Surfaces of three selected materials were investigated by means of low-energy ion-scattering technique: (1) the magnetite (Fe_3O_4) exhibiting the so-called Verwey transition (T_V(bulk)=125 K) accompanied by a small cubic-monoclinic crystal distortion, (2) the intermetallic compound NdMn_2 undergoing an antiferromagnetic-paramagnetic phase transition (T_N=104 K) accompanied by a large crystal distortion with a volume change of 1%, and (3) the typical insulator BaTiO_3 with two structural transitions below 300 K. The primary energy of the (Ne^+, Ar^+) ion beam was in the range of 4-8 keV, and the low-energy ion-scattering spectra were collected in the temperature range of 85-300 K. A large influence from the Verwey transition on the neutralization and re-ionization of scattered ions from magnetite surface was observed, while no visible change at the magnetic phase transition in NdMn_2 was revealed in the low-energy ion-scattering spectra. A strong dependence of the characteristics of the low-energy ion-scattering spectra on the irradiated time was observed for BaTiO_3 indicating that this surface was heavily charged by ion bombardments.