Approach of a digital twin for the high-frequency dynamics (FMR) of arbitrarily shaped, symmetric ferromagnetic polycrystalline samples

Soft polycrystalline ferro- or ferrimagnetic materials of arbitrary but symmetrical shape, which form their static magnetisation behaviour according to the demagnetisation Tensor N, were theoretically described in terms of their high-frequency dynamics and precession damping of the magnetic moments on the dependence of their microstructure, i.e., the grain size in association with the magneto-crystalline anisotropy. As the basic equation the Landau-Lifschitz-Gilbert (LLG) differential equation was used, in order to establish a general solution which expresses the frequency-dependent magnetisation, magnetic susceptibility χ(f) and permeability μ(f) spectra. By means of two examples, films and spherules, we present the dynamics when exposed to a high-frequency wave by taking parameters like the resistivity ρ_m, magneto-crystalline coefficient K₁, uniaxial anisotropy H_u, grain size D_grain, thickness t_m, diameter d and eddy-current generation into account. Damping of the magnetic spins is conspicuous by regarding the full width at half maximum (FWHM) of the frequency-dependent imaginary part of the permeability, and in this connection, the effective damping parameter α_eff which represents intrinsic as well as extrinsic damping mechanisms. In the papeŕs context, the latter are caused by grains of various size and generate energy dissipating two-magnon scattering.

The goal is to make a first step of an approach for a digital twin which ought to allow the prediction of the dynamic behaviour of ferromagnetic components. They are employed in r.f. devices like cores in (micro) inductors, memory storage devices, etc. or used for basic magnetisation dynamics research. The calculations were conducted by availing the mathematical program MAPLE. Various shapes and parameters now enable to conceive a variety of r.f. components and their very properties.