Pressure-Tuned Exchange Coupling of a Quantum Spin Liquid in the Molecular Triangular Lattice $\kappa \text{−}(\mathrm{ET}{)}_2{\mathrm{Ag}}_2(\mathrm{CN}{)}_3$

The effects of pressure on a quantum spin liquid are investigated in an organic Mott insulator $\kappa \text{−}(\mathrm{ET}{)}_2{\mathrm{Ag}}_2(\mathrm{CN}{)}_3$ with a spin-$1/2$ triangular lattice. The application of negative chemical pressure to $\kappa \text{−}(\mathrm{ET}{)}_2{\mathrm{Cu}}_2(\mathrm{CN}{)}_3$, which is a well-known sister Mott insulator, allows for extensive tuning of antiferromagnetic exchange coupling, with $J/k_B=175–310\mathrm{K}$, under hydrostatic pressure. Based on ${}^{13}\mathrm{C}$ nuclear magnetic resonance measurements under pressure, we uncover universal scaling in the static and dynamic spin susceptibilities down to low temperatures $\sim 0.1k_{B}T/J$. The persistent fluctuations and residual specific heat coefficient are consistent with the presence of gapless low-lying excitations. Our results thus demonstrate the fundamental finite-temperature properties of a quantum spin liquid in a wide parameter range.

Figure 1

(a) Pressure-temperature phase diagram of $\kappa \text{−}(\mathrm{ET}{)}_2{\mathrm{Ag}}_2(\mathrm{CN}{)}_3$. The circle and triangle symbols denote Mott and superconducting transition temperatures, respectively, determined by (b) resistivity $\rho$ measurements for various pressures. Inset: (a) triangular lattice of ET dimers, (b) low-temperature resistivity normalized at 7 K for 1.05–1.16 GPa.

Figure 2

(a) ${}^{13}\mathrm{C}$ (8.5 T) and (b) ${}^1\mathrm{H}$ (2.0 T) NMR spectra at ambient pressure, where the horizontal axis is defined as $(\omega -{\omega }_0)/{\omega }_0$ (${\omega }_0$: the resonance frequency of tetramethylsilane). (c) Spin susceptibility $\chi$ obtained from the magnetization (red solid curve) at ambient pressure and from the relative ${}^{13}\mathrm{C}$ Knight shift $\mathrm{\Delta }K$ (solid symbols) for various pressures. Dotted curves are fitted to a triangular-lattice Heisenberg model $\mathcal{H}=\sum _{i,j}J{\mathbf{S}}_i·{\mathbf{S}}_j$. The blue solid curve is $\chi$ of the Cu salt [6]. Inset: ${}^{13}\mathrm{C}$ enriched ET molecule. (d) $\chi T$ versus $k_{B}T/J$ plots for $P<P_c$. Inset: $\chi J/k_B$ versus $k_{B}T/J$ plots.

Figure 3

(a) Temperature dependence of nuclear spin-lattice relaxation rate divided by temperature, $({}^{13}{T}_{1}T{)}^{-1}$, and (b) ${}^{13}{T}_1^{-1}T$ versus $k_{B}T/J$ plots for $P<P_c$ in $\kappa \text{−}(\mathrm{ET}{)}_2{\mathrm{Ag}}_2(\mathrm{CN}{)}_3$.

Figure 4

(a) Nuclear spin-lattice relaxation rates ${}^i{T}_1^{-1}$ normalized with respect to square of gyromagnetic ratios, ${}^i{\gamma }_n^2/{\gamma }_e^2$ ($i=1$, 2, and 13), for 2.0 T (${}^1\mathrm{H}$) and 8.5 T (${}^2\mathrm{H}$ and ${}^{13}\mathrm{C}$). Inset: stretched exponent $\beta$ of the ${}^{13}\mathrm{C}$ magnetization recovery. (b) ${}^1{T}_1^{-1}$ measured at several magnetic fields. Dotted curves are fitted to Lorentzian-type fluctuations. Inset: field dependence of $T_{\max }$, ${}^1{T}_1^{-1}$ peak temperature.

Figure 5

Squared temperature dependence of specific heat divided by $T$ for magnetic field in the range 0–14 T in $\kappa \text{−}(\mathrm{ET}{)}_2{\mathrm{Ag}}_2(\mathrm{CN}{)}_3$. The inset shows $C{T}^{-2/3}$ versus $T^{7/3}$ plot at $H=0\mathrm{T}$.