Modified Kittel’s FMR Equation for Engineered Domain Patterns in Thin Film Permalloy Structures

In the realm of micromagnetics, the study of the Ferromagnetic Resonance (FMR) phenomenon is of importance to employ magnetic materials in circuits operating between 3 GHz and 30 GHz. In our earlier work, we demonstrated that permalloy micromagnetic patterns could be engineered to obtain specific domain and domain wall configuration, which boosts the performance factors of inductors. In this work, we focus on measuring the FMR experimentally and calculating it theoretically to ensure employability in the above mentioned frequency range. A FMR frequency of 42 GHz is observed for 30 μm x 3 μm x 20 nm permalloy patterns integrated on an inductor, attributed to its single domain structure in the absence of the Zeeman field. Attempting to correlate these observations with theoretical values derived using Kittel's standard FMR equation, we found a notable discrepancy between the experimental and theoretical outcomes. This highlighted the necessity for revising the traditional Kittel's equation to achieve better alignment with experimental findings. The traditional Kittel's equation has been modified and this modified equation is correlated with experimental results and a maximum error of 15% is observed.