Breaking of inversion symmetry in $\mathrm{NdGa}{\mathrm{O}}_3$

$\mathrm{NdGa}{\mathrm{O}}_3$ (NGO) is an important substrate material often used in depositing functional oxide thin films. We have carried out temperature-dependent polarized Raman and infrared spectroscopy studies along with theoretical calculations on single-crystal NGO, which revealed a structural phase transition from centrosymmetric space group Pbnm to noncentrosymmetric space group $Pbn{2}_1$ at ∼200 K. The microscopic origin of the phase transition is extracted using a unique protocol involving polarized Raman spectroscopy (PRS) studies carried out as a function of crystallographic orientation. Here, we demonstrate the power of PRS in probing directional atomic rearrangements across the phase transition.

Figure 1

The Raman and IR spectra at 300 K. (a) Raman spectra were collected on a (100)-oriented single crystal in several polarization configurations. (b) and (d) IR spectra collected on (110)- and (100)-oriented single crystals in the reflection mode. The red line represents the curve fitted using the Lorentz oscillator model and the resultant optical conductivities ${\sigma }^{\prime }$ are shown in (c) and (e), respectively.

Figure 2

Temperature-dependent Raman spectra in $bc$ and $cc$ polarization configurations. Stars indicate extra modes appearing below $T_{\mathrm{c}}$.

Figure 3

(a) The Raman spectra collected at various azimuthal angles in the parallel polarization configuration. (b) Schematic representation of the measurement geometry. $abc$ and XYZ represent the crystallographic and laboratory frame of references, respectively. (c)–(e) represent the intensity variations of the specific $A_g$ and $B_{3g}$ modes, respectively, as a function of azimuthal angle $\psi$ in the parallel polarization configuration.

Figure 4

Temperature-dependent IR spectra collected on NGO (100) and (110) single crystals. The red arrow indicates the new IR modes observed below $T_{\mathrm{c}}$. The spectra have been offset for clarity.

Figure 5

(a) Raman spectra in various polarization configurations at 90 K. (b) and (d) give the IR spectra collected on (110)- and (100)-oriented single crystals at 90 K fitted with the Lorentz oscillator model (red line) and the obtained optical conductivity ${\sigma }^{\prime }$ (real) is shown in (c) and (e). The red stars indicate the new modes appearing below $T_{\mathrm{c}}$ and black dots mark the polarization leakage mode. The inset of (c) and (e) gives the magnified view of ${\sigma }^{\prime }$. Color-shaded regions are the new IR modes obtained from the deconvolution of ${\sigma }^{\prime }$.

Figure 6

$T$-dependent Raman shift of new mode $B_2\left(1\right)$.

Figure 7

$T$-dependent PRS study on an NGO (100) single crystal. (a) Schematic of the measurement geometries corresponding to the $bb$ and $cc$ polarization configurations along with the crystallographic axes. $e_i$ and $e_s$ denote the unit vectors representing electric field polarization of the incident and scattered light. $abc$ represents the crystallographic axes. (b)–(g) show the $T$ dependence of FWHM and intensity of some selected modes in two polarization configurations. The red solid curve in (b)–(d) is the anharmonic curve for four phonon decay processes, while the red line in (e)–(g) is the linear fit to the experimental data. The dashed vertical (blue) line marks $T_{\mathrm{c}}$.

Figure 8

Deviation of the Raman mode intensity as a function of temperature of the (a) $A_g\left(4\right)$ and (b) $A_g\left(6\right)$ modes in the $bb$ polarization configuration. The red line represents the linear fitting of the experimental data.

Figure 9

Schematic lattice vibrations of some selected modes. The $A_g\left(4\right)$ mode represents the relative vibration of Nd and O atoms along the $b$ axis. The $A_g\left(6\right)$ mode represents the out-of-phase octahedral bending vibration and the $A_g\left(7\right)$ mode represents the octahedral stretching vibration.

Figure 10

Schematic representation of the octahedral distortion from the Pbnm to $Pbn{2}_1$ structures.