Anamolous, Anisotropic and Extended Nonlinear Susceptibility in a-RuCl3*

In proximate Kitaev a-RuCl3, we establish a radically new behavior of the nonlinear susceptibility hitherto not established. For T < Tc and B || ab-plane, a dual nonlinear response is observed. The high field response above 2 T yields a third order nonlinear susceptibility which peaks near Tc = 7.5 K, reminiscent of behavior in a classical 2D antiferromagnet, but with a large positive value for lowest T. The low field response, for B less than 2T - on the other hand, is positive quadratic and shows a rapid rise below Tc. This dual response vanishes for T beyond Tc where the nonlinear response is dominated by only the cubic term. This term is significantly > 0 and turns negative only for a temperature T > 50 K >> Tc. Classical Monte Carlo (CMC) simulations capture the observed quadratic response, albeit only near Tc. The CMC however fail to reproduce the large quadratic term at low T.. This discrepancy indicates inadequacy of current models and points to the importance of multi-spin correlations in a-RuCl3. For B || c-axis, we measure no dual response with only the cubic term being apparent. We also compare our results with exact diagonalization calculations performed on 16 x 16 cluster.