Electromagnetic modeling and analysis based on multilayer domain structure for GMI behavior in high frequency

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Existing theoretical models on the frequency dependence of the magnetoimpedance (MI) in ferromagnetic microwires primarily describe the MI phenomenon at the limiting cases of lower MHz (<several hundred MHz) or higher GHz (>several GHz) ranges. However, in the intermediate region between these two ranges, known as the transition region, MI curves undergo complex transformations. These transformations have been documented in the literature, but their underlying causes remain poorly understood. Unambiguous knowledge of the domain structure and its correlation with MI properties is essential for elucidating this behavior. In this study, we have, for the first time, observed the inner core magnetic structure of Co-based microwires and revealed its relationship with the high-frequency MI effect. A distinct magnetic structure comprising longitudinal domains in the inner core (IC), circular domains in the outer shell (OS), and a transition region (TR) has been identified. This structure originates from compositional gradients and residual stresses during microwire fabrication. The IC/TR/OS structure manifests in the complex transformations of the MI behavior, exhibiting a turning point at GHz frequencies before the characteristic double MI peak. We developed a multilayer planar model that considers this more realistic magnetic structure, including the TR layer. This model successfully reproduces the key features of the MI curves and provides deeper insights into the high-frequency MI phenomenon. Our findings pave the way for optimizing the sensing capabilities of Co-based ferromagnetic microwires and demonstrate the potential of using high-frequency MI measurements to map their magnetic microstructures.