Magnetic field effect on the dielectric properties of rare earth doped multiferroic BiFeO3

•The dielectric properties of La doped BiFeO3 are theoretically studied.•A kink in the dielectric function (DF) is observed near the Neel temperature TN.•TN and the ferroelectric transition temperature TC decrease with increasing La concentration x.•The DF shows a maximum at x = 0.15.•For small magnetic fields h the DF increases strongly, whereas for stronger h it begins to decrease slightly. The temperature, doping concentration and magnetic field dependence of the dielectric constant in lanthanum doped barium titanate are studied using a microscopic model and the Green’s function technique. A kink in the temperature dependence of the dielectric constant is observed near the Neel temperature. The Neel temperature and the ferroelectric transition temperature decrease with increasing doping concentration. The doping dependence of the dielectric constant shows a maximum value at 0.15. For small magnetic fields the dielectric constant increases strongly, whereas for stronger ones it begins to decrease slightly, i.e. there is a critical field for the transition from spiral cycloidal to antiferromagnetic spin arrangement.