Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics

A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell's equations reduce to a single equation.Comment: 8 page

Spin-dependent phenomena and device concepts explored in (Ga,Mn)As

Over the past two decades, the research of (Ga,Mn)As has led to a deeper understanding of relativistic spin-dependent phenomena in magnetic systems. It has also led to discoveries of new effects and demonstrations of unprecedented functionalities of experimental spintronic devices with general applicability to a wide range of materials. In this article we review the basic material properties that make (Ga,Mn)As a favorable test-bed system for spintronics research and discuss contributions of (Ga,Mn)As studies in the general context of the spin-dependent phenomena and device concepts. Special focus is on the spin-orbit coupling induced effects and the reviewed topics include the interaction of spin with electrical current, light, and heat.Comment: 47 pages, 41 figure

Control of Coercivities in (Ga,Mn)As Thin Films by Small Concentrations of MnAs Nanoclusters

We demonstrate that low concentrations of a secondary magnetic phase in (Ga,Mn)As thin films can enhance the coercivity by factors up to ~100 without significantly degrading the Curie temperature or saturation magnetisation. Magnetic measurements indicate that the secondary phase consists of MnAs nanoclusters, of average size ~7nm. This approach to controlling the coercivity while maintaining high Curie temperature, may be important for realizing ferromagnetic semiconductor based devices.Comment: 8 pages,4 figures. accepted for publication in Appl. Phys. Let

Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields in near-linear time solutions as well as upper bounds. Using various computational tools, we get solutions within considerably less than 1% of the optimum. An interesting feature of our approach is that, even though an FWP is hard to compute in theory and Edmonds' algorithm for maximum weighted matching yields a polynomial solution for the MWMP, the practical behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental Algorithms, 200

Reorientation Transition in Single-Domain (Ga,Mn)As

We demonstrate that the interplay of in-plane biaxial and uniaxial anisotropy fields in (Ga,Mn)As results in a magnetization reorientation transition and an anisotropic AC susceptibility which is fully consistent with a simple single domain model. The uniaxial and biaxial anisotropy constants vary respectively as the square and fourth power of the spontaneous magnetization across the whole temperature range up to T_C. The weakening of the anisotropy at the transition may be of technological importance for applications involving thermally-assisted magnetization switching.Comment: 4 pages, 4 figure

DC-transport properties of ferromagnetic (Ga,Mn)As semiconductors

We study the dc transport properties of (Ga,Mn)As diluted magnetic semiconductors with Mn concentration varying from 1.5% to 8%. Both diagonal and Hall components of the conductivity tensor are strongly sensitive to the magnetic state of these semiconductors. Transport data obtained at low temperatures are discussed theoretically within a model of band-hole quasiparticles with a finite spectral width due to elastic scattering from Mn and compensating defects. The theoretical results are in good agreement with measured anomalous Hall effect and anisotropic longitudinal magnetoresistance data. This quantitative understanding of dc magneto-transport effects in (Ga,Mn)As is unparalleled in itinerant ferromagnetic systems.Comment: 3 pages, 3 figure