Magnetic anisotropy of the alkali iridate Na$_{2}$IrO$_{3}$ at high magnetic fields: evidence for strong ferromagnetic Kitaev correlations.

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. We show using exact diagonalization calculations that such a distinctive signature in the torque response enables us to constrain the effective spin models for this material to ones with dominant ferromagnetic Kitaev and subdominant antiferromagnetic Heisenberg exchange, accompanied by smaller competing interactions. In contrast, alternative models with dominant antiferromagnetic Kitaev interactions do not exhibit such a characteristic peak-dip structure in the transverse magnetization. We further show that at high magnetic fields, long range spin correlation functions decay rapidly, suggesting that above the peak-dip feature, the zigzag ordered phase transitions into a phase with characteristics of a quantum spin liquid. Many of our conclusions are expected to apply more broadly to materials governed by the physics of a honeycomb Kitaev model, such as $\alpha-$RuCl$_{3}$.