The effect of nonlocal conductivity on the transmission of microwave radiation through ferromagnetic metals in the field-normal configuration

1986 ◽  
Vol 64 (7) ◽  
pp. 796-821 ◽  
Author(s):  
K. B. Urquhart ◽  
J. F. Cochran
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Microwave Radiation ◽  
Mean Free Path ◽  
Skin Depth ◽  
Charge Carriers ◽  
Surface Scattering ◽  
Field Distributions ◽  
Wide Range ◽  
Diffuse Surface

Procedures are described for the numerical calculation of the electric-field distributions generated in a model ferromagnetic metal slab of thickness d by incident microwave radiation when a static magnetic field is directed along the slab normal and the mean free path ℓ of the charge carriers becomes comparable to, or greater than, the skin depth δ. The model metal is characterized by a local, frequency-dependent permeability; a spherical Fermi surface; and a nonlocal relationship between the current density and the electric-field distribution. The two limiting cases of specular and diffuse scattering of the charge carriers at the slab faces are considered. Electric-field distributions, transmission amplitudes, and surface impedances have been calculated for a wide range of ℓ and d using parameters that simulate nickel. For diffuse surface scattering, the transmission of the magnetically active mode increases at both ferromagnetic resonance (FMR) and cyclotron resonance (CR). A most striking result is the total absence of structure in the magnetic-field dependence of the transmission amplitude near fields corresponding to FMR or to CR for the case of specular scattering. It is demonstrated that very simple formulae provide a good estimate of the free-space transmission amplitudes for both specular and diffuse surface scattering when [Formula: see text] and d/ℓ ≥ 1.

Note on the surface impedance and the transmission of radiation through metal slabs

1970 ◽  
Vol 48 (3) ◽  
pp. 370-375 ◽  
Author(s):  
J. F. Cochran
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Surface Impedance ◽  
Uniform Magnetic Field ◽  
Electric Field Distribution ◽  
Skin Depth ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Field Distributions ◽  
Simple Boundary

An arbitrary electric field distribution in a metal slab in a uniform magnetic field can be written as a linear combination of four functions each of which satisfies Maxwell's equations for particularly simple boundary conditions. In particular, if the slab is thick compared with the skin depth of the radiation, δ, and if (ω/c)δ « 1, then the reflection and transmission coefficients for the slab are proportional to Gx(0), Gy(0), Gx(d), Gy(d) respectively, where Gx(z), Gy(z) are the electric field distributions generated in a slab bounded by the planes z = 0, z = d by a unit alternating magnetic field applied to the surface z = 0 and directed along y.

DETERMINATION OF THE ELECTRICAL CONDUCTIVITY OF THE SEA BED IN SHALLOW WATERS

Geophysics ◽  
1968 ◽  
Vol 33 (6) ◽  
pp. 995-1003 ◽  
Author(s):  
Peter R. Bannister
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Sea Water ◽  
Field Measurements ◽  
Bottom Layer ◽  
Dipole Antenna ◽  
Skin Depth ◽  
Noise Component ◽  
Sea Bed ◽  
Magnetic Field Measurements

The electric and magnetic field components produced by horizontal dipole antennas (both electric and magnetic) located within the upper layer of a two‐layer conducting earth are derived for the quasi‐near range. This range is defined as that in which the measurement distance is much greater than an earth skin depth but much less than a free‐space wavelength. Ionospheric effects are neglected. It is assumed that the transmitting and receiving anterenna depths are much less than their horizontal separation, and that the fields in the horizontal direction vary only slightly in a distance of one skin depth. It is well known that if the conductivity and thickness of the first layer (sea water) are known, the conductivity of the bottom layer (the sea bed) may be determined from magnetic field measurements alone. However, when extremely low‐frequency magnetic field measurements are performed at sea, the movement of the magnetic field sensors in the static magnetic field of the earth (which is many times stronger than the field to be measured) introduces a very strong noise component. It is argued that electric field measurements are preferable because the induced noise component is smaller. It is shown that the sea bed conductivity may be determined by measuring only the horizontal electric field components produced by a subsurface horizontal magnetic dipole antenna.

scholarly journals GRAPHENE: KINKS, SUPERLATTICES, LANDAU LEVELS AND MAGNETOTRANSPORT

2012 ◽  
Vol 26 (21) ◽  
pp. 1242007 ◽  
Author(s):  
MATTHEW KILLI ◽  
SI WU ◽  
ARUN PARAMEKANTI
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Bilayer Graphene ◽  
Landau Levels ◽  
Monolayer Graphene ◽  
Dirac Fermion ◽  
Type Device ◽  
Wide Range ◽  
Switching Type ◽  
Device Applications

We review recent work on superlattices in monolayer and bilayer graphene. We highlight the role of the quasiparticle chirality in generating new Dirac fermion modes with tunable anisotropic velocities in one dimensional (1D) superlattices in both monolayer and bilayer graphene. We discuss the structure of the Landau levels and magnetotransport in such superlattices over a wide range of perpendicular (orbital) magnetic fields. In monolayer graphene, we show that an orbital magnetic field can reverse the anisotropy of the transport imposed by the superlattice potential, suggesting possible switching-type device applications. We also consider topological modes localized at a kink in an electric field applied perpendicular to bilayer graphene, and show how interactions convert these modes into a two-band Luttinger liquid with tunable Luttinger parameters. The band structures of electric field superlattices in bilayer graphene (with or without a magnetic field) are shown to arise naturally from a coupled array of such topological modes. We briefly review some bandstructure results for 2D superlattices. We conclude with a discussion of recent tunneling and transport experiments and point out open issues.

