  The leading order nonlinear (NL) susceptibility, $\chi_3$, in a paramagnet is
negative and diverges as $T \rightarrow 0$. This divergence is destroyed when
spins correlate and the NL response provides unique insights into magnetic
order. Dimensionality, exchange interaction, and preponderance of quantum
effects all imprint their signatures in the NL magnetic response. Here, we
study the NL susceptibilities in the proximate Kitaev magnet $\alpha$-RuCl$_3$
which differs from the expected antiferromagnetic behavior. For $T< T_c$ = 7.5
K 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 by
a 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 order
at low temperatures. Classical Monte Carlo (CMC) simulations in the standard
${K-H-\Gamma}$ model secure such a quadratic ${B}$ dependence of ${M}$, only
for ${T}$ $\approx$ ${T}_c$ 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 the
high field NL behavior well. ${\chi}_3$ is large and positive both below and
above ${T}_c$ crossing zero only for ${T}$ $>$ 50 K. In contrast, for
$B$~$\parallel$~c-axis, no separate low/high field behaviors is measured and
only a much smaller ${\chi}_3$ is apparent.
