Electrodynamic response of the charge ordering phase: Dielectric and optical studies of $\alpha$-(BEDT-TTF)${}_2$I${}_3$

We report on the anisotropic response, the charge and lattice dynamics of normal and charge ordered phases with horizontal stripes in single crystals of the organic conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ determined by dc resistivity and dielectric and optical spectroscopy. An overdamped Drude response and a small conductivity anisotropy observed in optics is consistent with a weakly temperature-dependent dc conductivity and anisotropy at high temperatures. The splitting of the molecular vibrations ${\nu }_{27}({\mathrm{B}}_u)$ evidences the abrupt onset of static charge order below $T_{\mathrm{CO}}=136$ K. The drop of optical conductivity measured within the $\mathit{ab}$ plane of the crystal is characterized by an isotropic gap that opens at approximately 75 meV with several phonons becoming pronounced below. Conversely, the dc conductivity anisotropy rises steeply, attaining at 50 K a value 25 times larger than at high temperatures. The dielectric response within this plane reveals two broad relaxation modes of strength $\Delta {\varepsilon }_{\mathrm{LD}}\approx 5000$ and $\Delta {\varepsilon }_{\mathrm{SD}}\approx 400$, centered at $1\mathrm{\hspace{0.5em}}\mathrm{kHz}<{\nu }_{\mathrm{LD}}<100$ MHz and ${\nu }_{\mathrm{SD}}\approx 1$ MHz. The anisotropy of the large-mode (LD) mean relaxation time closely follows the temperature behavior of the respective dc conductivity ratio. We argue that this phasonlike excitation is best described as a long-wavelength excitation of a $2k_F$ bond charge density wave expected theoretically for layered quarter-filled electronic systems with horizontal stripes. Conversely, based on the theoretically expected ferroelectriclike nature of the charge ordered phase, we associate the small-mode (SD) relaxation with the motion of domain-wall pairs, created at the interface between two types of domains, along the $a$ and $b$ axes. We also consider other possible theoretical interpretations and discuss their limitations.

Figure 1

(a) Schematic representation of donor layer in $\alpha$-(BEDT-TTF)${}_2$I${}_3$. Molecular sites belonging to stack I and stack II are denoted as A, ${\mathrm{A}}^{\prime }$ and B, C, respectively. (b) Stripe arrangement in the $\mathit{ab}$ conducting donor layer of $\alpha$-(BEDT-TTF)${}_2$I${}_3$ in the charge ordered state. Dark and light gray ovals denote charge-rich and charge-poor molecules, respectively. The stripes extend along the $b$ direction.

Figure 2

Optical properties of $\alpha$-(BEDT-TTF)${}_2$I${}_3$ for different temperatures as indicated. The upper panels (a) and (c) show the reflectivity, and the lower panels (b) and (d) show the corresponding conductivity. Note the different vertical scales. On the left side, (a) and (b) measurements are shown with the electric field polarized parallel to the stacks ($\mathbf{E}\parallel a$); the panels on the right side display the data for the polarization perpendicular to stacks ($\mathbf{E}\parallel b$).

Figure 3

The far-infrared conductivity for (a) $\mathbf{E}\parallel a$ and (b) $\mathbf{E}\parallel b$ for different temperatures above and below the charge order transition at $T_{\mathrm{CO}}=136$ K.

Figure 4

Temperature dependence of the optical conductivity of $\alpha$-(BEDT-TTF)${}_2$I${}_3$ for $T<T_{\mathrm{CO}}$ measured for the polarization (a) $\mathbf{E}\parallel a$ and (b) $\mathbf{E}\parallel b$. In order to illustrate the development of the charge order gap, the phonon lines have been subtracted to some extent. The dashed line shows the linear extrapolation, which gives the optical gap value of about 600 cm${}^{-1}$. Arrows denote the anisotropic dc transport gap.

Figure 5

Development of the spectral weight SW$({\omega }_c)$ as a function of cutoff frequency ${\omega }_c$, calculated by $\mathrm{SW}({\omega }_c)=8{\int }_0^{{\omega }_c}{\sigma }_1(\omega )d\omega ={\omega }_p^2=4\pi n{e}^2/m$ for both directions of $\alpha$-(BEDT-TTF)${}_2$I${}_3$.

