Figure 1

(a) Schematic lattice structure of herbertsmithite. The crystal is composed of layers of spin-$1/2$ copper atoms (blue dots) arranged in the kagome pattern in the $ab$ plane, separated by nonmagnetic zinc atoms (orange dots) along the perpendicular $c$ axis. The chlorine, oxygen, and hydrogen atoms in herbertsmithite are neglected here for simplicity. (b) The orientation of the herbertsmithite sample used in our experiment. The $ab$ planes are aligned vertically, making an angle of 67° with the sample surface. $E_o$, $E_e$, and $k$ denote, respectively, the ordinary and extraordinary optical axes of the crystal and the wave vector of the incident terahertz beam.Reuse & Permissions

Figure 2

(a) The in-plane real optical conductivity ${\sigma }_{ab}$ in the spectral range 0.6–2.2 THz at temperatures $T=4$, 50, and 150 K. The spectra consist of a high-frequency component arising from a phonon resonance at $\sim 3\mathrm{THz}$, and a low-frequency component that exhibits a power-law dependence on frequency as ${\sigma }_{ab}\sim {\omega }^{\beta }$ with $\beta \approx 1.4$ (dotted line). The data are plotted on a log-log scale to highlight this power-law behavior. (b) The integrated values of the in-plane conductivity ${\sigma }_{ab}$ from panel (a) and of the out-of-plane conductivity ${\sigma }_c$ from Fig. 3 from 0.6 to 1.4 THz for temperatures $T=4–160\mathrm{K}$. ${\sigma }_{ab}$ decreases as the temperature increases up to $T\sim 60\mathrm{K}$, after which it remains constant. In contrast, ${\sigma }_c$ increases monotonically with temperature. Dashed lines are guides to the eye.Reuse & Permissions

Figure 3

Out-of-plane real optical conductivity of herbertsmithite (${\sigma }_c$) (blue line), measured in the spectral range 0.6–2.2 THz at $T=4\mathrm{K}$, in comparison with the in-plane conductivity ${\sigma }_{ab}$ (green line). The inset displays the ${\sigma }_c$ spectra at $T=4$, 30, 80, and 160 K. The magnitude of ${\sigma }_c$ increases with temperature.Reuse & Permissions

Figure 4

In-plane real conductivity of herbertsmithite (${\sigma }_{ab}$) measured in the spectral range 0.6–2.2 THz at magnetic fields 0, 3, 5, and 7 T. No systematic magnetic-field dependence is observed. The small variation between measurements is attributed to experimental uncertainties.Reuse & Permissions