In this thesis, pure phase LuFe2O4 polycrystalline have been fabricated by high temperature sintering. The low temperature dielectric property, magnetocapacitance and magnetoelectric effects are investigated. It is found that the magnetocapacitance effect is caused by the magnetoresistance effect from both the bulk and the interface. Epitaxial R-like BFO thin films are grown on STO (001) substrates by magneto sputtering method. The growing conditions are optimized to grow samples with high crystal quality and ferroelectric property. Low temperature Impedance Spectroscopy of R-like BFO thin films are studied in detail, the relationship between the dielectric anomaly and the low temperature phase transition are discussed. Besides, we have successfully grown the T and R like phase BFO on STO (001) substrate with sputtering method. The appearance of T like BFO is not solely depending on the lattice or the existence BiOx, which enable the growth of pure T-like phase on STO substrate.