Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice

${}^1\mathrm{H}$ NMR and static susceptibility measurements have been performed in an organic Mott insulator with a nearly isotropic triangular lattice, $\kappa \mathrm{\text{−}}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\mathrm{\text{−}}\mathrm{T}\mathrm{T}\mathrm{F}{)}_2{\mathrm{C}\mathrm{u}}_2(\mathrm{C}\mathrm{N}{)}_3$, which is a model system of frustrated quantum spins. The static susceptibility is described by the spin $S=1/2$ antiferromagnetic triangular-lattice Heisenberg model with the exchange constant $J\sim 250\mathrm{K}$. Regardless of the large magnetic interactions, the ${}^1\mathrm{H}$ NMR spectra show no indication of long-range magnetic ordering down to 32 mK, which is 4 orders of magnitude smaller than $J$. These results suggest that a quantum spin liquid state is realized in the close proximity of the superconducting state appearing under pressure.

Figure 1

(a) Crystal structure of an ET layer of $\kappa \mathrm{\text{−}}(\mathrm{E}\mathrm{T}{)}_2{\mathrm{C}\mathrm{u}}_2(\mathrm{C}\mathrm{N}{)}_3$ viewed along the long axes of ET molecules [4]. The transfer integrals between ET molecules, $t_{\mathrm{b}\mathrm{1}}$, $t_{\mathrm{b}\mathrm{2}}$, $t_{\mathrm{p}}$, and $t_{\mathrm{q}}$, are calculated as 224, 115, 80, and $-29\mathrm{m}\mathrm{e}\mathrm{V}$, respectively [5]. For the large $t_{\mathrm{b}\mathrm{1}}$ compared with other transfer integrals, the face-to-face pair of ET molecules connected with $t_{\mathrm{b}\mathrm{1}}$ can be regarded as a dimer unit consisting of the triangular lattice. (b) Schematic representation ofthe electronic structure of $\kappa \mathrm{\text{−}}(\mathrm{E}\mathrm{T}{)}_{2}X$, where the dots represent the ET dimer units. They form the anisotropic triangular lattice with $t=(|t_{\mathrm{p}}|+|t_{\mathrm{q}}|)/2$ and $t^{\prime }=t_{\mathrm{b}\mathrm{2}}/2$.

Figure 2

Temperature dependence of the magnetic susceptibility of the randomly orientated polycrystalline samples of $\kappa \mathrm{\text{−}}(\mathrm{E}\mathrm{T}{)}_2{\mathrm{C}\mathrm{u}}_2(\mathrm{C}\mathrm{N}{)}_3$ and $\kappa \mathrm{\text{−}}(\mathrm{E}\mathrm{T}{)}_2\mathrm{C}\mathrm{u}[\mathrm{N}(\mathrm{C}\mathrm{N}{)}_2]\mathrm{C}\mathrm{l}$ [9]. The core diamagnetic susceptibility is already subtracted. The solid and dotted lines represent the result of the series expansion of the triangular-lattice Heisenberg model using $[6/6]$ and $[7/7]$ Padé approximants, respectively, with $J=250\mathrm{K}$. The low-temperature data of $\kappa \mathrm{\text{−}}(\mathrm{E}\mathrm{T}{)}_2{\mathrm{C}\mathrm{u}}_2(\mathrm{C}\mathrm{N}{)}_3$ below 30 K are expanded in the inset.

Figure 3

(a) ${}^1\mathrm{H}$ NMR absorption spectra for single crystals of $\kappa \mathrm{\text{−}}(\mathrm{E}\mathrm{T}{)}_2{\mathrm{C}\mathrm{u}}_2(\mathrm{C}\mathrm{N}{)}_3$ and $\kappa \mathrm{\text{−}}(\mathrm{E}\mathrm{T}{)}_2\mathrm{C}\mathrm{u}[\mathrm{N}(\mathrm{C}\mathrm{N}{)}_2]\mathrm{C}\mathrm{l}$ [9] under the magnetic field perpendicular to the conducting planes.

Figure 4

${}^1\mathrm{H}$ nuclear spin-lattice relaxation rate $T_1^{-1}$ above 1 K for a single crystal (open circles) and a polycrystalline sample (closed circles) of $\kappa \mathrm{\text{−}}(\mathrm{E}\mathrm{T}{)}_2{\mathrm{C}\mathrm{u}}_2(\mathrm{C}\mathrm{N}{)}_3$ and a single crystal of $\kappa \mathrm{\text{−}}(\mathrm{E}\mathrm{T}{)}_2\mathrm{C}\mathrm{u}[\mathrm{N}(\mathrm{C}\mathrm{N}{)}_2]\mathrm{C}\mathrm{l}$ (open diamonds) [9]. The inset shows the data down to 32 mK in logarithm scales.