  We apply a strong magnetic field to a kagome Mott insulator with
antiferromagnetic interactions which does not show magnetic ordering down to
low temperatures. We observe a plateau at magnetization 1/9 Bohr magneton per
magnetic ion (Cu). Furthermore, in the vicinity of this plateau we observe sets
of strong oscillations in the magnetic torque, reminiscent of quantum
oscillations in metals. Such oscillations have never been seen in a wide gap
insulator and point to an exotic origin. While the temperature dependence of
these oscillations follows Fermi-liquid-theory predictions, they are
approximately periodic in the magnetic field $H$, as opposed to $1/H$ in
conventional metals. Furthermore, a strong angular dependence is observed for
the period, which indicates an orbital origin for this effect. We show that the
1/9 plateau and the associated oscillations are consistent with the appearance
of a quantum-spin-liquid state whose excitations are fermionic spinons that
obey a Dirac spectrum. The oscillations are in response to an emergent gauge
field. Our results provide strong evidence that fractionalized particles
coupled to the elusive emergent gauge field have been observed.
