Lattice vibrations of the charge-transfer salt $\kappa -\left(\text{BEDT-TTF}{)}_2{\mathrm{Cu}}_2\right(\mathrm{CN}{)}_3$: Comprehensive explanation of the electrodynamic response in a spin-liquid compound

The dimer Mott insulator $\kappa -\left(\text{BEDT-TTF}{)}_2{\mathrm{Cu}}_2\right(\mathrm{CN}{)}_3$ exhibits unusual electrodynamic properties. Numerical investigations of the electronic ground state and the molecular and lattice vibrations reveal the importance of the ${\mathrm{Cu}}_2(\mathrm{CN}{)}_3{}^{-}$ anion network coupled to the bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) molecules: The threefold cyanide coordination of copper and linkage isomerism in the anion structure cause a loss of symmetry, frustration, disorder, and domain formation. Our findings consistently explain the temperature and polarization-dependent THz and infrared measurements, reinforce the understanding of dielectric properties, and have important implications for the quantum spin-liquid state, which should be treated beyond two-dimensional, purely electronic models.

Figure 1

(a) Sketch of the bis-(ethylenedithio)tetrathiafulvalene molecule, called BEDT-TTF. (b) For $\kappa -\left(\text{BEDT-TTF}{)}_2{\mathrm{Cu}}_2\right(\mathrm{CN}{)}_3$ they are arranged in dimers, which constitute an anisotropic triangular lattice within the $bc$ conduction layers. (c) These BEDT-TTF layers are sandwiched along the $a$ axis by insulating anion sheets. The polymerized ${\mathrm{Cu}}_2$(CN)${}_3{}^{-}$ form interconnected elongated hexagons with the terminal ethylene groups of a BEDT-TTF dimer fitting into the opening. The ratio of the interdimer transfer integrals is close to unity: $t^{\prime }/t\approx 0.83$ [15, 16]; the intradimer transfer integral $t_d\approx 0.2$ eV [17, 18]. With $U\approx 2t_d$ [19], one obtains at ambient conditions $U/t=7.3$; a slight variation of $U$ and orbital overlap $t$ causes magnetic order, on the one hand, and superconductivity, on the other hand.

Figure 2

THz spectra of the optical conductivity of $\kappa -\left(\text{BEDT-TTF}{)}_2{\mathrm{Cu}}_2\right(\mathrm{CN}{)}_3$ measured at different temperatures for both polarizations using a coherent-source Mach-Zehnder interferometer. The data are shifted with respect to each other for clarity reasons. The red line corresponds to the fit of the data.

Figure 3

Relaxed structure of the ${\mathrm{Cu}}_2$(CN)${}_3{}^{-}$ anion layer in the $bc$ plane of $\kappa -\left(\text{BEDT-TTF}{)}_2{\mathrm{Cu}}_2\right(\mathrm{CN}{)}_3$as obtained by the DFT calculations. The unit cell contains two formula units ($Z=2$) with two distinct configurations of Cu ions. When the positions of C and N in the encircled links are specified, the symmetry is reduced to P1. For the sake of simplicity, only the inequivalency between the bridging ${\mathrm{c}}_1$ and ${\mathrm{c}}_2$ is shown. The coordination at the Cu site (${\theta }_1=118.7^{\circ }, {\theta }_2=102.3^{\circ },{\theta }_3=138.8^{\circ }$) is closer to the ideal ${120}^{\circ }$ than for other polyanions [37]. This constellation is prone to frustration, disorder, and domain formation.

Figure 4

Midinfrared conductivity of $\kappa -\left(\text{BEDT-TTF}{)}_2{\mathrm{Cu}}_2\right(\mathrm{CN}{)}_3$ recorded for the polarization $E\parallel b$ and $E\parallel c$ at different temperatures. The CN stretching modes are seen between 2115 and 2140 ${\mathrm{cm}}^{-1}$. On the right the different cyanide arrangements in the lowest energy state are sketched. For $E\parallel c$ the two arrangements ${\mathrm{c}}_1$ and ${\mathrm{c}}_2$ are degenerate in energy.