Medium Amplitude Field Susceptometry (MAFS) for magnetic nanoparticles

The linear dynamic susceptibility is arguably the most important property to specify the magnetization dynamics of a given system. Therefore, this quantity has been studied in great detail and the corresponding measurements known as susceptometry are well-established. Notwithstanding its relevance, the linear susceptibility is inherently limited to describe the magnetization response to weak external fields only. Here, we suggest the framework of Medium Amplitude Field Susceptometry (MAFS) to study the non-linear response which complements the linear susceptibility and provides additional information on the magnetic properties of the system and is applicable to magnetic fields of medium amplitudes. In particular, we introduce the general third-order nonlinear susceptibility χ ˆ 3 as a central quantity that completely specifies the lowest-order non-linear response to arbitrary time-dependent magnetic fields. We show that response functions in medium amplitude oscillatory magnetic fields and parallel superposition susceptometry are contained in χ ˆ 3 as special cases. Also included in χ ˆ 3 are interesting intermodulation effects when the system is probed by a superposition of oscillating magnetic fields with different frequencies. We work out the explicit form of χ ˆ 3 for several model systems for the dynamics of magnetic nanoparticles (MNPs). We expect this unifying framework to be not only of theoretical interest, but also useful for a deeper characterization of MNP systems, giving additional information on their suitability for various applications. • Extend traditional alternating current (AC) susceptometry from the linear regime to magnetic fields of moderate amplitude. • Introduce third-order nonlinear susceptibility χ ˆ 3 ( ω 1 , ω 2 , ω 3 ) as central new quantity. • Weakly nonlinear regime fully specified by χ ˆ 3 for arbitrary time-dependent fields. • Mean amplitude and parallel superposition susceptometry are special cases of χ ˆ 3 . • Intermodulation effects provide additional insights. • Explicit form of χ ˆ 3 ( ω 1 , ω 2 , ω 3 ) worked out for particular model systems of magnetic nanoparticles.