High frequency susceptibility of closure domain structures calculated using micromagnetic modeling

Abstract

In this work we use micromagnetic simulation to compute the complex magnetic susceptibility of several Permalloy elements having closure domain structures. The average imaginary susceptibility of the structures typically shows multiple maxima, indicating multiple ferromagnetic resonance modes. Two-dimensional maps of the susceptibility show that the lower frequency resonances (0.9–1.5GHz) are typically associated with 90° domain walls, while higher frequency resonances (2–4GHz) are associated with regions of more uniform magnetization oriented orthogonal to the driving field. This trend is understood by looking at the total local fields within each resonating regions. Quantitative agreement is found between the resonance frequencies predicted by a simple Kittel analysis and those observed in these different regions, when all components of the local field (demagnetization, exchange, anisotropy, and external fields) are considered. In the lower resonant frequency domain wall regions, the resonance condition is set by the small positive difference between a large demagnetizing field that stiffens the magnetic system and a large internal exchange fields that softens the magnetic system. In contrast, the relatively uniform magnetization regions are marked either by a large exchange field acting as the stiffening term and slightly overcoming a large demagnetizing term or a small demagnetizing term acting as the stiffening term and overcoming an even smaller exchange field.