Simple boundary element method for three-dimensional magnetostatic problems

For numerical solution of three-dimensional magnetostatic problems the applications of finite-difference (FDM) and finite-element (FEM) methods require long calculating time and large storage capacity. In some cases these requirements can be reduced by the use of boundary element methods (BEM). A simple boundary element solution, and its application to the calculation of magnetization and stray fields of magnetic bodies, is described. The results are compared with experimental stray-field measurements performed using a vibrating pick-up loop magnetometer with high geometrical resolution [14].     

Magnetization Properties of Microstructured NiFe Rings Investigated Using Semiconductor/Ferromagnet Hybrid Structures

Magnetization reversal processes in microstructured NiFe rings are studied by fringe-field-induced local Hall magnetometry. This semiconductor-based technique yields a high sensitivity of magnetic stray fields and allows us to detect magnetization hysteresis loops of single NiFe rings. The transition fields can be controlled by the ratio between inner- and outer-ring diameter. Comparison between Hall measurements and numerical simulation suggests that there are four different magnetization states in two integrated rings.

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Weak Delocalization in Graphene on a Ferromagnetic Insulating Film

Graphene has been predicted to develop a magnetic moment by proximity effect when placed on a ferromagnetic film, a promise that could open exciting possibilities in the fields of spintronics and magnetic data recording. In this work, the interplay between the magnetoresistance of graphene and the magnetization of an underlying ferromagnetic insulating film is studied in detail. A clear correlation between both magnitudes is observed but through a careful modeling of the magnetization and the weak localization measurements, that such correspondence can be explained by the effects of the magnetic stray fields arising from the ferromagnetic insulator is found. The results emphasize the complexity arising at the interface between magnetic and 2D materials.     

Quantitative Imaging of the Magnetic Configuration of Modulated Nanostructures by Electron Holography

By means of off‐axis electron holography the local distribution of the magnetic induction within and around a poly‐crystalline Permalloy (Ni₈₁Fe₁₉) thin film is studied. In addition the stray field above the sample is measured by magnetic force microscopy on a larger area. The film is deposited on a periodically nanostructured (rippled) Si substrate, which was formed by Xe⁺ ion beam erosion. This introduces the periodical ripple shape to the Permalloy film. The created ripple morphology is expected to modify the magnetization distribution within the Permalloy and to induce dipolar stray fields. These stray fields play an important role in spinwave dynamics of periodic nanostructures like magnonic crystals. Micromagnetic simulations estimate those stray fields in the order of only 10 mT. Consequently, their experimental determination at nanometer spatial resolution is highly demanding and requires advanced acquisition and reconstruction techniques such as electron holography. The reconstructed magnetic phase images show the magnetized thin film, in which the magnetization direction follows mainly the given morphology. Furthermore, a closer look to the Permalloy/carbon interface reveals stray fields at the detection limit of the method in the order of 10 mT, which is in qualitative agreement with the micromagnetic simulations.     

Using a Single Toroidal Sample to Determine the Intrinsic Complex Permeability and Permittivity of Mn–Zn Ferrites

Analysis of the principle of the published lumped circuit methods for determination of the intrinsic complex permeability and permittivity of the Mn-Zn ferrites reveals that as long as the electric and the magnetic field distributions in the core(s) in two measurements are different, the two intrinsic values can be determined. Using this principle, we developed a set of general lumped circuit methods based on a toroidal Mn-Zn ferrite core as the measurement sample. We examined two possible different excitation modes: magnetic field excitation and electric field excitation. The two different excitation modes result in significantly different field distributions in the sample. Thus, high accuracy can be guaranteed in principle. For the magnetic field excitation, we present in this paper a general finite-difference method to solve the fields in the core and the impedance of the ferrite core inductor. To avoid the stray capacitance among the coils of the ferrite core winding inductor in the measurement, we made a set of short-ended coaxial test fixtures. We performed experiments to determine the intrinsic complex permeability and permittivity of a Mn-Zn ferrite core up to 10 MHz by using the two general methods and validated the measured intrinsic values experimentally.     

Electromagnetic control of convective heat transfer during electron beam evaporation: model experiments

The present paper aims to demonstrate that melt-flow during electron beam evaporation can be effectively controlled by using external magnetic fields to considerably reduce the convective heat transfer. We discuss the various effects of a static magnetic field, a static field combined with an applied electrical current, and a rotating magnetic field. We perform model experiments using GaInSn in eutectic composition as a test liquid. The liquid metal is heated locally at its free surface by an electric resistance heater. The results of the measurements are compared to prediction of numerical simulations.     

