Polarized Raman spectroscopy study of metallic ${\left(\mathrm{S}{\mathrm{r}}_{1\text{−}x}\mathrm{L}{\mathrm{a}}_x\right)}_3\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$: A consistent picture of disorder-interrupted unidirectional charge order

We have used rotational anisotropic polarized Raman spectroscopy to study the symmetries, the temperature, and the doping dependence of the charge ordered state in metallic ${\left(\mathrm{S}{\mathrm{r}}_{1\text{−}x}\mathrm{L}{\mathrm{a}}_x\right)}_3\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$. Despite the fact that the Raman probe size is greater than the charge ordering length, we establish that the charge ordering breaks the fourfold rotational symmetry of the underlying tetragonal crystal lattice into twofold, as well as the translational symmetry, and forms short-range domains with ${90}^{\circ }$ rotated charge order wave vectors, as soon as the charge order sets in below $T_{\mathrm{CO}}=\sim 200\mathrm{K}$ and across the doping-induced insulator metal transition. We observe that this charge order mode frequency remains nearly constant over a wide temperature range and up to the highest doping level. These features above are highly reminiscent of the ubiquitous unidirectional charge order in underdoped high-$T_{\mathrm{C}}$ copper-oxide-based superconductors (cuprates). We further resolve that the charge order damping rate diverges when approaching $T_{\mathrm{CO}}$ from below and increases significantly as increasing the La-doping level, which resembles the behaviors for a disorder-interrupted ordered phase and has not been observed for the charge order in cuprates.

Figure 1

(a) Schematic of the RA polarized Raman spectroscopy experiment. The incident and scattered light propagates along the crystalline $c$ axis, and their polarizations are varied within the $ab$ plane. The polarization of the incident light (solid double arrows) is tuned by a half-wave plate, and the polarization of the scattered light (dashed double arrows) is selected by an analyzer to be either parallel or perpendicular to that of the incident light. The selected scattered polarization is then rotated back to vertical by a half-wave plate before sent into the spectrometer. All these optical components are strain free to minimize the light depolarization. (b) Raman spectra of ${\left(\mathrm{S}{\mathrm{r}}_{1\text{−}x}\mathrm{L}{\mathrm{a}}_x\right)}_3\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7(x=0.075)$ acquired in $aa,a^{\prime }{a}^{\prime },ab$, and $a^{\prime }{b}^{\prime }$ channels at 80 K. The insets indicate the polarization channels and the corresponding selected symmetry modes under $D_{4h}$ point group. The spectra in the low-frequency region is multiplied by a factor of 3 and highlighted in yellow shadow and a dashed vertical line. Black curves are fits to the one-oscillator function. The uncertainty represents $+/-$ one standard error of the fitted frequencies. The shaded profiles in $aa$ and $ab$ channels are Lorentzian fits to the modes marked by the black triangles, and the superposition of these two profiles accounts for the mode near $330\mathrm{c}{\mathrm{m}}^{-1}$ in the $a^{\prime }{a}^{\prime }$ channel.

Figure 2

Polar plots of the fitted peak intensities of the charge order mode as a function of the rotation angle $\phi$ in ${\left(\mathrm{S}{\mathrm{r}}_{1\text{−}x}\mathrm{L}{\mathrm{a}}_x\right)}_3\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7(x=0.075)$ at 80 K in the parallel (top) and perpendicular (bottom) configurations. The RA patterns are fitted to the sum of the Raman intensities from two domains with ${90}^{\circ }$ rotated charge order wave vectors. The solid (empty) petals denote a positive (negative) phase for the scattered electric field. The error bars, $+/-$ one standard error of the fitted peak intensities, are smaller than the symbol sizes and therefore are not visible in the polar plots.

Figure 3

(a) Temperature dependence of the charge order mode in ${\left(\mathrm{S}{\mathrm{r}}_{1\text{−}x}\mathrm{L}{\mathrm{a}}_x\right)}_3\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7(x=0.032)$. The spectra are vertically offset for clarity. The gray dots are raw data and solid curves are fits to the one-oscillator function. (b)–(d) Temperature dependence of the peak intensity $\mathrm{[}I\left({\omega }_0\right)$, red solid circles], the coupling constant $(\kappa$, blue empty squares), the damping rate $(\mathrm{\Gamma }$, black empty circles), and the frequency $({\omega }_0$, black solid squares) of the charge order mode extracted from fits to the one-oscillator function. Red, blue, and black solid curves are fits to $I\left({\omega }_0\right)=I_0\left(T_{\mathrm{CO}}-T\right)$ for the peak intensity, $\kappa ={\kappa }_0{\left(T_{\mathrm{CO}}-T\right)}^{\zeta }$ for the coupling constant, and $\mathrm{\Gamma }={\mathrm{\Gamma }}_0{\left(T_{\mathrm{CO}}-T\right)}^{-1/2}$ for the damping rate, respectively. The error bars are chosen to be $+/-$ one standard error of the fitted parameters.

Figure 4

(a) Raman spectra of the charge order mode at 80 K in ${\left(\mathrm{S}{\mathrm{r}}_{1\text{−}x}\mathrm{L}{\mathrm{a}}_x\right)}_3\mathrm{I}{\mathrm{r}}_2{\mathrm{O}}_7$ with $x=0,0.032,0.065$, and 0.075, respectively. The spectra are acquired without an analyzer and are vertically offset for clarity. (b) Doping dependence of the charge order frequency $({\omega }_0$, red solid circles) and the damping rate $(\mathrm{\Gamma }$, blue empty diamonds) at 80 K. The error bars are set to be $+/-$ one standard error of the fitted parameters.