A free-space measurement set-up and a Born approximation model have been used to retrieve permittivity and permeability spatial distribution of heterogeneous media. Results for various magnetic and dielectric materials are presented to assess the validity of the method.

RCS issues lead to problems of hundreds of thousands of unknowns as soon as the target gets greater than the wavelength. For computational limiting reasons, details of the coating cannot thus be meshed, even if they play a key role like in metamaterial design. Equivalent boundary conditions or effective medium approximation are then necessary. In this paper we consider spheres with plasmonic coatings. Exact and approximated RCS computations are compared over a broad range of RF frequencies.

A new analysis method of the magnetization dispersion in a thin magnetic film is presented. It is based on the angular measurement of the permeability spectra and on the evaluation of the integral relation. It provides the average orientation of the magnetization in the layer and a dispersion parameter which quantifies the magnetic dispersion. The method is successfully applied on a soft CoNbZr 800nm magnetic layer which possesses a helical anisotropy profile. This helical profile is obtained by rotating continuously the sample during the sputtering deposition on a scale from R = 0 to 16 turns. The study reveals that, for about 1/2 turn, a maximal dispersion is achieved and, for more elevated rotation speed, the magnetization no longer follows the anisotropy profile but lines up along an easiest axis direction. The experimental data are well described by a one-dimensional micromagnetic model which takes both exchange coupling and a helical anisotropy into account. The analytical cases with an exchange constant null and infinite are also considered in order to gain more insight onto the observed magnetic behaviour in the soft magnetic thin film.

The static and dynamic properties of a soft magnetic layer presenting a helical anisotropy profile have been studied both experimentally and theoretically with the help of one-dimensional (1D) micromagnetic calculations. The aim is to investigate the possibility of achieving an evanescent anisotropy by randomizing the effective anisotropy thanks to a continuous rotation of the samples during a growth process. A general method to evaluate the magnetization dispersion based on the angular measurement of the complex permeability spectra and on the determination of the integral criterion is presented. The maximum randomization of the magnetization in Co86Nb10.5Zr3.5 layers is found for the sample rotated 1/2 turn. A significant decrease of the effective anisotropy from 15 to 7 Oe is obtained. The 1D simulations give a good explanation and description of the angular dispersive behavior of the magnetization observed as a function of the rotation speed imposed during growth. However, a discrepancy between measured and calculated resonance frequencies is observed and attributed to short-range fluctuations of the magnetization known as the ripplelike phenomenon. Compared to literature, this effect is particularly strong for a high rotation speed.

An experimental method is presented which allows to probe the shape of a magnetic domain wall. The method is based on the precession of the spin of neutrons traveling across the domain wall structure. This technique is experimentally demonstrated on a planar (half) Bloch wall created within the thickness of a soft magnetic film with in-plane crossed anisotropies.

We study soft magnetic bilayers having orthogonal, in-plane easy axes. The layers are thicker than the Bloch wall width linked to the anisotropy, so that a helical magnetization with a large angle exists across the sample thickness. The magnetic domains structure has been investigated at both sample surfaces, using magneto-optical microscopy. The domain structure is found to be similar to that of double films with biquadratic coupling. Two kinds of domain walls are identified, namely with a 90° and 180° rotation of the average magnetization. The detailed structure and energy of these walls are studied by micromagnetic calculations.

It has previously been shown that the quantity M-mu = 1/4 pi(gamma) over bar root 2/pi integral(infinity)(0) mu ''(f)fdf, called the "efficient dynamic magnetization", is a powerful tool for characterizing magnetic layers dedicated to microwave applications. It correlates the imaginary part of permeability and the magnetization distribution. This paper presents microwave permeability spectra of a Py/Ru/Py trilayer, which have been measured in the layer plane under an external magnetic static field (H-DC) using a single coil cell. The efficient dynamic magnetization versus H-DC was found to exhibit a significant decrease for 0 < H-DC < 5 Oe, and it is demonstrated that this decrease was induced by an optic mode excitation.

In ferromagnetic thin films, the effect of the magnetic anisotropy dispersion on the quasi-static susceptibility measured under a static magnetic field is shown. An approach is presented to estimate the anisotropy distribution both in angle and intensity from static and dynamical magnetic measurements. Because the transverse biased susceptibility is not fully described by the single anisotropy model, in particular for H ¿ HK, either a full magnetic anisotropy dispersion P(¿,HK) without exchange energy or a double anisotropy modeling coupled by the exchange energy are introduced to access the observed behavior. These two extreme magnetic configurations are discussed.

