Viscoelastic modeling of magnetic losses in a nanocrystalline core using fractional derivative operators

Abstract Nanocrystalline ferromagnetic materials have emerged as advanced solutions for improving magnetic performance, offering reduced core losses and high permeability. However, despite their superior properties, magnetic losses remain critical, particularly under high-frequency conditions. Existing simulation methods, including empirical models, time-dependent hysteresis models, and space-discretized approaches, often fail to accurately capture their complex magnetic properties over wide frequency ranges and amplitudes. This study evaluates the use of fractional derivative operators as innovative tools to model magnetic losses in nanocrystalline ferromagnetic cores. Four simulation approaches are analyzed: an analytical expression of the magnetic losses, two time-dependent hysteresis models (using first-order and fractional differential equations), and a space-discretized method coupling Maxwell’s equations with a material law including a fractional derivative operator. The analytical method provides simplicity and reliable results for total losses but cannot capture temporal or spatial distributions. The lumped hysteresis models, particularly the fractional-order variant, offer improved accuracy by accounting for dynamic effects and frequency dependencies. The space-discretized method is the most robust, achieving the highest precision and providing detailed insights into the local distribution and contributions of magnetic losses. Key findings indicate that fractional derivative operators enable highly accurate simulations of magnetic losses with relatively low derivative orders, reflecting a lower viscous-to-elastic loss ratio in nanocrystalline materials. Additionally, the substantial excess losses observed are attributed to the unique microstructure of the nanocrystalline ribbon, which induces distinctive domain wall motions.