  Second harmonic generation has been applied to study lattice, electronic and
magnetic proprieties in atomically thin materials. However, inversion symmetry
breaking is usually required for the materials to generate a large signal. In
this work, we report a giant second-harmonic generation that arises below the
N\'eel temperature in few-layer centrosymmetric FePS$_3$. Layer-dependent study
indicates the detected signal is from the second-order nonlinearity of the
surface. The magnetism-induced surface second-harmonic response is two orders
of magnitude larger than those reported in other magnetic systems, with the
surface nonlinear susceptibility reaching 0.08--0.13 nm$^2$/V in 2 L--5 L
samples. By combing linear dichroism and second harmonic generation
experiments, we further confirm the giant second-harmonic generation is coupled
to nematic orders formed by the three possible Zigzag antiferromagnetic
domains. Our study shows that the surface second-harmonic generation is also a
sensitive tool to study antiferromagnetic states in centrosymmetric atomically
thin materials.
