Tuning Dynamic Susceptibility in Barium Hexaferrite Core–Shell Nanoparticles through Size-Dependent Resonance Modes

M-type hexagonal ferrites present compelling prospects for the design of high-performance multifunctional absorbers operating within the Ku, K, and Ka frequency ranges, spanning 12 to 40 GHz at a zero-applied magnetic field. While it is widely acknowledged that the operational frequency of this compound can be manipulated through chemical substitution, the ongoing challenge lies in achieving precise control over the absorption bandwidth via the spectral line width of its dynamic susceptibility. For this purpose, we investigate by means of micromagnetic simulations core–shell nanoparticles with an M-type hexagonal ferrite shell grown on top of a nonmagnetic core. This configuration allows the modulation of the number and the frequency of the resonance modes only by controlling the thickness and the size of the ferrite magnetic shell. This phenomenon is produced at microwave frequencies for relatively large particles (external diameter from 150 to 500 nm) and produces supplementary resonance peaks at amplitudes comparable to the main ferromagnetic mode of a solid sphere. The study of the magnetization dynamics of these size-dependent modes confirmed their nature as essentially exchange resonance modes. The limitations of available analytical models for describing the behavior of such modes in hollow spheres are highlighted. As for most commercial applications, these properties are present at a zero-applied magnetic field, and the simulations performed evidence that the system is resistant to experimental deviations.