Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagom\'e Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$

We report the determination of the Dzyaloshinsky-Moriya interaction, the dominant magnetic anisotropy term in the \kagome spin-1/2 compound {\herbert}. Based on the analysis of the high-temperature electron spin resonance (ESR) spectra, we find its main component $\mathrm{\mid }{D}_z\mathrm{\mid }=15(1)$ K to be perpendicular to the \kagome planes. Through the temperature dependent ESR line-width we observe a building up of nearest-neighbor spin-spin correlations below $\sim$150 K.