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Ti0.97Co0.03O2 (TC3), Ti0.93Co0.03Ce0.04O2 (TCC34), Ti0.97Fe0.03O2 (TF3) and Ti0.93Fe0.03Ce0.04O2 (TFC34) nanoparticles were prepared by a chemical route. The x-ray diffraction pattern shows the coexistence of anatase and rutile phases and the value of the average particle size is measured using the Scherrer relation. The images from transmission electron microscopy show that the average particle size is 24, 27, 28 and 30 nm, respectively, for TC3, TCC34, TF3 and TFC34 and they are also represented by a particle distribution histogram. Fourier transform infrared spectroscopy has been used to confirm the stretching of Ce with the Co–O–Ti and Fe–O–Ti bond. Magnetic measurements detect ferromagnetism in all samples with the saturation magnetization increasing abruptly with Ce co-doping. All the samples show large photocatalytic activity and co-doping of Ce exhibits large-scale photocatalytic activity, and the value of the resulting band gap is calculated. This effect is due to the insertion of Ce3+/4+ in the TiO2 matrix, which generates an n-type impurity band. The dielectric behaviour is explained by the interface polarization, the decreasing trend of dielectric permittivity with increasing frequency by a Maxwell–Wagner and Koops' theory and is constant up to higher frequency regions due to the nano size effect. The dielectric behaviour is also explained by measuring frequency dependent ac conductivity.

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