $\epsilon ={\epsilon }_1+i{\epsilon }_2$ at room temperature as a function of excitation energy. The imaginary part $\left({\epsilon }_2\right)$ displays a clear peak at approximately $2.4\mathrm{eV}$. The measurements were made on a polished sample of $\mathrm{La}{\mathrm{Fe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$.

Figure 3

Raman spectra of the isostructural compounds $\mathrm{La}{\mathrm{Fe}}_{1-x}{\mathrm{Cr}}_x{\mathrm{O}}_6$. Considerable higher order scattering appears in the compounds with both Fe and Cr present. Higher energy bands in the $x=0$ and $x=1$ compounds are believed to be of magnetic origin. Samples $x=0.9$ and $x=1$ are unoriented powders. The inset shows the low-energy region for $x=0$, 0.5, and 0.9 using $\lambda =515\mathrm{nm}$ and $x=0.5$ using $\lambda =676\mathrm{nm}$.

Figure 4

First and higher order excitations in the compound $\mathrm{La}{\mathrm{Fe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ for temperatures $T=300$, 150, and $60\mathrm{K}$. The inset shows the sixth, seventh, and a possible eighth order of the $700{\mathrm{cm}}^{-1}$ peak at $T=80\mathrm{K}$. Both the main figure and the inset show data collected using the $\lambda =515\mathrm{nm}$ excitation wavelength and parallel $x^{\prime }{x}^{\prime }∕z^{\prime }{z}^{\prime }$ scattering configuration.

Figure 5

Top shows the intensity ratio $I_N∕I_1$ in $\mathrm{La}{\mathrm{Fe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ of the higher order excitations $N$ at $T=300$, 180, and $60\mathrm{K}$ in parallel scattering configuration and at $T=60\mathrm{K}$ in cross-polarized scattering configuration. Bottom shows the temperature dependence of the ratio between the second and first order excitation and the temperature dependence of the intensity of the principal excitation $(N=1)$ compared to its maximum value at $60\mathrm{K}$ in $\mathrm{La}{\mathrm{Fe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$. Error bars indicate errors associated with fitting the peaks to Lorentzian profiles.

Figure 6

Polarization dependence of the Raman spectra at $T=60\mathrm{K}$ of the compound $\mathrm{La}{\mathrm{Fe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ for parallel $x^{\prime }{x}^{\prime }∕z^{\prime }{z}^{\prime }$ and cross-polarized $x^{\prime }{z}^{\prime }∕z^{\prime }{x}^{\prime }$ scattering configurations using $\lambda =515\mathrm{nm}$. The intensities of the higher orders in cross polarization approach those of parallel scattering configuration. Note, in particular, that the spectra in the inset are shown without offset.

Figure 7

First and second order excitations in $\mathrm{La}{\mathrm{Fe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_3$ using $\lambda =515\mathrm{nm}$ and $\lambda =676\mathrm{nm}$ and the Sr-substituted compound ${\mathrm{La}}_{0.835}{\mathrm{Sr}}_{0.165}{\mathrm{Fe}}_{0.5}{\mathrm{Cr}}_{0.5}{\mathrm{O}}_{3-\delta }$ using $\lambda =515\mathrm{nm}$. The inset shows the decrease in second order scattering compared with first order scattering when changing the laser energy from 2.41 $(\lambda =515\mathrm{nm})$ to $1.83\mathrm{eV}$ $(\lambda =676\mathrm{nm})$. The first order scattering using $\lambda =676\mathrm{nm}$ is normalized to the first order scattering using $\lambda =515\mathrm{nm}$ through a multiplication of the scattering intensity by a factor of 2.

Figure 8

A CT with an activation energy of $2.4\mathrm{eV}$ moves an electron from the Fe to the Cr ion. This leaves both the Fe and the Cr in the strongly coupling $d^4$ configuration with half-filled $e_g$ bands causing a self-trapping mechanism of the oxygen octahedra $\left(\Delta q_n\right)$. For the FC effect to be present for a vibrational mode with a normal coordinate $q_n$, the FC factor given by the overlap integral $⟨{\nu }_{0,f}\mid {\nu }_r⟩⟨{\nu }_r\mid {\nu }_{0,i}⟩$ must be nonzero. Here, the virtual state $\mid {\nu }_r⟩$ of the Raman process must coincide with some vibrational state of the electronically excited state $\mid {\nu }_{e,n}⟩$. The initial and final vibrational states of the Raman process ($\mid {\nu }_{0,i}⟩$ and $\mid {\nu }_{0,f}⟩$) are both in the electronic ground state.