Microwave magnetometer: Magnetic hysteresis reconstruction via microwave resonance spectroscopy

Abstract

We present a model-driven framework—termed the microwave magnetometer—for reconstructing magnetic hysteresis loops and quantitatively extracting intrinsic magnetic parameters directly from broadband frequency–field ferromagnetic resonance (FMR) spectra. By analytically inverting the Kittel equation and introducing a hysteresis ratio model, we extract the normalized magnetization curve M(H)/Ms and determine key parameters including the anisotropy field Hk, saturation magnetization Ms, coercivity Hc, and saturation field Hs, using only high-frequency dynamic measurements. This method is experimentally validated on four sputtered thin films—two with uniaxial anisotropy (FeCoB and FeGaB) and two isotropic stripe-domain FeNi samples—through direct comparison with vibrating sample magnetometry (VSM) data. The reconstructed loops show strong agreement with VSM results in easy-axis configurations and retain fidelity even in domain-rich or weakly anisotropic systems. Deviations in low-field, non-saturated regimes are identified and attributed to nonuniform dynamic responses such as domain-wall motion and localized spin-wave excitations. The microwave magnetometer framework offers a contactless, non-invasive alternative to conventional magnetometry and extends the utility of FMR into static characterization, enabling high-resolution hysteresis reconstruction in magnetic films and integrated magnetic devices.