Multidimensional Harmonic Generation Determines Halide Perovskite Crystal Symmetry: Disentangling Second Harmonic Generation from Multiphoton Photoluminescence

Metal halide perovskites are an intriguing class of semiconductor materials being explored for their linear and non-linear optical, and potentially ferroelectric properties. In particular, layered two-dimensional Ruddlesden-Popper (RP) halide perovskites have shown ferroelectric properties. Optical second harmonic generation (SHG) is commonly used to screen for ferroelectric materials, however, SHG measurements of perovskites are complicated by their intense multiphoton photoluminescence (mPL) which can be mistaken for SHG signal. In this work, we introduce multidimensional harmonic generation as a method to eliminate the complications caused by mPL. By scanning and correlating both excitation and emission frequencies, we un-ambiguously assess whether a material supports SHG by examining if an emission feature scales as twice the excitation frequency. Careful multidimensional harmonic generation measurements of a series of n=2 and n=3 RP perovskites reveal that, contrary to previous belief, n-butylammonium (BA) RP perovskites display no SHG, thus they have inversion symmetry; but RP perovskites with phenylethylammonium (PEA) and 2-thiophenemethylammonium (TPMA) spacer cations display SHG. Multidimensional harmonic generation is also able to confirm the SHG and thus non-centrosymmetry of a recently reported ferroelectric RP perovskite even in the presence of an obscuring mPL background. This work establishes multidimensional harmonic generation as a definitive method to measure the SHG properties of materials and demonstrates that tuning organic cations can allow the design of new non-centrosymmetric or even ferroelectric RP perovskites.