Electrodynamic model and calculation of the effective permeability tensor for 3D magnetic opal-based nanocomposites at microwaves

The electrodynamic model of propagating of electromagnetic waves in 3D magnetic opal nanocomposites based on the solution of the Maxwell´s equations with electrodynamic boundary conditions, complemented by the Landau-Lifshitz equation with the exchange term is developed by using the decomposition approach on autonomous blocks with Floquet channels. By solving the system of quasi-simultaneous equations the real and imaginary parts of the diagonal and off-diagonal components of the effective permeability tensor of the Ni_0.7Zn_0.3Fe₂O₄ particles-containing magnetic opal as a function of DC magnetic field were calculated at a frequency f=26 GHz. The results of simulation taking into account the different number of ferromagnetic spherical nanoparticles, filling the octahedral SiO₂ opal void regions, for the constant value of the filling factor show good agreement with the experimental data.