Recording with magnetic bubbles

We propose to use the stray field of a magnetic domain (e.g, a bubble) for magnetic recording. It is shown that these stray fields are large enough to write information into a conventional disc or tape. An experiment in which an audio signal is recorded on a conventional tape with the aid of a stripe domain is described. We consider the feasibility of an integrated recording head for "one head per track recording" by using a multitude of bubbles in one crystal plate as well as the possibility of realizing a scanning head for video recording. Our preliminary experiments demonstrate the feasibility of recording based on this new principle.     

Control of domain wall pinning in ferromagnetic nanowires by magnetic stray fields

We have found that the depinning field of domain walls (DWs) in permalloy (Ni(81)Fe(19)) nanowires can be experimentally controlled by interactions between magnetic stray fields and artificial constrictions. A pinning geometry that consists of a notch and a nanobar is considered, where a DW traveling in the nanowire is pinned by the notch with a nanobar vertical to it. We have found that the direction of magnetization of the nanobar affects the shape and local energy minimum of the potential landscape experienced by the DW; therefore, the pinning strength strongly depends on the interaction of the magnetic stray field from the nanobar with the external pinning force of the notch. The mechanism of this pinning behavior is applied for the instant and flexible control of the pinning strength with respect to various DW motions in DW-mediated magnetic memory devices.     

Magnetic properties of thin-film Co/Fe/Ni magnetic systems

The magnetic properties of Co/Fe/Ni thin-film structures grown by magnetron sputtering have been studied using magnetooptical techniques. The results of x-ray diffraction measurements showed that all samples possessed a nanocrystalline structure. The magnetization curves and hysteresis loops were measured using the equatorial Kerr effect for two orientations of the external magnetic field. It is established that the Co/Fe/Ni thinfilm structures exhibit a planar magnetic anisotropy. The magnetic behavior of each layer in the initial inhomogeneous Co/Fe/Ni structure is substantially influenced by stray fields of the adjacent layers. This circumstance accounts for the complex shapes of hysteresis loops. The annealing in vacuum at T = 500°C renders Co/Fe/Ni thin-film structures magnetically hard compared to the initial state. The experimental results are explained by certain features of the microstructure of samples.     

Decoding of digital magnetic recording with longitudinal magnetization of a tape from a magneto-optical image of stray fields

For digital magnetic recording of encoded information with longitudinal magnetization of the tape, the connection between the domain structure of a storage medium and magneto-optical image of its stray fields obtained using a magnetic film with a perpendicular anisotropy and a large Faraday rotation has been studied. For two-frequency binary code without returning to zero, an algorithm is developed, that allows uniquely decoding of the information recorded on the tape based on analysis of an image of stray fields.     

Determination of stray light at the PTB goniophotometer facility

For improved luminous flux measurements, the Physikalisch-Technische Bundesanstalt (PTB) was equipped with a new robotic goniophotometer. In order to characterize this instrument, to reduce the combined measurement uncertainty, and to determine the respective uncertainty components, the influence of stray light on the measurement results was investigated. Considering the specific structure of the robotic goniophotometer, stray light was measured on-line by means of a purpose-built “back-looking” photometer. By this means, the influence of the luminous intensity distribution of each individual light source with regard to its stray light could be considered. Before the first experimental application, the invented procedure was tested by means of calculations using mathematical models. In this paper, the mathematical model for the calculation of stray light in the goniophotometer room is presented together with the calculation results and the results of the first measurements. The achieved results indicate that the recommended stray light measurements can decrease the total relative standard measurement uncertainty of luminous flux measurements down to 2 × 10⁻³.     

Symplectic Finite-Difference Time-Domain Method for Maxwell Equations

We introduce a symplectic finite-difference time-domain method for electromagnetic field simulation. Our method can successfully solve Maxwell equations involving conductor loss, which cannot be solved by the symplectic integration methods that have been presented in previous works. A class of high-order symplectic schemes for computing the time-dependent electric and magnetic fields are derived on the basis of an s-stage symplectic partitioned Runge–Kutta method. We present numerical results to illustrate the validity and accuracy of the algorithm.     

Integral analysis of a magnetic field for an arbitrary geometry coil with rectangular cross section

The integral method can effectively analyze magnetic fields, but the traditional integral method can analyze only coils with regular geometries. Therefore, a new integral method was developed to calculate the three-dimensional (3-D) magnetic field created by an arbitrary geometry coil with a rectangular cross section using the local coordinate method and a 3-D coordinate transformation. However, when the field points are on the surface of the coil or the basic segment is the right angle trapezoidal prism, singularities occur that make the numerical analysis of the magnetic field more difficult. Thus, we present here some mathematical methods to eliminate the singularities to allow accurate numerical analysis of the magnetic field. We validate the integral method by comparing it with the analytical solutions for regular geometry coils.     

