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The leading order nonlinear (NL) susceptibility, $\chi_3$, in a paramagnet isnegative and diverges as $T \rightarrow 0$. This divergence is destroyed whenspins correlate and the NL response provides unique insights into magneticorder. Dimensionality, exchange interaction, and preponderance of quantumeffects all imprint their signatures in the NL magnetic response. Here, westudy the NL susceptibilities in the proximate Kitaev magnet $\alpha$-RuCl$_3$which differs from the expected antiferromagnetic behavior. For $T< T_c$ = 7.5K and field $B$ in the ab-plane, we obtain contrasting NL responses in low ($<$2 ${T}$) and high field regions. For low fields the NL behavior is dominated bya quadratic response (positive $\chi_2$), which shows a rapid rise below $T_c$.This large $\chi_2 >0$ implies a broken sublattice symmetry of magnetic orderat low temperatures. Classical Monte Carlo (CMC) simulations in the standard${K-H-\Gamma}$ model secure such a quadratic ${B}$ dependence of ${M}$, onlyfor ${T}$ $\approx$ ${T}_c$ with ${\chi}_2$ being zero as ${T}$ $\rightarrow$0. It is also zero for all temperatures in exact diagonalization calculations.On the other hand, we find an exclusive cubic term (${\chi}_3$) describes thehigh field NL behavior well. ${\chi}_3$ is large and positive both below andabove ${T}_c$ crossing zero only for ${T}$ $>$ 50 K. In contrast, for$B$~$\parallel$~c-axis, no separate low/high field behaviors is measured andonly a much smaller ${\chi}_3$ is apparent.

Anomalous and Anisotropic Nonlinear Susceptibility in the Proximate Kitaev Magnet $\alpha$-RuCl$_3$