Comparison of the charge-crystal and charge-glass state in geometrically frustrated organic conductors studied by fluctuation spectroscopy

We present a systematic investigation of the low-frequency charge carrier dynamics in different charge states of the organic conductors $\theta \text{−}(\mathrm{BEDT}\text{−}{\mathrm{TTF})}_{2}M\mathrm{Zn}{\left(\mathrm{SCN}\right)}_4$ with $M=\text{Rb,}\text{Tl}$, which result from quenching or relaxing the charge degrees of freedom on a geometrically frustrated triangular lattice. Due to strong electronic correlations these materials exhibit a charge-ordering transition, which can be kinetically avoided by rapid cooling resulting in a so-called charge-glass state without long-range order. The combination of fluctuation spectroscopy and a heat pulse method allows us to study and compare the resistance fluctuations in the low-resistive quenched and the high-resistive charge-ordered state, revealing striking differences in the respective noise magnitudes. For both compounds, we find strongly enhanced resistance fluctuations right at the metal-insulator transition and a broad noise maximum in the slowly cooled charge-crystal state with partly dominating two-level processes revealing characteristic activation energies.

Figure 1

Different setups for fluctuation spectroscopy: (a) Two-point DC setup ($◯$) for measurements of current (conductance) fluctuations in high-impedance samples, (b) four-point DC setup ($\square$), and (c) four-point AC setup ($▵$) for measurements of voltage (resistance) fluctuations in more conductive samples. The fluctuating signal in each case is fed into a signal analyzer (SR785) to obtain the noise power spectral density (PSD). The data symbols shown in the figures below indicate which setup has been used.

Figure 2

(a) Typical noise spectra either of $1/f$-type or superimposed with a Lorentzian contribution for selected temperatures in ${\theta }_o\text{−}\mathrm{RbZn}$ (sample #1). (b) Comparison of the single and distributed Lorentzian model, where the latter can better reproduce the line width of the measured spectrum.

Figure 3

(a) Resistance, (b) normalized current or voltage noise PSD, and (c) frequency exponent $\alpha$ of the $1/f^{\alpha }$-noise contribution vs temperature of ${\theta }_o\text{−}\mathrm{RbZn}$ (sample #1) for the slow- and fast-cooled state. Only the first term of Eq. (1) is evaluated here. The shaded areas mark the regions where additional, superimposed Lorentzian spectra emerge, see also Fig. 6 below. Different symbols mark different measurement techniques (see Experiment).

Figure 4

Power-law exponents of the (a) nonlinear $IV$ curves and of the (b) noise PSD in dependence of the current, $dln\left(S_I\right)/dln\left(I\right)$, of ${\theta }_o\text{−}\mathrm{RbZn}$ (sample #1). The dashed lines indicate ohmic behavior and quadratic current dependence of the noise, which is valid above the charge-ordering transition. Insets show the $IV$ curves (upper inset) and the current-dependent PSDs (lower inset) in a double-logarithmic plot at $T=80\mathrm{K}$ for the slow- (red) and fast-cooled state (green).

Figure 5

(a) Normalized PSD taken at $1\mathrm{Hz}$ vs temperature for different currents of ${\theta }_o\text{−}\mathrm{RbZn}$ (sample #1). Dark symbols indicate the values for the maximum current or voltage, transparent symbols represent the values for smaller currents and voltages. (b) Spectra for different currents are exemplarily shown for $T=85\mathrm{K}$.

Figure 6

(a) Examples of Lorentzian contribution superimposed on the $1/f$ spectra in the temperature region 125–205 K measured in the CC state of ${\theta }_o\text{−}\mathrm{RbZn}$. (b) $f_{\text{c}1}$ and $f_{\text{c}2}$ stands for the high- and low-frequency cutoffs, $f_0=\sqrt{f_{\text{c}1}{f}_{\text{c}2}}$ for the center frequency. (c) Extracted energies from the center frequency and (d) line width of the distributed Lorentzian contribution.

Figure 7

(a) Resistance and (b) normalized PSD taken at $1\mathrm{Hz}$ of ${\theta }_o\text{−}\mathrm{RbZn}$ (sample #2) for the slow- and fast-cooled state, which was generated by using a heat pulse.

Figure 8

(a) Resistance, (b) normalized PSD, and (c) frequency exponent of the $1/f$ spectra measured on ${\theta }_m\text{−}\mathrm{TlZn}$ for the slow- (red) and fast-cooled state (green). The symbols mark different measurement techniques for fluctuation spectroscopy.

Figure 9

Molecular arrangement of the orthorhombic (left) and monoclinic (right) $\theta \text{−}{\left(\mathrm{ET}\right)}_{2}M{M}^{\prime }{\left(\mathrm{SCN}\right)}_4$ within the conducting layers viewed along different crystallographic axes.

Figure 10

Simple model for the thermal conductance in the heat pulse technique after Ref. [21]. The cold heat bath with constant temperature $T_{\text{bath}}$ is indicated by the lower rectangle, whereas the sample with temperature $T_{\text{s}}$ and specific heat $C$ corresponds to the smaller rectangle. The Joule heat $P$ (orange) is deposited by a large current flowing through the sample with resistance $R$.

Figure 11

Logarithmic resistance of ${\theta }_o\text{−}\mathrm{RbZn}$ (sample #1) against the inverse temperature of the slow- (red) and fast-cooled (green) state.

Figure 12

Logarithmic resistance of ${\theta }_o\text{−}\mathrm{RbZn}$ (sample #2) against the inverse temperature of the slow- (red) and fast-cooled (green) state after the application of a heat pulse.

Figure 13

Power-law exponents of the PSD in dependence of the current, $dln\left(S_I\right)/dln\left(I\right)$, (filled circles) as well as in dependence of the voltage, $dln\left(S_I\right)/dln\left(V\right)$ (empty circles), for the slow- (red) and fast-cooled state (green). The red and green dashed lines are the calculates values according to $c=2/b$ assuming the Hooge law under consideration of nonlinear $IV$ curves.