The oscillatory galvanomagnetic size-effect in multilayered structures

Open Physics ◽  
2007 ◽  
Vol 5 (1) ◽  
Author(s):  
Leonid Dekhtyaruk
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electron Scattering ◽  
Oscillation Amplitude ◽  
Mean Free Path ◽  
Transverse Magnetic ◽  
Multilayered Structures ◽  
Adjacent Layer ◽  
Wide Range ◽  
Electron Mean Free Path

AbstractWithin the framework of the modified semi-classical Fuchs-Sondheimer model, we investigated theoretically the electrical resistivity of multilayered structures (MLS) consisting of alternating metallic layers (of different purity and different thicknesses) in a transverse magnetic field as functions of the ratio of the adjacent layer thicknesses and the magnetic field value. We have derived both a general formula (valid at arbitrary values of layer thicknesses) and asymptotic expressions that are valid when metallic layers are thick or thin compared with the electron mean free path. We found a non-monotonic behavior in the resistivity vs. the value of an applied magnetic field. As we demonstrated, this behavior is sensitive to the characteristics of the electron scattering in the interlayer interfaces in low magnetic fields. Moreover, the MLS resistivity oscillates in high magnetic fields with the field value (or with the layer thicknesses). The oscillation includes the harmonics that correspond both to the each layer thicknesses and the total thickness. The intensity of the oscillation is determined by the diffusive electron scattering in the interfaces, and the oscillation amplitude is proportional to the coefficient of the electron transmission through the interlayer interfaces. We have calculated numerically the resistivity in a wide range of fields and layer thicknesses at various values of the parameters of the interface and bulk electron scattering.

Thin-skin electromagnetic fields in the neighbourhood of surface-breaking cracks in metals

1991 ◽  
Vol 434 (1892) ◽  
pp. 587-603 ◽  
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Free Space ◽  
Skin Depth ◽  
Rectangular Slot ◽  
Numerical Predictions ◽  
First Case ◽  
Wide Range ◽  
Thin Skin ◽  
The Magnetic Field

Electromagnetic non-destructive evaluation techniques are widely used to detect and size surface-breaking cracks in metal structures and components. The precise distribution of the electromagnetic field around such a crack depends on the frequency of the applied field, the material properties of the metal and the crack geometry. In many situations, the skin depth of the electromagnetic field in the metal is small compared with the crack dimensions. If this is the case, the crucial parameter that determines the way the electromagnetic field in air couples to the field in the metal is m = μ 0 l / μδ , where μ and μ 0 are the metal and free space permeabilities respectively and l / δ is the ratio of the crack length scale l to the skin depth δ . If the metal is ferromagnetic, m can take a wide range of values and the distribution of the electromagnetic field around the crack is very different in the two limiting cases m = 0 and m ≫ 1. In the first case, the magnetic flux emerging from the crack is directed into the metal surface whereas in the second case, the flux is directed into free space. In this work, the distribution of the electromagnetic field around a surface-breaking crack is determined for arbitrary values of m . The theory is developed for cracks of general shape and numerical calculations of the free-space components of the magnetic field are made for rectangular and semi-elliptical shaped cracks. The numerical predictions are found to be in good agreement with experimental measurements of the magnetic field above a rectangular slot, cut in a flat plate of mild steel.

scholarly journals Разогрев электронов в чистом Ge в квантовом магнитном поле при термическом возбуждении носителей заряда

2020 ◽  
Vol 54 (3) ◽  
pp. 221
Author(s):  
В.Ф. Банная ◽  
Е.В. Никитина
Keyword(s):  
Magnetic Field ◽  
Experimental Study ◽  
Electric Field ◽  
Low Temperatures ◽  
Qualitative Agreement ◽  
Carrier Lifetime ◽  
Charge Carriers ◽  
Thermal Excitation ◽  
Ionization Coefficient ◽  
Electric And Magnetic Fields

The results of an experimental study on charge carriers heating by an electric field (E) in pure Ge in a quantum magnetic field (H) at (E⊥H) at low temperatures (T=4,2;1,8 K) under thermal excitation are considered. It is shown that the dependence of E and H thermal ionization coefficient affects the average carrier lifetime under these conditions. The obtained results are in qualitative agreement with the theory of cascade capture of carriers on isolated centers in crossed electric and magnetic fields.

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