Magnetization Curves and Numerical Analysis of Energy Losses in Fe₃O₄ and CoFe₂O₄ Composite Materials Doped with Magnetic Nanoparticles

In this study, the magnetic properties and energy losses of polyester doped with Fe₃O₄ and CoFe₂O₄ magnetic nanoparticles were investigated at room temperature using the finite element analysis method. The magnetic hysteresis loops were calculated using numerical integration methods such as the Trapezoidal rule, Simpson\\\'s 1/3 rule, Simpson\\\'s 3/8 rule, and Newton-Cotes. The effects of different doping ratios on magnetization and energy losses were analyzed. As a result of the comparison of integration methods, it was revealed that the Newton-Cotes method provides more reliable findings compared to other methods. It was also reported that the Simpson\\\'s 1/3 rule method has lower error rates compared to the Trapezoidal method in iron-containing composites. Besides, the obtained results show that the Newton-Cotes method is more effective in calculating the integral of complex magnetic hysteresis curves. It was emphasized that the results of these analyses can be used in improvements and developments for the design and optimization of magnetic materials.