Simulations of High-Frequency Magnetic Properties of Ferromagnetic Nanoparticles with Magnetic Interactions

In this work, the microwave permeability of iron-cobalt magnetic alloy nanoparticles was simulated in the range of 2–18 GHz based on the micromagnetic method. To study the dependence of dynamic permeability on nanoparticle interactions, the equivalent model of two identical nanoparticles with a distance range of 10–30 nm under an external magnetic field pulse was established by using three-dimensional micromagnetic simulation. The results show that as the nanoparticle distance gradually decreases, the permeability value in general shows an increasing trend. Also, the dynamical magnetization component along the magnetic field direction decreases from 1620 A/m to 1340 A/m as the nanoparticle distance decreases. In addition, the Gibbs free energy analyses indicate that the change of exchange energy and demagnetization energy of the system is caused by the nanoparticle interactions with a shorter distance, destroying the initial steady magnetization distribution, which makes the decrease of the total free energy by about 0.36%, resulting in the increase of high-frequency permeability. Moreover, the damping factor in the range of 0.3–0.7 has a crucial effect on the calculated high-frequency permeability.