Anisotropic magnetoresistance: materials, models and applications

Resistance of certain (conductive and otherwise isotropic) ferromagnets turns out to exhibit anisotropy with respect to the direction of magnetisation: R$_\parallel$ different from R$_\perp$ with reference to the electric current direction. This century-old phenomenon is reviewed both from the perspective of materials and physical mechanisms involved. More recently, this effect has also been extended to antiferromagnets. This opens the possibility for industrial applications reaching far beyond the current ones, e.g. hard drive read heads or position sensors.Comment: 50 pages (excl. references), 16 figure

Gap formation in helical edge states with magnetic impurities

Helical edge states appear at the surface of two dimensional topological insulators and are characterized by spin up traveling in one direction and the spin down traveling in the opposite direction. Such states are protected by time reversal symmetry and no backscattering due to scalar impurities can occur. However, magnetic impurities break time reversal symmetry and lead to backscattering. Often their presence is unintentional, but in some cases they are introduced into the sample to open up gaps in the spectrum. We investigate the influence of random impurities on helical edge states, specifically how the gap behaves in the realistic case of impurities having both a magnetic and a scalar component. It turns out that for a fixed magnetic contribution the gap closes when either the scalar component, or Fermi velocity is increased. We compare diagrammatic techniques in the self-consistent Born approximation to numerical calculations which yields good agreement. For experimentally relevant parameters we find that even moderate scalar components can be quite detrimental for the gap formation.Comment: 6 pages, 6 figure

Sensitivity of the MnTe valence band to orientation of magnetic moments

An effective model of the hexagonal (NiAs-structure) manganese telluride valence band in the vicinity of the A-point of the Brillouin zone is derived. It is shown that while for the usual antiferromagnetic order (magnetic moments in the basal plane) band splitting at A is small, their out-of-plane rotation enhances the splitting dramatically (to about 0.5 eV). We propose extensions of recent experiments (Moseley et al., Phys. Rev. Materials 6, 014404) where such inversion of magnetocrystalline anisotropy has been observed in Li-doped MnTe, to confirm this unusual sensitivity of a semiconductor band structure to magnetic order.Comment: 5+epsilon pages, 4 figures; to appear in PR

Microscopic mechanism of the noncrystalline anisotropic magnetoresistance in (Ga,Mn)As

Journals published by the American Physical Society can be found at http://journals.aps.org/Starting with a microscopic model based on the Kohn-Luttinger Hamiltonian and kinetic p-d exchange combined with Boltzmann formula for conductivity we identify the scattering from magnetic Mn combined with the strong spin-orbit interaction of the GaAs valence band as the dominant mechanism of the anisotropic magnetoresistance (AMR) in (Ga,Mn)As. This fact allows to construct a simple analytical model of the AMR consisting of two heavy-hole bands whose charge carriers are scattered on the impurity potential of the Mn atoms. The model predicts the correct sign of the AMR (resistivity parallel to magnetization is smaller than perpendicular to magnetization) and identifies its origin arising from the destructive interference between electric and magnetic part of the scattering potential of magnetic ionized Mn acceptors when the carriers move parallel to the magnetization

Gap formation in helical edge states with magnetic impurities

Helical edge states appear at the surface of two dimensional topological insulators and are characterized by spin up traveling in one direction and the spin down traveling in the opposite direction. Such states are protected by time reversal symmetry and no backscattering due to scalar impurities can occur. However, magnetic impurities break time reversal symmetry and lead to backscattering. Often their presence is unintentional, but in some cases they are introduced into the sample to open up gaps in the spectrum. We investigate the influence of random impurities on helical edge states, specifically how the gap behaves in the realistic case of impurities having both a magnetic and a scalar component. It turns out that for a fixed magnetic contribution the gap closes when either the scalar component, or Fermi velocity is increased. We compare diagrammatic techniques in the self-consistent Born approximation to numerical calculations which yields good agreement. For experimentally relevant parameters we find that even moderate scalar components can be quite detrimental for the gap formation.publishe

Transport gap in a v=1/3 quantum Hall system: a probe for skyrmions

Transport measurements of the activation gap at fractional filling factor 1/3 are compared to results of exact diagonalization, allowing identification of a small anti-skyrmion as the lowest excitation in the low-field regime. In agreement with theory, a crossover to spinless excitations at higher electron densities is observed. Two samples of different quality are investigated. A detailed description of the theoretical calculation of activation gaps is presented and features which should be taken into account are summarized: finite thickness, Landau level mixing, and comparison between different sizes of the model system and-whenever possible-also between different geometries (torus and sphere). Within the chosen model of disorder (entailing a single fit parameter) we obtain a good agreement between calculated energies and experimental results

Effect of disorder on spin and charge excitations in the fractional quantum hall effect

A simple model of disorder in fractional quantum Hall systems is combined with the standard exact diagonalisation technique. Electron-density--dependent gaps at filling factors 1/3,2/3,2/5, and 3/5 measured by activated transport can then be fitted with a single reasonable value of d which has the meaning of the separation of ionized donors from the quasi-2D electron gas