Characterization of multiferroic Bi0.8RE0.2FeO3 powders (RE=Nd3+, Eu3+) grown by the sol–gel method

•Changes of nonlinear optical response shown in BiFeO3 doped by the Eu and Nd.•Materials synthesized by the sol–gel method.•Microscopic and structural analysis show their possible impact on the grain sizes.•Photoinduced optics was performed by the Nd:YAG laser.

A possibility of changes the non-linear optical response was shown for the first time in the BiFeO3 doped by the Eu and Nd materials synthesized by the sol–gel method. Grain size here plays a substantial role. At the same time the latter is responsible for the non-linear optical response. The photoinduced optics was performed by the Nd:YAG lasers of different powers for samples of different nanosizes.