Dynamical Reduction of the Dimensionality of Exchange Interactions and the “Spin-Liquid” Phase of $\kappa$-$(\mathrm{BEDT}\text{−}\mathrm{TTF}{)}_{2}X$

We show that the anisotropy of the effective spin model for the dimer Mott insulator phase of $\kappa$-$(\mathrm{BEDT}\text{−}\mathrm{TTF}{)}_{2}X$ salts is dramatically different from that of the underlying tight-binding model. Intradimer quantum interference results in a model of coupled spin chains, where frustrated interchain interactions suppress long-range magnetic order. Thus, we argue, the “spin liquid” phase observed in some of these materials is a remnant of the Tomonaga-Luttinger physics of a single chain. This is consistent with previous experiments and resolves some outstanding puzzles.

Figure 1

Models of organic charge transfer salts: (a) Hopping integrals between monomers (bars). To an excellent approximation $t_q=t_{q^{\prime }}$ and $t_p=t_{p^{\prime }}$ [10]. (b) The dimer model. (c) Heisenberg model in the dimer Mott insulator phase, the staggered interlayer component of DM interaction is also indicated—we adopt the convention that the leftmost spin appears first in the DM interaction, ${\mathit{D}}_{ij}·{\mathit{S}}_i\times {\mathit{S}}_j$.

Figure 2

Superexchange from perturbation theory for the monomer (solid lines) and dimer (dashed lines) models compared with the exact singlet-triplet splitting of the tetramers marked in Fig. 1 (dots and squares). Tight-binding parameters as calculated from first principles for $\kappa$-Cl and $V_m=0$.

Figure 3

Classical sketches of exchange process. (a)–(c) An exchange pathway that remains finite as $(U_m-V_m)/t_{b1}\to \infty$ contributing $\propto t_p{t}_q/t_{b1}$ to $J_2$. (d)–(f) An exchange pathway that vanishes as $U_m\to \infty$, contributing $\propto |t_{b2}{|}^2/U_m$ to $J_1$ for $U_m-V_m\gg t_{b1}$.

Figure 4

Comparison of dimer (dashed lines) and monomer (solid lines) models for CuCN and $\kappa$-Cl (hopping integrals from [10] and $U_m=12t_{b1}$). The dimer approximation predicts lattices between the square ($J_2/J_1\to \infty$) and triangular ($J_2/J_1=1$) limits, whereas the monomer model gives lattices in the quasi-1D regime ($|J_2/J_1|<1$) for reasonable parameters (say, $1/3\lesssim V_m/U_m\lesssim 2/3$).

Figure 5

Calculated Néel temperature, $T_N/J_1$, for the Heisenberg model with interchain coupling treated at the RPA level. For reasonable parameters, a critical temperature $\sim 20\mathrm{K}$ can be realized (cf. Fig. 2), as observed in $\kappa$-Cl.