A generalization of Snoek's law to ferromagnetic films and composites

The present paper establishes characteristics of the relative magnetic permeability spectrum $\mu$(f) of magnetic materials at microwave frequencies. The integral of the imaginary part of $\mu$(f) multiplied with the frequency f gives remarkable properties. A generalisation of Snoek's law consists in this quantity being bounded by the square of the saturation magnetization multiplied with a constant. While previous results have been obtained in the case of non-conductive materials, this work is a generalization to ferromagnetic materials and ferromagnetic-based composites with significant skin effect. The influence of truncating the summation to finite upper frequencies is investigated, and estimates associated to the finite summation are provided. It is established that, in practice, the integral does not depend on the damping model under consideration. Numerical experiments are performed in the exactly solvable case of ferromagnetic thin films with uniform magnetization, and these numerical experiments are found to confirm our theoretical results. Microwave permeability measurements on soft amorphous films are reported. The relation between the integral and the saturation magnetization is verified experimentally, and some practical applications of the theoretical results are introduced. The integral can be used to determine the average magnetization orientation in materials with complex configurations of the magnetization, and furthermore to demonstrate the accuracy of microwave measurement systems. For certain applications, such as electromagnetic compatibility or radar absorbing materials, the relations established herein provide useful indications for the design of efficient materials, and simple figures of merit to compare the properties measured on various materials

A laminate of ferromagnetic films with high effective permeability at high frequencies

The paper reports on development of magnetodielectric material with high microwave permeability. The material is a laminate of multi-layer permalloy films deposited onto a thin mylar substrate by magnetron sputtering. The deposited films are arranged into a stack and glued together under pressure to obtain the laminate. With the content of ferromagnetic component in the laminate being 22 % vol., its measured quasistatic permeability is 60. The peak value of imaginary permeability attains 50 and the peak is located near 1 GHz. As compared with the multi-layer films, which the laminate is made of, it exhibits lower magnetic loss tangent at frequencies below the magnetic loss peak and may therefore be useful for many technical applications. Lower low-frequency loss may be attributed to pressing of the glued sample. This rectifies wrinkling appearing due to sputtering of rigid multi-layer film onto flexible mylar substrate and, therefore, makes the magnetic structure of the film more uniform

Control over magnetic spectrum of multilayer magnetic film metamaterial

A RLC electric circuit with magnetic core is studied experimentally and theoretically as a promising design of a metamaterial cell. Laminates made of multilayered ferromagnetic films are used as the magnetic core. The wire coiled around the core allows the frequency dependence of permeability to be adjusted according to needs of a particular task by creating a region of intensive magnetic loss below the ferromagnetic resonance frequency of the bare core. The theoretic analysis is based on the quasi-statics of magnetic fields and electric currents. The intensity of the loss peak is proportional to the value of μ′2/μ″, where μ′ and μ″ are the frequency-dependent components of permeability of the core material. The magnetic spectra of cells with cores made of laminates of NiFe films and FeCo films have been measured. It is shown that the application of the winding allows the magnetic loss peak to be shifted from 1 GHz to 0.3 GHz for NiFe and from 5 GHz to 0.7 GHz for FeCo. The effective imaginary permeability at the resonant frequency increases by the factors of 5 and 6, correspondingly. The theory agrees well with the measured data

Metal-cluster ionization energy: A profile-insensitive exact expression for the size effect

The ionization energy of a large spherical metal cluster of radius R is I(R)=W+(+c)/R, where W is the bulk work function and c≈-0.1 is a material-dependent quantum correction to the electrostatic size effect. We present 'Koopmans' and 'displaced-profile change-in-self-consistent-field' expressions for W and c within the ordinary and stabilized-jellium models. These expressions are shown to be exact and equivalent when the exact density profile of a large neutral cluster is employed; these equivalences generalize the Budd-Vannimenus theorem. With an approximate profile obtained from a restricted variational calculation, the 'displaced-profile' expressions are the more accurate ones. This profile insensitivity is important, because it is not practical to extract c from solutions of the Kohn-Sham equations for small metal cluster