Magnetic energy loss in permalloy thin films and microstructures

Magnetic switching and energy loss scaling is studied in permalloy thin films and microstructures over a nine-decade frequency range. The dynamic coercive field H-c(*)(omega) of both the films and the microstructures can be accurately described by a three-parameter scaling function H-c(*)(omega)=H-dp+K(dH/dt)(alpha) derived from a domain-wall dynamics model driven by a linear ramp field. The scaling function describes frequency-dependent evolution from adiabatic to domain-wall dominated power-law loss behavior without invoking mechanism crossover (to nucleation-dominated behavior) and manifests scaling exponents that depend only weakly on static coercivity. High-quality thin-film microstructures produced by vacuum evaporation yield alpha=1/2, a universal exponent associated with domain-wall dominated magnetization reversal based on a linear-mobility model. Corresponding films and microstructures prepared by sputtering also exhibit power-law scaling based on a smaller alpha, but still consistent with domain-wall rather than nucleation-based reversal. The results suggest that in the thin-film limit large-angle local spin damping mechanisms account for magnetic energy loss at both low frequencies (Barkhausen regime in which pinning dominates average domain-wall velocity) and high frequencies (power-law scaling regime in which the mobility dominates average domain-wall velocity).