Micromagnetic studies of high frequency permeability in Fe–M–N thin films with macroscopic and mesoscopic sizes

A micromagnetic model is established to analyze the permeability of Fe–Ta–N and Fe–Al–N thin films in a wide frequency range from 10 to 2200 MHz. The simulated real part of the permeability is about 2500 and 5000 at low frequencies for macroscopic Fe–Al–N and Fe–Ta–N films, respectively. It then decreases by a factor of 2 around 500 and 300 MHz. The corresponding imaginary part of the permeability increases from zero to a maximum value. In mesoscopic Fe–M–N films, huge magnetic poles on the edge of a layer play a significant role in the frequency response. As a result, the real part of the permeability in a mesoscopic film becomes much smaller than that in a macroscopic film. The spin patterns of mesoscopic Fe–M–N films in an external oscillatory field are also shown to understand the frequency response with strong magnetic poles.