Calculation of the magnetic susceptibility of yttrium iron garnet films with linear structural defects such as straight-through crack in an external magnetic field

The authors propose the method of calculating the scattering field and its linear characteristics of nanoscale defects in ferromagnetic films on the basis of the Hubbard model which describes the movement of electrons on the grid and the local Coulomb interaction when they are on the same node. Yttrium iron garnet (YIG) in the form of single crystals and epitaxial films is the most important for practical applications. We use the strong coupling approximation for the calculation of the yttrium iron garnet films magnetic susceptibility. We obtained the analytical expression for the dynamic magnetic susceptibility in the random phase approximation. Longitudinal and transverse dynamics of magnetic susceptibility of quasi thin films containing linear defects was calculated. Distributions of the magnetic susceptibility were analyzed in the films of yttrium iron garnet with a linear structural defect such as straight-through crack. Distribution of magnetic susceptibility was analyzed for YIG films without defects, and for films with defects of varying widths. The yttrium iron garnet crystal lattice can be approximately considered as cubic. The dependence of the longitudinal dynamic magnetic susceptibility of the coordinates was obtained using the Fourier transform. Simulation for different spatial arrangement of linear structural defect such as straight-through crack in YIG films was produced. The influence of the geometric dimensions of the ferromagnetic films was investigated according to the characteristics of the stray field.