Probabilistic model of microwave magnetic resonance in $3D$-magnetic nanocomposites from opal matrices

The authors have developed a unique probabilistic model of microwave ferromagnetic resonance (FMR) in $3D$ magnetic opal nanocomposites taking into account normal distribution of a random value $H_r$ of FMR magnetic field of nanoparticles. To simulate the random value $H_r$ the researchers use a random-number generator. The bias field dependences of the expectation values of random values $Re\mu^\Sigma$, $Im\mu^\Sigma$, $Re\mu_a^\Sigma$, $Im\mu_a^\Sigma$ (the real and imaginary parts of complex diagonal $\mu^\Sigma$ and off-diagonal $\mu_a^\Sigma$ components of the effective permeability tensor for the $3D$ $Ni_{0,7}Zn_{0,3}Fe_{2}O_{4}$ particles-containing opal nanocomposites were obtained at a frequency $f = 26$ GHz for different values of damping parameter $\alpha$ of magnetic nanoparticles and the standard deviation of the random value $H_r$ of the FMR magnetic field, determined by strucrure types of nanocomposites.