Mathematical Model of the Effect of Temperature and Annealing Time on Magnetization of the Alloy of BaFe12O19 Nanocrystals and the Amorphous Phase of BaTiO3 and TiO2

Magnetization of a compact alloy sample, prepared by sintering a mixture of powders 50.0 wt% Fe, 47.0 wt% BaTiO3 and 3.0 wt% TiO2 composed of BaFe12O19 nanocrystals and amorphous TiO2 nanoparticles embedded in an amorphous BaTiO3 matrix, raises with increasing the strength of the external magnetic field. When heating the alloy to up 65°C the magnetization does not change, however further heating from 65 to 350°C results in its slow decline. A rapid drop in magnetization in the temperature range from 350 to 500°C is caused by transformation of directed paramagnetic, ferromagnetic and weakly ferromagnetic domains into disordered states. Reverse processes occur during cooling of the alloy causing an increase in magnetization. This rise is proportional to the strength of the external magnetic field. During the cooling of the sample, a part of disordered weakly ferromagnetic domains transforms into directed ferromagnetic domains, which then convert into directed weakly ferromagnetic domains. The kinetic expression of this process was established. At optimal cooling time at given temperature ensuring the maximum magnetization and dependence of magnetization on the strength of the external magnetic field was determined. The agreement of the experimental results with theoretical values from the kinetic model corroborates the assumed magnetization mechanism.