Implementation of field-differential phase-resolved microwave magnetic spectroscopy

Microwave spectroscopies are central to the investigation of magnetic systems by enabling the identification of dynamical resonance modes and by providing quantitative information on key magnetic parameters. Experiments on magnetization dynamics based on inductive microwave techniques usually rely on either field-modulated power detection or phase-resolved detection using a vector network analyzer. While these two approaches bring separate advantages, they have rarely been combined together. In this work, we develop customized microwave instrumentation combining phase-resolved detection and magnetic field modulation to perform microwave spectroscopy of magnetic systems. We apply this technique to ferromagnetic resonance (FMR), where it enables a quantitative measurement of the magnetic susceptibility in systems with small volume and magnetization. This method of field-differential phase-resolved microwave magnetic spectroscopy is compared with other approaches and is shown to greatly improve the resolution of finely separated FMR peaks and the detection of small signals. Furthermore, we model and characterize comprehensively the inductive coupling of the magnetic system to the microwave circuit, which enables a quantitative analysis of the resonance peaks and the rejection of potential errors originating from too strong permeability, imperfect impedance matching, broadening induced by field inhomogeneity, and varying sample placement.