Deconvolution of ferromagnetic resonance spectrum of magnetic nanoparticle assembly using genetic algorithm

The ferromagnetic resonance (FMR) spectra of dilute random assemblies of magnetite nanoparticles with cubic magnetic anisotropy and various aspect ratios are calculated using the stochastic Landau–Lifshitz equation at a finite temperature, T = 300 K, taking into account the thermal fluctuations of the particle magnetic moments. Particles of non-spherical shape in the first approximation are described as elongated spheroids with a given semiaxes ratio a/b, where a and b are the long and transverse semiaxes of a spheroid, respectively. A representative database of FMR spectra is created for assemblies of randomly oriented spheroidal magnetite nanoparticles with various transverse diameters D = 5–25 nm, moderate aspect ratios a/b = 1.0–1.8, and magnetic damping constants κ = 0.1, 0.2. The basic FMR spectra of assemblies with D = 25 nm at different aspect ratios can be considered as representatives of assemblies of single-domain magnetite nanoparticles with transverse diameters D > 25 nm. The database is calculated at exciting frequency f = 4.9 GHz (S-band) to clarify the details of the FMR spectrum that depend on the particle magnetic anisotropy nature. The data obtained make it possible to analyze arbitrary combined FMR spectra constructed as weighted linear combinations of FMR spectra of the base assemblies. In addition, using a genetic algorithm, the corresponding inverse problem is solved. The latter consists in determining the volume fractions of the base assemblies in some arbitrary nanoparticle assembly, which is represented by its FMR spectrum.