Charge disproportionation in the spin-liquid candidate $\kappa -{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$ at 6 K revealed by ${}^{63}\mathrm{Cu}$ NQR measurements

The spin-liquid candidate $\kappa -{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$ [ET: bis(ethylenedithio)tetrathiafulvalene] does not exhibit magnetic ordering down to a very low temperature, but shows a mysterious anomaly at 6 K. The origin of the so-called 6-K anomaly is still under debate. We carried out nuclear quadrupole resonance (NQR) measurements on the copper sites of the insulating layers, which are sensitive to the charge dynamics unlike conventional spin-$1/2$ nuclear magnetic resonance (NMR). The main finding of this Rapid Communication is that the observation of a sharp peak behavior in the nuclear spin-lattice relaxation rate $T_1^{-1}$ of ${}^{63}\mathrm{Cu}$ NQR at 6 K while $T_1^{-1}$ of both ${}^{13}\mathrm{C}$ and ${}^1\mathrm{H}$ NMR show no clear anomaly. This behavior can be understood as a second-order phase transition related to charge disproportionation in the ET layers.

Figure 1

(a) ZF NQR spectra at 4.3 K (black circles) and 10 K (red squares). (b) Structure of the ${\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$ insulating layer. (c) $T$ dependence of $T_2^{-1}$ measured at the peak around 40.7 MHz.

Figure 2

(a) $T$ evolution of NQR spectra. Solid lines are the fitting curves using the Gaussian function. (b) $T$ dependence of ${\nu }_{\mathrm{NQR}}$. The dashed curve is the calculated result with the empirical formula ${\nu }_{\mathrm{NQR}}={\nu }_{0}exp(-\alpha T^2)$ (see text). (c) $T$ dependence of the linewidth.

Figure 3

$T$ dependencies of ${}^{63}{T_1}^{-1}$ (black circles) and ${}^{13}{T}_1^{-1}$ (open blue squares) from Ref. [27]. The values of ${}^{13}{T}_1^{-1}$ are reduced by a factor of 0.023. Dashed black and solid red curves represent $T_{1,Q}^{-1}$ due to the thermal lattice vibration, and $T_{1,Q}^{-1}+0.055T^{1/2}$, respectively. The inset shows the $T$ dependence of $\beta$.

Figure 4

(a) Field-swept ${}^{63,65}\mathrm{Cu}$-NMR spectra at 75 MHz and 1.7 K (black symbols) and the simulation result of four observed NQR frequencies and $\eta =0.5$ (red line). (b) $T$ dependence of ${}^{63}{T_1}^{-1}$ in the magnetic fields.