Wave vector | EPFL Graph Search

In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), and its direction is perpendicular to the wavefront. In isotropic media, this is also the direction of wave propagation. A closely related vector is the angular wave vector (or angular wavevector), with a typical unit being radian per metre. The wave vector and angular wave vector are related by a fixed constant of proportionality, 2π radians per cycle. It is common in several fields of physics to refer to the angular wave vector simply as the wave vector, in contrast to, for example, crystallography. It is also common to use the symbol '''k''' for whichever is in use. In the context of special relativity, wave vector can refer to a four-vector, in which the (angular) wave vector and (angular) frequency are combined

A MATLAB-based tool for visualizing the plane wave propagation in multilayer structures containing metamaterials

Juan Ramon Mosig

The paper reports on a graphical user interface developed in MATLAB to aid the visualization of the plane wave impinging from a lossless half-space onto a multilayer structure. Individual layers are assumed to be homogeneous and isotropic with electric permittivity (∊) and magnetic permeability (μ) taking arbitrary complex values. Double-positive, single-negative and double-negative media (real parts of ∊ and μ) as well as lossless, dissipative and amplifying media (imaginary parts of ∊ and μ) are allowed. 2D field distribution, transmission and reflection coefficients, and the wave vectors' z-component locations in the complex plane are presented to the user.

2012

Long-range magnetic ordering in Li2MnGeO4 and precursor short-range spin correlations

Artem Korshunov, Irina Safiulina

Long-range magnetic ordering and short-range spin correlations in layered noncentrosymmetric orthogermanate Li2MnGeO4 were studied by means of polarized and unpolarized neutron scattering. The combined Rietveld refinement of synchrotron and neutron powder diffraction data at room temperature within the Pmn2(1) space group allowed us to specify the details of the crystal structure. According to the additional Bragg peaks in low-temperature neutron diffraction patterns a long-range antiferromagnetic ordering with the propagation vector k = (1/2 1/2 1/2) has been found below T-N approximate to 8 K. Symmetry analysis revealed the model of the ground state spin structure within the C(a)c (no. 9.41) magnetic space group. It is represented by the noncollinear ordering of manganese atoms with a refined magnetic moment of 4.9 mu(B)/Mn2+ at 1.7 K, which corresponds to the saturated value for the high-spin configuration S = 5/2. Diffuse magnetic scattering was detected on the neutron diffraction patterns at temperatures just above T-N. Its temperature evolution was investigated in detail by polarized neutron scattering with the following XYZ-polarization analysis. Reverse Monte Carlo simulation of diffuse scattering data showed the development of short-range ordering in Li2MnGeO4, which is symmetry consistent on a small scale with the long-range magnetic state below T-N. The reconstructed radial spin-pair correlation function S(0)S(r) displayed the predominant role of antiferromagnetic correlations. It was found that spin correlations are significant only for the nearest magnetic neighbors and almost disappear at r approximate to 12 angstrom at 10 K. Temperature dependence of the diffuse scattering implies short-range ordering long before the magnetic phase transition. Besides, the spin arrangement was found to be similar in both cases above and below T-N. As a result, an exhaustive picture of the gradual formation of magnetic ordering in Li2MnGeO4 is presented.

2020

Magnetic states and spin-wave modes in single ferromagnetic nanotubes

Daniel Rüffer

In this thesis the electrical properties, magnetic states and spin wave resonances of individual magnetically hollow ferromagnetic nanotubes have been studied. They were prepared from the different materials Nickel (Ni), Permalloy (Py) and Cobalt-Iron-Boron (CoFeB), deposited as shells onto non-magnetic Gallium-Arsenide (GaAs) semiconductor nanowires via Atomic Layer Deposition (ALD), thermal evaporation and magnetron sputtering, respectively. The resulting nanotubes had lengths between 10 to 20 μm, diameters of 150 to 400 nm and tube walls (shells) which were 20 to 40nm thick. Structural analysis of the tubes by Transmission Electron Microscopy revealed a poly(nano)crystalline (Ni, Py) and amorphous (CoFeB) structure. Electrical transport experiments as a function of temperature revealed different transport mechanisms for each of the materials. Electron-phonon scattering dominated the temperature dependence of the resistivity in Ni, while a clear evidence for electron magnon scattering was observed in Py. Electron-electron interaction in granular and amorphous media was identified as the major contribution to the temperature dependence in CoFeB. The Anisotropic Magnetoresistance (AMR) ratios have been determined for all tubes and different temperatures. Ni nanotubes exhibited a large relative AMR effect of 1.4% at room temperature. The AMR measurements provided information about the magnetic configurations as well as the magnetization reversal mechanism. Indications for the formation of vortex segments in Ni tubes were found for the magnetization reversal when the magnetic field was perpendicular to the nanotube axis. In cooperation with the Poggio group in Basel, cantilever magnetometry has been used for the further characterization of the nanotube magnetization. The magnetization curves were compared to the AMR measurements and finite element method (FEM) micromagnetic simulations. The comparison between the experimental results and the simulations suggested that the roughness of Ni tubes gave rise to segmented magnetic switching. An almost perfect axial alignment of the remanent magnetization has been observed in Py and CoFeB nanotubes. The influence of the inhomogeneous internal field in transverse magnetic fields was investigated by simulation. The segment-wise alignment of spins with the field direction is argued to provoke characteristic kinks in the hysteresis curve and measured AMR effect. Magnetothermal spatial mapping experiments using the anomalous Nernst effect (ANE) complemented the magnetotransport experiments in cooperation with the group of Prof. Grundler in Munich. Here, first evidence of end-vortices entering the nanotube before reversal could be found. Electrically detected spin wave resonance experiments have been performed in cooperation with the group of Prof. Grundler on individual nanotubes. The detected voltage, generated by the spin rectification effect, revealed multiple resonances in the GHz frequency. The experimentally observed resonances were compared to calculated ones extracted from dynamic simulations. With this comparison, the signatures could be attributed to azimuthally confined spin-wave modes. The deduced dispersion relation suggested the quantization of exchange dominated spin waves in that resonance frequencies follow roughly a quadratic dependence on the wave vector.

EPFL2014