  It is of fundamental importance but challenging to simultaneously identify
atomic and magnetic configurations of two-dimensional van der Waals materials.
In this work, we show that the nonreciprocal second-harmonic generation (SHG)
can be a powerful tool to answer this challenge. Despite the preserved lattice
inversion symmetry, the interlayer antiferromagnetic order and spin-orbit
coupling generate enhanced SHG in PT-symmetric bilayer chromium triiodide
(CrI3). Importantly, the in-plane polarization-resolved SHG is sensitive to
subtly different interlayer structures that cannot be told by linear optical
spectra. Beyond bilayer, we further predict that the intensity and
angle-resolved SHG can be employed to identify both interlayer atomic and
magnetic configurations of trilayer CrI3. Our first-principles results agree
with available measurements and show the potential of SHG as a non-contacting
approach to explore correlations between interlayer structures and magnetic
orders of emerging ultra-thin magnetic materials.
