Nonlinear refraction in CH$_3$NH$_3$PbBr$_3$ single crystals

Hybrid lead halide perovskites, such as CH$_3$NH$_3$PbX$_3$ (X=I, Br), are direct gap semiconductors that offer many superior optoelectronic properties combined with extremely simple solution-processing fabrication methods. This makes them very attractive for use in applications like solar cells or light-emitting devices. Recently, also their nonlinear optical properties have received increased attention due to reports of high nonlinear refraction in thin films and nanoparticles. However, understanding of the underlying mechanisms is poor and limited by the lack of knowledge of fundamental parameters like the nonlinear refractive index of the bulk material. Here, we measure both nonlinear absorption and nonlinear refraction in a CH$_3$NH$_3$PbBr$_3$ single crystal using the Z-scan technique with femtosecond laser pulses. At 1000 nm, we obtain values of 5.2 cm/GW and 9.5$\cdot$10$^{-14}$ cm$^2$/W for nonlinear absorption and nonlinear refraction, respectively. Sign and magnitude of the observed refractive nonlinearity are reproduced well by the two-band model. To our knowledge, these measurements mark the first characterization of nonlinear refraction in any metal halide perovskite single crystal and thus will serve as an important reference for assessing the potential of this emerging material class for nonlinear optical applications.