We describe a method of extrapolation based on a truncated Kramers-Kronig relation for the complex permittivity ($epsilon$) and permeability ($mu$) parameters of a material, based on finite frequency data. Considering a few assumptions, such as the b
ehavior of the loss tangent and the overall nature of corrections, the method is robust within a small relative error, if the assumed hypotheses hold at the extrapolated frequency range.
This paper presents the results of simulations of the magnetization field {it ac} response (at $2$ to $12$ GHz) of various submicron ferrite particles (cylindrical dots). The ferrites in the present simulations have the spinel structure, expressed he
re by M$_{1-n}$Zn$_{n}$Fe$_2$O$_4$ (where M stands for a divalent metal), and the parameters chosen were the following: (a) for $n=0$: M = { Fe, Mn, Co, Ni, Mg, Cu }; (b) for $n=0.1$: M = { Fe, Mg } (mixed ferrites). These runs represent full 3D micromagnetic (one-particle) ferrite simulations. We find evidences of confined spin waves in all simulations, as well as a complex behavior nearby the main resonance peak in the case of the M = { Mg, Cu } ferrites. A comparison of the $n=0$ and $n=0.1$ cases for fixed M reveals a significant change in the spectra in M = Mg ferrites, but only a minor change in the M = Fe case. An additional larger scale simulation of a $3$ by $3$ particle array was performed using similar conditions of the Fe$_3$O$_4$ (magnetite; $n=0$, M = Fe) one-particle simulation. We find that the main resonance peak of the Fe$_3$O$_4$ one-particle simulation is disfigured in the corresponding 3 by 3 particle simulation, indicating the extent to which dipolar interactions are able to affect the main resonance peak in that magnetic compound.
