Raman signatures of charge ordering in ${\text{K}}_{0.3}{\text{WO}}_3$

We present polarization- and temperature-dependent Raman spectroscopic study of hexagonal tungsten bronze, ${\text{K}}_{0.3}{\text{WO}}_3$. The observed asymmetry in phonon line shapes indicate the presence of strong lattice anharmonicity arising due to the nonstoichiometry of the material. We observed a broad multipeak Raman feature at low frequency due to the local modes of K atoms known as local structural excitations. The observed vibrational features indicate a second-order phase transition around $T=200\text{K}$ accompanied by a frequency softening of low-frequency phonon modes. The observed phonon anomalies hint a physical picture involving a continuous symmetry change toward a charge-ordered state below 200 K. These observations indicate that ${\text{K}}_{0.3}{\text{WO}}_3$ may exhibit a weak charge-density-wave ground state at low temperatures.

Figure 1

Raman spectra at 275 and 30 K for (cc) configuration in panel (a) and for (aa) in panel (b). The spectra are normalized by their respective Boltzman factors, $1/\left[1+n\right]$, where $n\left(\omega ,T\right)=1/\left(1+e^{\left(\hslash \omega /k_{b}T\right)}\right)$.

Figure 2

Temperature-dependent Raman spectra of ${\text{K}}_{0.3}{\text{WO}}_3$ in (cc). The spectra are vertically shifted for clarity. The modes indicated by arrows tend to vanish around $T=200\text{K}$, indicating a second-order transition.

Figure 3

Temperature-dependent low-frequency Raman spectra of ${\text{K}}_{0.3}{\text{WO}}_3$ in (cc). Left panel shows the unscaled Raman spectra and the right panel shows the Raman spectra divided by their respective Boltzman factors, $1/\left[1+n\right]$, where $n\left(\omega ,T\right)=1/\left(1+e^{\left(\hslash \omega /k_{B}T\right)}\right)$. The dashed vertical arrow indicates new mode coming up at $35{\text{cm}}^{-1}$ between $T=70$ and 100 K.

Figure 4

Temperature-dependent frequency and linewidth of 60 and $35{\text{cm}}^{-1}$ phonon modes. The vertical arrow indicates the temperature above which the frequency of the modes start to harden slightly.

Figure 5

The top three panels show temperature dependence of the line shape of low-frequency ${\text{A}}_g$ band. The symbols represent experimental data and solid lines represent fit to a sum of Lorentzian functions. The relative intensities of 35 and $60{\text{cm}}^{-1}$ phonon modes reverse order with temperature. The bottom panel shows the temperature-dependent intensity ratio, $R$, of 35 and $60{\text{cm}}^{-1}$ modes. See text for details.

Figure 6

Left panel: the temperature-dependent frequency (left panel) and the anomalous integrated intensity (right panel) of $97{\text{cm}}^{-1}$.

Figure 7

Top panel: the temperature-dependent Raman spectra of the octahedral modes in (cc) showing the frequency softening (the spectra are vertically shifted for clarity). The temperature-dependent frequency softening and line-width broadening (bottom panels) indicate a second-order phase transition taking place near 200 K.

Figure 8

Temperature-dependent intensities of some phonon modes (as indicated in Fig. 2) showing that the modes vanish around 200 K.