Simulation of the AC susceptibility for a core-shell magnetic nanoparticle

A core-shell structure magnetic nanoparticle model with Heisenberg exchange interaction and vertical surface anisotropy is established. The anisotropy of the internal spins is D1 and the anisotropy of the surface spins is D2, both along the z axis. The surface spins also have surface anisotropy D3, and the direction is along the particle radius. The dynamic process of spins in particle is described by Landau Lifshitz Gilbert (LLG) equation, and the AC susceptibility of the nanoparticle is calculated. It is found that in the absence of external DC magnetic field, with the change of surface vertical anisotropy of the shell, there may be a new resonance peak in the AC susceptibility of the system in addition to the two resonance peaks corresponding to core and shell anisotropies respectively. The contribution of surface spins to the resonance peaks of the system is analyzed. When the external magnetic field is applied along the z direction, it is found that with the increase of the external magnetic field, all resonance peaks move to the high frequency direction. However, when an external magnetic field is applied in a direction 4 pi /9 from the z axis, the positions of the resonance peaks are almost unchanged with the different DC fields increasing. When the angle between a DC field with a constant strength and the direction of z axis of the particle gradually increases, there are many resonance peaks in AC susceptibility, and all resonance peaks move to the low frequency direction.

Automated summary

A core-shell structure of magnetic nanoparticles with Heisenberg exchange interaction and vertical surface anisotropy has been studied. The dynamic behavior of the nanoparticle's spins was described using the Landau Lifshitz Gilbert equation, and the AC susceptibility was calculated. It was found that the system exhibits new resonance peaks in the absence of an external DC magnetic field, due to changes in the surface vertical anisotropy. The position of the resonance peaks was influenced by the applied external magnetic field and the angle between the DC field and the z-axis of the particle.