  We report 17O NMR measurements in the S=1/2 Cu2+ kagome antiferromagnet
Herbertsmithite ZnCu3(OH)6Cl2 down to 45mK in magnetic fields ranging from 2T
to 12T. While Herbertsmithite displays a gapless spin-liquid behavior in zero
field, we uncover an instability toward a spin-solid phase at sub-kelvin
temperature induced by an applied magnetic field. The latter phase shows
largely suppressed moments $\lesssim 0.1\muB$ and gapped excitations. The H-T
phase diagram suggests the existence of a quantum critical point at the small
but finite magnetic field mu0 Hc=1.55(25)T. We discuss this finding in light of
the perturbative Dzyaloshinskii-Moriya interaction which was theoretically
proposed to sustain a quantum critical regime for the quantum kagome Heisenberg
antiferromagnet model.