Optimizing active and passive magnetic shields in induction heating by a genetic algorithm

This paper presents a method for designing optimal passive and active shields for axisymmetric induction heaters. Such shields are needed to protect human operators and external electronic equipment from stray magnetic fields. The method uses a genetic algorithm (GA) to minimize an objective function. This function reduces the magnetic field in the target area, the power dissipation in the active and passive shields, and the influence of the shields on the heating process. The GA returns the position and height of the passive shield, the optimal current for the active shield, and the number of turns of all coils. The paper describes two optimization modes: 1) optimization of only the active shield with fixed passive shield and 2) global optimization of both active and passive shields. Several passive shields are studied: electrically conductive shields and both electrically and magnetically conductive shields. The field reduction depends on the optimization mode and the passive shield properties, but always exceeds 25 dB for combined active and passive shields. Finally, the paper compares the results of the simulations to experimental measurements.     

Lateral Magnetic Near‐Field Imaging of Plasmonic Nanoantennas With Increasing Complexity

The design of many promising, newly emerging classes of photonic metamaterials and subwavelength confinement structures requires detailed knowledge and understanding of the electromagnetic near‐field interactions between their building blocks. While the electric field distributions and, respectively, the electric interactions of different nanostructures can be routinely measured, for example, by scattering near‐field microscopy, only recently experimental methods for imaging the magnetic field distributions became available. In this paper, we provide direct experimental maps of the lateral magnetic near‐field distributions of variously shaped plasmonic nanoantennas by using hollow‐pyramid aperture scanning near‐field optical microscopy (SNOM). We study both simple plasmonic nanoresonators, such as bars, disks, rings and more complex antennas. For the studied structures, the magnetic near‐field distributions of the complex resonators have been found to be a superposition of the magnetic near‐fields of the individual constituting elements. These experimental results, explained and validated by numerical simulations, open new possibilities for engineering and characterization of complex plasmonic antennas with increased functionality.     

Magnetic properties and noise in cylindrical Permalloy thin-film magnetometers

The magnetic properties and low-frequency noise measurements of thin films of Permalloy are described. The films are obtained by electrodeposition. They are polycrystalline and single domain. The noise due to the film is shown to be an increasing function of the dispersion angle α90. A model for the noise mechanism taking into account the magnetostatic stray field arising in the grain boundaries and the thermal agitation energy is given. It is in qualitative agreement with the experimental results.     

Influence of the Microstructure on Magnetic Stray Fields of Low-Carbon Steel Welds

This study examines the relationship between the magnetic mesostructure with the microstructure of low carbon steel tungsten inert gas welds. Optical microscopy revealed variation in the microstructure of the parent material, in the heat affected and fusion zones, correlating with distinctive changes in the local magnetic stray fields measured with high spatial resolution giant magneto resistance sensors. In the vicinity of the heat affected zone high residual stresses were found using neutron diffraction. Notably, the gradients of von Mises stress and triaxial magnetic stray field modulus follow the same tendency transverse to the weld. In contrast, micro-X-ray fluorescence characterization indicated that local changes in element composition had no independent effect on magnetic stray fields.     

Ionization kinetics in a supersonic xenon plasma flow entering electric field

We have studied xenon plasma moving in a supersonic diffuser in external electric and magnetic fields. The main physical parameters of the plasma (electron temperature and density) were determined using specially developed methods based on the theory of continuous optical emission from inert gas atoms. These experimental data are compared to the results of theoretical calculations. Based on an analysis of the results of spectroscopic measurements, a mechanism of plasma ionization is established which is capable of maintaining a high degree of ionization in the supersonic xenon plasma flow.     

Ginzburg–Landau Study of Superconductor with Regular Pinning Array

The vortex distributions and dynamics in superconductors with triangular and honeycomb pinning arrays are investigated by numerical simulation of the two- dimensional (2-D) time-dependent Ginzburg–Landau equations. Periodic boundary conditions are implemented through specific gauge transformations under lattice translations. We model the pinning sites as holes. The simulation results at different magnetic fields are presented. For film with regular triangular pinning array, the vortices are all captured within the holes for a wide range of magnetic fields. For film with regular honeycomb pinning array, the interstitial vortices appear at relatively low magnetic fields. With an increase of magnetic field, the new vortices may enter the holes again and keep the number of vortices at the interstitial positions unchanged. These results confirm our explanations of the experimental results we obtained earlier.