The static and dynamic magnetic properties of samples consisting of two soft magnetic layers with in-plane easy axes at right angles are studied by micromagnetics and experiments. A one-dimensional micromagnetic model is developed, and solved quasianalytically for statics and dynamics. In particular, it is shown that the magnetic permeability arises from a set of eigenmodes, each with a macrospin (or gyromagnetic) response, that are excited differently depending on ac field orientation. Experiments (magnetization curves, permeability under field and in several directions) on cobalt-based amorphous alloy bilayers are well reproduced by the model with a single set of parameters. Such samples are therefore model one-dimensional nonuniform magnetic systems, simple yet with a rich behavior, for statics and dynamics.

The microwave permeability of CoZr films with different thicknesses is investigated. While Landau–Lifschitz model accounts for the response of the thinnest samples, several peaks are observed on the permeability of thicker layers. A simple model commonly used to account for the permeability of layers in the presence of skin effect is compared to a more sophisticate model taking into account the exchange–conduction coupling. Both models are found to be equivalent. They fail to account for the observed high frequency peaks. Introducing pinning conditions at the interface reproduces qualitatively observed behavior, suggesting the presence of standing spinwaves.

Collections of magneto-mechanical oscillators are proposed as high permeability media. The permeability of these systems is investigated theoretically. It is shown that these systems are described by equations similar to that of gyromagnetism. The figures of merit of conventional soft permeable materials and of these magneto-mechanical systems are discussed.

The impedance of a planar coil suspended on a torsion beam and placed in a strong magnetic field is analyzed. It exhibits an inductive behavior with high inductance values. Numerical examples are provided for this "galavanometer type" inductor. An experimental demonstration of a magneto-mechanical system with high inductance is also shown. Potential applications and limitations are discussed

The high frequency permeability of two types of artificial materials are investigated. Composites made of ferromagnetic wires and conductive wires have been manufactured, and their microwave properties have been investigated. Experimental results are reported, and a model is proposed that accounts for the observations. It is underlined that textile technology is very attractive and cost-effective to manufacture metamaterials. The permeability of systems composed of magneto-mechanical oscillators has been investigated theoretically. It has been shown that these systems are described by equations similar to that of gyromagnetism. The figure of merits of conventional soft permeable materials and of these magneto-mechanical systems is discussed.

Ferromagnetic materials are of great interest today for high frequency applications in microelectronics (M-RAMs, planar inductors, etc.) or magnetic recording systems, taking advantage of the high levels of saturation magnetization of ferromagnetics. We are presenting a setup permitting permeability measurements from 10 MHz up to 6 GHz in the 77–400 K temperature range. An existing single-coil perturbation technique is modified to allow precise and accurate microwave measurements. An experimental validation of the technique is performed. Measurements on a CoFeSiB thin film are presented. The clear effect of the temperature on the whole permeability spectra is shown for soft ferromagnetic thin films, including CoNbZr.

We establish in a fairly general case that the integral of the imaginary permeability times the frequency is bounded by a quantity related to the square of the saturation magnetization. Experimental results obtained on a variety of bulk and composite materials are in agreement with this relation.

A new method to measure the microwave permeability of ferromagnetic thin film or microwires from 50 MHz up to 18 GHz is presented. In contrast with all previous permeameters based on perturbation techniques, our permeameter does not require any reference sample for calibration, which is a definite advantage, as it is very difficult to have a reference magnetic sample of known permeability. In our technique, a network analyzer detects the small perturbation of the impedance of a coaxial line cell loaded by the magnetic sample. Satisfactory sensitivity is achieved, even for magnetic volume fraction as low as 10−4. To assess the validity of this new technique, comparisons are performed with three other methods on different samples, in particular on ferromagnetic wires. It is shown that in the case of very soft magnetic materials, the shape of the sample affects the permeability measured with a conventional permeameter.

Different effective-medium theories (EMT's) are used to describe the high-frequency and optical properties of composite materials. However, these theories reveal not only differences in the evaluation of the effective permeability and permittivity, but also in their definitions. Rytov gave definitions of the effective permeability and permittivity that are clearly incompatible with the extended Bruggeman definitions when the skin effect occurs. An analysis of the exactly solvable case of a lamellar composite is performed using both approaches. Since most experimental determinations of the permeability and permittivity of composites rely on reflection-transmission measurements, it is of foremost importance to determine which definitions of the permeability and permittivity should be used to express the Fresnel coefficients under the conventional farm. For that purpose, we derive the reflection and transmission coefficients at an interface between a composite material and the air, without any effective-medium hypothesis for the composite. This derivation is performed on a periodic composite containing conducting inclusions separated by a dielectric plane. We point out that in the interface region, evanescent modes are present and cannot be described by an effective-medium approach. We infer the proper definitions of the permeability and the permittivity of a composite from the expression of the Fresnel coefficients and from the expression of the refractive index of the propagative mode. We show that the extended Bruggeman definitions are basically correct, but that small correction terms due to the modes at the interface should be taken into account in some cases. A numerical example is given to show these interface effects. An experimental result is also presented. It illustrates that the permeability determined from reflection-transmission measurement disagrees with the definitions given by Rytov but agrees with our definitions.