Magnetic field at Ce impurities in La sites of La$_{0.5}$Ba$_{0.5}$MnO$_{3}$ double perovskites

Due to its rich variety of electromagnetic properties, such as a colossal magnetoresistance, charge and orbital ordering, and metal-insulator transition, the magnetic behavior in La$_{0.5}$Ba$_{0.5}$MnO$_{3}$ double perovskite compounds has been investigated by several techniques, however more experimental data, especially from atomic resolution techniques, are still necessary to understand such complex behavior. In this paper, we have used a nuclear and short-range technique, the Perturbed Angular Correlation (PAC) spectroscopy, to investigate the magnetic hyperfine interaction at the $^{140}$Ce and $^{111}$Cd probe nuclei as impurities occupying La sites. This double perovskite samples were synthesized by Sol-Gel route. The crystal structure was determined by X-ray diffraction and the analyses showed that this method produced perovskite oxides with cubic structure in $Pm-3m$ space group and the homogeneity was determined by Transmission Electron Microscopy (TEM). The local properties investigated by PAC spectroscopy revealed a ferromagnetic transition temperature above 300 K and a pure antiferromagnetic interaction below 100 K. Moreover, it also indicates an anomalous behavior of the temperature dependence of magnetic hyperfine field at La sites measured with $^{140}$Ce probe nuclei, which can be ascribed to the contribution of 4$f$ band of Ce to Magnetic Hyperfine Field (B$_{hf}$) at low temperatures due to the increase in its localized character.