Figure 6

Temperature dependence of the intramolecular vibrations of the BEDT-TTF molecule measured for the perpendicular direction $\mathbf{E}\parallel c$. The curves for different temperatures are shifted by 10 $(\Omega \mathrm{cm}){}^{-1}$ for clarity reasons. The ${\nu }_{27}$ mode becomes very strong right at the charge order transition ($T=295$, 210, 160, $136.0$, 135.9, 135.8, $135.7$, 135.6, 135.5, $135.0$, 80, and $10$ K).

Figure 7

Temperature dependence of the intramolecular vibrations ${\nu }_{14}$(A${}_g$) of the BEDT-TTF molecule. The curves for different temperatures are shifted by 10 $(\Omega \mathrm{cm}){}^{-1}$ for clarity reasons. For the polarizations (a) $\mathbf{E}\parallel a$ and (b) $\mathbf{E}\parallel b$, the ${\nu }_{14}$ grows and is split in three distinct peaks ($T=120$, 90, 60, $50$, 40, 30, and $17$ K).

Figure 8

Resistivity (upper panel) and logarithmic resistivity derivative (lower panel) vs inverse temperature of $\alpha$-(BEDT-TTF)${}_2$I${}_3$ for $\mathbf{E}\parallel a$ (red line) and $\mathbf{E}\parallel b$ (blue line).

Figure 9

Logarithmic resistivity derivative (main panel) and resistivity (inset) vs inverse temperature of $\alpha$-(BEDT-TTF)${}_2$I${}_3$ for $\mathbf{E}\parallel [1\overline{1}0]$, i.e., in the diagonal direction of the $\mathit{ab}$ plane.

Figure 10

Double logarithmic plot of the frequency dependence of the real (${\varepsilon }^{\prime }$) and imaginary (${\varepsilon }^{″}$) part of the dielectric function in $\alpha$-(BEDT-TTF)${}_2$I${}_3$ at representative temperatures for $\mathbf{E}\parallel [1\overline{1}0]$. Below 75 K, two dielectric relaxation modes are observed: solid lines for 47 K show a fit to a sum of two generalized Debye functions and dashed lines represent contributions of the two modes. Above 75 K, only one mode is detected, and the solid lines represent fits to single generalized Debye functions.

Figure 11

Dielectric strength (upper panel) and mean relaxation time with dc resistivity (points and line, respectively, lower panel) in $\alpha$-(BEDT-TTF)${}_2$I${}_3$ as a function of inverse temperature for $\mathbf{E}\parallel [1\overline{1}0]$.

Figure 12

Dielectric strength (upper panel) and mean relaxation time (lower panel) in $\alpha$-(BEDT-TTF)${}_2$I${}_3$ as a function of inverse temperature; solid and open symbols represent parameters of the large and small dielectric mode, respectively, for $\mathbf{E}$ along the $a$ (red circles) and $b$ axes (blue triangles). Compared to Fig. 11, the relatively large error bars are due to a somewhat unfavorable sample geometry, which results in higher resistances and a smaller capacitive response.

Figure 13

Anisotropy of the large-dielectric-mode mean-relaxation time (points) closely follows the temperature behavior of dc conductivity anisotropy (line) in $\alpha$-(BEDT-TTF)${}_2$I${}_3$.

Figure 14

Broad-band conductivity spectra of $\alpha$-(BEDT-TTF)${}_2$I${}_3$ for (a) $\mathbf{E}\parallel a$ and (b) $\mathbf{E}\parallel b$ at a few selected temperatures. Vertical arrows show the CO optical gap. The dashed lines are guides for the eye.

Figure 15

Schematic representation of a $2k_F$ bond CDW in $\alpha$-(BEDT-TTF)${}_2$I${}_3$. Triple, double, single, and dashed lines show relative strengths of overlap integrals, from strongest to weakest, along $p_1$ and $p_2$ directions (Ref. 25). Also denoted are dimerized bonds along the $a$ axis in the AA${}^{\prime }$ and BC stacks.

Figure 16

Two different types of domain wall pairs in the charge ordered phase of $\alpha$-(BEDT-TTF)${}_2$I${}_3$. (A,B)- and (A${}^{\prime }$,B)-rich unit cells are symbolically represented as $+/-$ or $-/+$ cells, which form CO stripes. For simplicity, we omit the B and C molecules. Gray thick lines stand for charge-rich stripes. Thin black lines denote a domain-wall pair.