Calculation of complex permeability of magnetic composite materials using ferromagnetic resonance model

Abstract

The Landau–Lifshitz–Gilbert (LL-G) formula has been widely used in modeling of complex permeability of magnetic thin films and particle composites. In this paper, a approach which is based on Landau–Lifshitz ferromagnetic resonance (LL-FMR) model has been developed to calculate the complex permeability of magnetic particles/insulator matrix composite. It has found that the LL-FMR model can be used to compute the intrinsic permeability of a magnetic particle with different alignments of its magnetic domains with the respect to the incident wave. Through integration with respect to its resonant frequency, this method offers a neat closed-form formula for the case of isotropic composite. Its results compared relatively well with our previous method which computes the isotropic permeability by taking the average of the permeability of a large number of randomly oriented magnetic domains with respect to incident wave based on the LL-G model. For carbonyl bcc-Fe and Fe3O4, the calculated permeability agrees relatively well with the measurement results.

Applications of exchange coupled bi-magnetic hard/soft and soft/hard magnetic core/shell nanoparticles

“…Thus, although larger H A leads to high resonance frequencies, it also results in lower µ' and µ''. Notably, for more complex materials such as core/shell nanoparticles embedded in a non-magnetic medium the analytical expressions of µ' and µ'' can be rather complex [333][334][335]. Some of the limitations of hard ferrites stem from the so-called Snoek's limit, where the permeability and the resonance frequency are limited by the saturation magnetization, i.e., µ FMR = 2M S α/3 [336].…”

Frequency-dependent effective permeability tensor of unsaturated polycrystalline ferrites

“…In the demagnetized state m = 0, µ e z is the volume addition of both the permeability of the domain and domain-wall by reason of the superposition of the z-component of the magnetic induction in all media. When κ e = 0, µ e is the solution of a single equation in (13) which is written directly in a third-order polynomial form…”

“…Derivation of non diagonal permeability tensors for magnetized granular composites has been then reported 11 and several models for the calculation of complex permeability of magnetic composite materials have been proposed 12,13 . By using the EMA, even the influence of porosity induced by non-magnetic inclusions in magnetized heterogeneous materials has been computed 14 .…”

Effect of carbon shell thickness on the microwave absorption of magnetite-carbon core-shell nanoparticles

“…In the current research, the matching of the microwave permeability spectra with the model suggested by Neo et al [19] and the Rousselle effective medium theory [20] were investigated. The experimental data (solid lines) and curve-fitted values (dotted lines) are shown in Fig.…”

“…Based on the Neo model, the microwave permeability is a scalar when there is no external field. This scalar permeability can be obtained from the following equations for an arbitrary domain [19,21,22]: in which ω m ¼ 2πγM S , ω 0 ¼2πγH a , γ¼2.8 MHz/Oe, α is the damping factor, H a is the anisotropy field and ω¼2πf [24]. The scalar permeability can be determined by integrating over all domains for a demagnetized polycrystalline magnetic material.…”