Phonon renormalization effects accompanying the 6 K anomaly in the quantum spin liquid candidate $\kappa \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$

The low-temperature state of the quantum spin liquid candidate $\kappa \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$ emerges via an anomaly at $T^{*}\sim 6$ K. Although signatures of this anomaly have been revealed in various quantities, its origin has remained unclear. Here we report inelastic neutron scattering measurements on single crystals of $\kappa \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$, aiming at studying phonon renormalization effects at $T^{*}$. A drastic change was observed in the phonon damping across $T^{*}$ for a breathing mode of BEDT-TTF dimers at $E=4.7$ meV. The abrupt change in the phonon damping is attributed to a phase transition into a valence bond solid state based on an effective model describing the spin-charge coupling in this dimer-Mott system.

Figure 1

(a)–(e) Temperature dependence of constant-Q scans at (060). The red curves are the sum of the fits to damped harmonic oscillator functions at $E\sim 2.0$, 2.9, 3.7, 4.7, 5.7, and 7.2 meV convolved with the experimental resolution. The dashed curves show the peak profiles for each mode. The breathing mode of the ET dimer at 4.7 meV is marked in red. The horizontal bars represent the instrumental energy resolution at $E=4.7$ meV. (f) Top view of the ET layer. (g) Wave vector $Q$=(060) used for phonon measurements in the ($0kl$) scattering plane. Red arrows in (f) and (g) show the polarization vector $\xi$ of the breathing mode of the ET dimers, which can be detected at (060).

Figure 2

Temperature dependence of (a) the phonon energy $E$ and (b) the damping factor $\mathrm{\Gamma }$ of the breathing mode of ET dimers at $E\sim 4.7$ meV. (c) Thermal variation of the energy integrated intensity of the phonon modes ($I_{\mathrm{phonon}}$). (d) Temperature dependence of the uniform magnetic susceptibility $\chi$ measured on a single crystal in a magnetic field of 5 T perpendicular to the $\mathit{bc}$ plane and for $\kappa$-Cl taken from Ref.[24]. Inset in (d) shows the temperature derivative of $\chi$ around the 6 K anomaly.

Figure 3

Schematic phase diagrams of temperature ($T$) vs. interdimer Coulomb interaction ($V$) for (a) the QSL and (b) VBS states. The broken lines represent $T_{\mathrm{N}}$ for the case of $\kappa$-Cl whereas they correspond to a crossover for $\kappa$-CN. Insets: Spheres connected by thick orange lines represent ET dimers. White and red spheres correspond to charge-poor and charge-rich sites, respectively.