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 σ(ab)(ω) from the spin degree of freedom. This spin-induced conductivity exhibits a power-law dependence on frequency σ(ab)(ω) ~ ω(β) with β ≈ 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.