Spin-Induced Optical Conductivity in the Spin-Liquid Candidate Herbertsmithite

We report a direct measurement of the low-frequency optical conductivity of large-area single-crystal herbertsmithite, a promising spin-liquid candidate material, by means of terahertz time-domain spectroscopy. In the spectral range below 1.4 THz, we observe a contribution to the real part of the in-plane conductivity sigma(ab)(omega) from the spin degree of freedom. This spin-induced conductivity exhibits a power-law dependence on frequency sigma(ab)(omega) similar to omega(beta) with beta approximate to 1.4. Our observation is consistent with the theoretically predicted low-frequency conductivity arising from an emergent gauge field of a gapless U(1) Dirac spin liquid.