Revealing hidden orders in correlated electron systems with nonlinear optics

The symmetries of a crystal form the basis for understanding its mechanical, electrical and magnetic responses. Here we describe an optical high harmonic generation based technique for resolving the local (micron scale) crystallographic and electronic point group symmetries of crystals. Using the spin-orbit coupled correlated oxide Sr
₂
IrO
₄
as an example, we demonstrate how this technique can be used to resolve broken crystallographic and electronic symmetries that evaded diffraction based probes.