Algebraic charge dynamics of the quantum spin liquid ${\beta }^{\prime }-{\mathbf{EtMe}}_3\mathbf{Sb}{\left[\mathbf{Pd}{\left(\mathbf{dmit}\right)}_2\right]}_2$

Nuclear spin-lattice ($1/T_1$) and spin-spin ($1/T_2$) relaxation rates of the cation sites of a candidate quantum spin-liquid ${\beta }^{\prime }-{\mathrm{EtMe}}_3\mathrm{Sb}{\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2$ and its deuterated sample are presented. The enhanced $1/T_1$ of ${}^1\mathrm{H}$ and ${}^2\mathrm{D}$ is thoroughly analyzed considering the rotations of methyl and ethyl groups of the cation with activation energies of $2\times {10}^2$ K and $1.2\times {10}^3$ K respectively. Contrasting charge dynamics with an algebraic temperature dependence is found at the Sb site in the ${\mathrm{EtMe}}_3\mathrm{Sb}$ cation. The charge fluctuation remains active down to the lowest temperature, as has been observed in the ac response of dielectric constants.

Figure 1

(a) Crystal structure of ${\beta }^{\prime }-{\mathrm{EtMe}}_3\mathrm{Sb}{\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2$. The ${\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2$ and cation layers are alternately stacked. (b) ${\mathrm{EtMe}}_3\mathrm{Sb}$ cation. The Sb atom is located on the twofold rotation axis of the unit cell. In a d9-deuterated sample, protons of three methyl groups are labeled by deuterons.

Figure 2

NMR spectra of (a) ${}^2\mathrm{D}$ of d9-deuterated and (b) ${}^{121}\mathrm{Sb}$ of pristine samples of ${\mathrm{EtMe}}_3\mathrm{Sb}{\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2$. In Fig. 2 (b), ${}^{63}\mathrm{Cu}$ signal from NMR coil is visible at $\sim 5\%$.

Figure 3

Nuclear spin-lattice relaxation rates ($1/T_1$) of ${}^1\mathrm{H}$ and ${}^{121}\mathrm{Sb}$ for the pristine sample and those of ${}^1\mathrm{H}$ and ${}^2\mathrm{D}$ for the d9-deuterated sample. We plot $1/T_1$ for $X={\mathrm{Me}}_4\mathrm{Sb}$ as reference data of a cation with tetrahedral symmetry. The black diamonds $♦$ show the nuclear spin-spin relaxation rate ($1/T_2$) of Sb for the pristine sample measured at 79.2 MHz.

Figure 4

Replot of $1/T_1$ shown in Fig. 3. The solid and dashed lines are fits assuming that ${\tau }_c$ follows the activation temperature dependence $1/{\tau }_c\propto exp(-\mathrm{\Delta }/T)$.

Figure 5

Temperature-dependent correlation time ${\tau }_c$ of the cation sites of $X{\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2$ obtained by fitting the data by Eq. (1). The peak temperature of the dielectric constant as a function of the oscillating frequency (unit is radian) is shown as closed triangles [13]. Corrected microscopic time constants ${\tau }_m$ of the dielectric constants are shown as open triangles. Solid and dashed curves follow the activation temperature dependence. $1/{\tau }_c$ for ${}^{121}\mathrm{Sb}$ NMR and the dielectric constant appear linear in the plot and follow an algebraic temperature dependence.