Absence of charge order in the dimerized $\kappa$-phase BEDT-TTF salts

Utilizing infrared vibrational spectroscopy we have investigated dimerized two-dimensional organic salts in order to search for possible charge redistribution that might constitute electronic dipoles and ferroelectricity: the quantum spin liquid $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$ [BEDT-TTF: bis-(ethylenedithio)tetrathiafulvalene], the antiferromagnetic Mott insulator $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl, and the superconductor $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Br. None of them exhibit any indication of charge disproportionation. Upon cooling to low temperatures all BEDT-TTF molecules remain homogeneously charged within $\pm 0.005e$. No modification in the charge distribution is observed around $T=6$ K where a low-temperature anomaly has been reported for the spin-liquid material $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$. In this compound the in-plane optical response and vibrational coupling are rather anisotropic, indicating that the tilt of the BEDT-TTF molecules in $c$ direction and their coupling to the anion layers has to be considered in the explanation of the electromagnetic properties.

Figure 1

(a) Sketch of the BEDT-TTF molecule. (b) For $\kappa$-(BEDT-TTF)${}_{2}X$ the molecules are arranged sideways in dimers (strongly coupled by $t_d$), which constitute an anisotropic triangular lattice. The interdimer transfer integrals are labeled by $t$ and $t^{\prime }$. In the case of $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Br and $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl the plane is labeled as $ac$, while it is the $bc$ plane in the case of $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$, as denoted by the arrows, labeled red and blue, respectively. (c) The side view on $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl demonstrates the staggered layers of BEDT-TTF molecules separated by sheets of polymeric anions. (d) The structure of $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$ consists of one layer tilted by $\beta ={123}^{\circ }$ at room temperature (${125}^{\circ }$ at low temperatures).

Figure 2

For $\kappa$-(BEDT-TTF)${}_{2}X$ the molecules are arranged in dimers of two BEDT-TTF molecules. Commonly each molecule is assumed to carry equal charge (symbolized by the blue dots); this can be (a) static or (b) fluctuating. Alternatively, it is suggested that the molecules carry unequal charge. This charge disproportionation could form a dipolar solid with the net polarization along the (c) vertical or (d) horizontal direction.

Figure 3

Optical conductivity of $\kappa$-(BEDT-TTF)${}_{2}X$ measured within (upper frames) and perpendicular (lower frames) to the BEDT-TTF planes. In the lower row the room-temperature spectra (red lines) are shifted by $50{\left(\Omega \mathrm{cm}\right)}^{-1}$ with respect to the one measured at $T=12$ K (black curves). For $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Br and $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl, the light was polarized $E\parallel b$ and $E\perp b$, while for $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$ the polarizations were $E\parallel b$ and $E\parallel a^{*}$, respectively.

Figure 4

Sketch of the three most charge-sensitive C=C stretching modes of the BEDT-TTF molecule: ${\nu }_2\left(a_g\right)$, ${\nu }_3\left(a_g\right)$, and ${\nu }_{27}\left(b_{1u}\right)$, according to $D_{2h}$ symmetry (Ref. 37).

Figure 5

Temperature evolution of the out-of-plane optical conductivity of $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Br, $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl, and $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$, measured at the small side of crystals with the electric field polarized perpendicular to the BEDT-TTF planes. The dominant vibrational mode ${\nu }_{27}\left(b_{1u}\right)$ is a very sensitive local probe of charge per molecule.

Figure 6

(a) Powder absorption of $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$ in the range of the C=C molecular vibrations. The curves for selected temperatures are displaced for clarity reasons. (b) Temperature dependence of the center frequency. The vibrational mode ${\nu }_{27}\left(b_{1u}\right)=1464$ cm${}^{-1}$ slightly hardens upon cooling and remains basically unchanged for $T\le 100$ K, in accord with the reflection data.

Figure 7

Temperature dependence of the mode parameters obtained from the Fano fit of the ${\nu }_{27}\left(b_{1u}\right)$ vibrational features of $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Br, $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl, and $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$. (a) The resonance frequency ${\nu }_0$ of the dominant mode, (b) the damping $\gamma$, (c) the mode strength, and (d) the Fano coupling parameter $q$. The error bars indicate the uncertainty of the fits and might be overestimated.

Figure 8

Temperature evolution of the in-plane optical conductivity of (a) $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Br, (b) $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl, and [(c),(d)] $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$ in the range of the emv-coupled ${\nu }_3\left(a_g\right)$ mode. For clarity reasons the curves are shifted with respect to each other.

Figure 9

Temperature evolution of the in-plane optical conductivity of (a) $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Br, (b) $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl, and [(c),(d)] $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$ in the range of the ${\nu }_{60}\left(b_{3u}\right)$ mode.