  The magnetic field response of the Mott-insulating honeycomb iridate
Na$_{2}$IrO$_{3}$ is investigated using torque magnetometry measurements in
magnetic fields up to 60 tesla. A peak-dip structure is observed in the torque
response at magnetic fields corresponding to an energy scale close to the
zigzag ordering ($\approx 15~K$) temperature. Using exact diagonalization
calculations, we show that such a distinctive signature in the torque response
constrains the effective spin models for these classes of Kitaev materials to
ones with dominant ferromagnetic Kitaev interactions, while alternative models
with dominant antiferromagnetic Kitaev interactions are excluded. We further
show that at high magnetic fields, long range spin correlation functions decay
rapidly, signaling a transition to a long-sought-after field-induced quantum
spin liquid beyond the peak-dip structure. Kitaev systems are thus revealed to
be excellent candidates for field-induced quantum spin liquids, similar physics
having been suggested in another Kitaev material $\alpha-$RuCl$_{3}$.
