Thermodynamics of the quantum spin liquid state of the single-component dimer Mott system $\kappa \text{−}{\mathrm{H}}_3{\left(\mathrm{Cat}\text{−}\mathrm{EDT}\text{−}\mathrm{TTF}\right)}_2$

Thermodynamic properties of the proton-mediated single component dimer-Mott insulator of $\kappa \text{−}{\mathrm{H}}_3{\left(\mathrm{Cat}\text{−}\mathrm{EDT}\text{−}\mathrm{TTF}\right)}_2$, which has a two-dimensional triangle lattice structure of $S=1/2$ spins, are reported. The extraordinary large electronic heat capacity coefficient $\gamma =58.8\mathrm{mJ}{\mathrm{K}}^{-2}\mathrm{mo}{\mathrm{l}}^{-1}$ observed by the low-temperature heat capacity measurements up to 6 T suggests the formation of the gapless spin liquid ground state. Although the magnetic interaction $J/k_{\mathrm{B}}$ is quite different from those of other dimer-Mott spin liquids, the thermodynamic feature scales well with the Wilson ratio of 1.4–1.6. The heat capacity measurements also detected that the deuteration of the proton-linkage changes the ground state to the nonmagnetic one with almost vanishing γ. Using the data of the deuterated compound, the accurate temperature dependence of the magnetic heat capacity reflecting on the low-energy excitations from the gapless spin liquids ground state is discussed.

Figure 1

The temperature dependencies of the heat capacity of the $\kappa \text{−}{\mathrm{H}}_3{\left(\mathrm{Cat}\text{−}\mathrm{EDT}\text{−}\mathrm{TTF}\right)}_2$ in logarithm plot. The data obtained by multipieces crystal sample (crystal) and those obtained by pellet sample (pellet) are indicated by red square and green circles, respectively. The data of $\kappa \text{−}{\mathrm{D}}_3{\left(\mathrm{Cat}\text{−}\mathrm{EDT}\text{−}\mathrm{TTF}\right)}_2$ and two other dimer Mott spin liquid compounds ($\kappa \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{C}{\mathrm{u}}_2{\left(\mathrm{CN}\right)}_3$ and $\mathrm{EtM}{\mathrm{e}}_3\mathrm{Sb}{\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2$) are also indicated by purple open circle, green line, and ocher line, respectively. The inset shows the temperature dependence of the magnetic susceptibility of the $\kappa \text{−}{\mathrm{H}}_3{\left(\mathrm{Cat}\text{−}\mathrm{EDT}\text{−}\mathrm{TTF}\right)}_2$.

Figure 2

(a) The $C_p{T}^{-1}$ vs $T^2$ plot of the heat capacity of $\kappa \text{−}{\mathrm{H}}_3{\left(\mathrm{Cat}\text{−}\mathrm{EDT}\text{−}\mathrm{TTF}\right)}_2$ at a low temperature region. The field dependencies up to 6 T are also plotted. The dashed lines show the data of other two spin liquid compounds of $\kappa \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{C}{\mathrm{u}}_2{\left(\mathrm{CN}\right)}_3$ and $\mathrm{EtM}{\mathrm{e}}_3\mathrm{Sb}{\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2$. (b) Comparison of $C_p{T}^{-1}$ vs $T^2$ plots of multipieces crystal sample and pellet sample of $\kappa \text{−}{\mathrm{H}}_3{\left(\mathrm{Cat}\text{−}\mathrm{EDT}\text{−}\mathrm{TTF}\right)}_2$. The data of $\kappa \text{−}{\mathrm{D}}_3{\left(\mathrm{Cat}\text{−}\mathrm{EDT}\text{−}\mathrm{TTF}\right)}_2$ obtained under fields up to 6 T are also plotted.

Figure 3

Relation between the electronic heat capacity coefficient γ and magnetic susceptibility extrapolated down to zero ${\chi }_0$. The dashed line indicate the relation of the value in the case of $R_{\mathrm{w}}=1,1.4$, and 1.6, where $R_{\mathrm{w}}$ denotes the Wilson ratio.

Figure 4

(a) The temperature dependencies $\mathrm{\Delta }{C}_p{T}^{-1}$ of $\kappa \text{−}{\mathrm{H}}_3{\left(\mathrm{Cat}\text{−}\mathrm{EDT}\text{−}\mathrm{TTF}\right)}_2$. The $\mathrm{\Delta }{C}_p{T}^{-1}$ was evaluated as a discrepancy of proton compound and deuteron compound. The inset shows the temperature dependence of magnetic entropy of $\kappa \text{−}{\mathrm{H}}_3{\left(\mathrm{Cat}\text{−}\mathrm{EDT}\text{−}\mathrm{TTF}\right)}_2$. (b) The fitting of the electronic heat capacity of crystalline sample using the formula of $\mathrm{\Delta }{C}_p={\gamma }^{*}T+a{T}^2,\mathrm{\Delta }{C}_p=\delta T^{2/3}+a{T}^2,\mathrm{\Delta }{C}_p={\gamma }^{*}T+\mathrm{\Delta }\beta T^3$, and $\mathrm{\Delta }{C}_p=\delta T^{2/3}+\mathrm{\Delta }\beta T^3$. The latter fitting of the latter two models are not successful. The obtained parameters for the former two are ${\gamma }^{*}=39.7\mathrm{mJ}{\mathrm{K}}^{-2}\mathrm{mo}{\mathrm{l}}^{-1},a=24.4\mathrm{mJ}{\mathrm{K}}^{-4}\mathrm{mo}{\mathrm{l}}^{-1}$ and $\delta =35.4\mathrm{mJ}{\mathrm{K}}^{-5/3}\mathrm{mo}{\mathrm{l}}^{-1},29.9\mathrm{mJ}{\mathrm{K}}^{-4}\mathrm{mo}{\mathrm{l}}^{-1}$, respectively.