Comment on half-integer quantum numbers for the total angular momentum of photons in light beams with finite lateral extensions

Recently the spectacular result was derived quantum mechanically that the total angular momentum of photons in light beams with finite lateral extensions can have half-integer quantum numbers. In a circularly polarized Gauss light beam it is half of the spin angular momentum which it would have in a respective infinitely extended wave. In another paper it was shown by a classical calculation that the magnetic moment induced by such a beam in a metal is a factor of two smaller than the one induced by a respective infinitely extended wave. Since the system's angular momentum is proportional to its magnetic moment it could be assumed that the classical result for the magnetic moment reflects the transfer of the total angular momenta of the beam photons to the metal. Here we show that there is no hint that this is indeed the case

Ab-initio investigation of the covalent bond energies in the metallic covalent superconductor MgB2 and in AlB2

The contributions of the covalent bond energies of various atom pairs to the cohesive energy of MgB2 and AlB2 are analysed with a variant of our recently developed energy-partitioning scheme for the density-functional total energy. The covalent bond energies are strongest for the intralayer B-B pairs. In contrast to the general belief, there is also a considerable covalent bonding between the layers, mediated by the metal atom. The bond energies between the various atom pairs are analysed in terms of orbital- and energy-resolved contributions.Comment: 6 pages, 1 figure, 2 tables, submitted to PR

Physical and mathematical justification of the numerical Brillouin zone integration of the Boltzmann rate equation by Gaussian smearing

Scatterings of electrons at quasiparticles or photons are very important for many topics in solid state physics, e.g., spintronics, magnonics or photonics, and therefore a correct numerical treatment of these scatterings is very important. For a quantum-mechanical description of these scatterings Fermi's golden rule is used in order to calculate the transition rate from an initial state to a final state in a first-order time-dependent perturbation theory. One can calculate the total transition rate from all initial states to all final states with Boltzmann rate equations involving Brillouin zone integrations. The numerical treatment of these integrations on a finite grid is often done via a replacement of the Dirac delta distribution by a Gaussian. The Dirac delta distribution appears in Fermi's golden rule where it describes the energy conservation among the interacting particles. Since the Dirac delta distribution is a not a function it is not clear from a mathematical point of view that this procedure is justified. We show with physical and mathematical arguments that this numerical procedure is in general correct, and we comment on critical points

Three-dimensional Character of the Magnetization Dynamics in Magnetic Vortex Structures - Hybridization of Flexure Gyromodes with Spin Waves

Three-dimensional linear spin-wave eigenmodes of a Permalloy disk having finite thickness are studied by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. The eigenmodes found in the simulations are interpreted as linear superpositions (hybridizations) of 'approximate' three-dimensional eigenmodes, which are the fundamental gyromode $G_0$, the spin-wave modes and the higher-order gyromodes $G_N$ (flexure modes), the thickness dependence of which is represented by perpendicular standing spin waves. This hybridization leads to new and surprising dependencies of the mode frequencies on the disk thickness. The three-dimensional character of the eigenmodes is essential to explain the recent experimental results on vortex-core reversal observed in relatively thick Permalloy disks

Magnetism in systems with various dimensionality: A comparison between Fe and Co

A systematic ab initio study is performed for the spin and orbital moments and for the validity of the sum rules for x-ray magnetic circular dichroism for Fe systems with various dimensionality (bulk, Pt-supported monolayers and monatomic wires, free-standing monolayers and monatomic wires). Qualitatively, the results are similar to those for the respective Co systems, with the main difference that for the monatomic Fe wires the term in the spin sum rule is much larger than for the Co wires. The spin and orbital moments induced in the Pt substrate are also discussed.Comment: 4 page

Polarisation selective magnetic vortex dynamics and core reversal in rotating magnetic fields

A magnetic vortex occurs as an equilibrium configuration in thin ferromagnetic platelets of micron and sub-micron size and is characterised by an in-plane curling magnetisation. At the centre, a magnetic singularity is avoided by an out-of-plane magnetisation core. This core has a gyrotropic excitation mode, which corresponds to a circular motion of the vortex around its equilibrium position, where the rotation sense is determined by the direction of the vortex core magnetisation, its polarisation. Unlike linear fields or spin polarised currents, which excite both polarisation states, an in-plane rotating field can selectively excite one of the polarisation states. Here we report the observation of vortex dynamics in response to rotating magnetic fields, imaged with time-resolved scanning X-ray microscopy. We demonstrate that the rotating field only excites the gyrotropic mode if the rotation sense of the field coincides with the vortex gyration sense and that such a field can selectively reverse the vortex polarisation

Anisotropy of the orbital methods and the magnetic dipole term TzT_z in CrO2{\rm CrO_2}: An {\it ab-initio} studt

A systematic study is performed by the {\it ab-initio} density functional theory of the anisotropy of the orbital moments $$and the magnetic dipole term$$ in bulk ${\rm CrO_2}$. Two different band-structure techniques are used (FLAPW and LMTO-ASA), and the electronic correlations are treated by the local-spin-density approximation (LSDA), the LSDA+ orbital polarization method, and the LSDA+$U$ method. The calculated anisotropies of $$and$$ are very large compared to Fe, Ni and Co but still a factor of 5 and 2 smaller than the anisotropies obtained from a recently suggested analysis of the X-ray magnetic circular dichroism spectra for a thick layer of ${\rm CrO_2}$

Micromagnetism and the microstructure of ferromagnetic solids

Here is a fundamental introduction to microstructure magnetic property relations where microstructures on atomic, nano- and micrometer scales are considered. The authors demonstrate that outstanding magnetic properties require an optimization of microstructural properties where the microstructures in crystalline materials are point defects and dislocations as well as grain and phase boundaries. In amorphous alloys the type of microstructures on atomic scales are defined and used to describe intrinsic and extrinsic properties