Transport through zincblende magnetic semiconductors with magnetic domain walls is studied theoretically. We show that these magnetic domain walls have an intrinsic resistance due to the effective hole spin-orbit interaction. The intrinsic resistance is independent of the domain wall shape and width, and survives the adiabatic limit. For typical parameters, the intrinsic domain wall resistance is comparable to the Sharvin resistance and should be experimentally measurable.Understanding magnetic topological defects is crucial in developing devices that utilize the electron spin. Domain walls are topological defects between homogeneous magnetic domains. The domain wall dynamics has traditionally been induced by external magnetic fields. There has recently been a large interest in the scientific community on current induced magnetization dynamics, where domain walls and domains change in response to applied electric currents [1]. Domain walls can also be electrically detected, by their electrical resistance. Knowledge of the domain wall's effect on the electrical resistance is important for the understanding of spin transport in condensed matter and for the electrical detection of magnetic topological defects.Transport through domain walls have been extensively studied in metallic systems, theoretically [2] and experimentally [3]. The domain wall resistance is defined as R w = R − R 0 , where R and R 0 are resistances with a domain wall and with homogeneous magnetization, respectively. When the domain wall is thinner than the mean free path, in the ballistic regime, R w is positive. In diffusive systems, when the domain wall is wider than the mean free path, the sign of the domain wall resistance is still under debate, i.e. the domain wall can increase or decrease the resistance of the ferromagnet. In ballistic and diffusive metal systems, R w approaches zero with increasing domain wall width and vanishes in the adiabatic limit when the domain wall is much wider than the Fermi wavelength.Ferromagnetic semiconductors integrate magnetization controlled spin transport with gate controlled carrier densities in semiconductors. Domain walls in these systems have been recently studied experimentally [4,5,6,7]. The strong interaction between the spin of the effective holes and their orbits in dilute magnetic semiconductors changes the transport properties of magnetic domain walls qualitatively. In this Letter, we show that domain walls in zincblende magnetic semiconductors have an intrinsic resistance R I w which is the part of R w that survives the adiabatic limit. R I w is independent of the width and detailed shape of the domain walls and is due to the effective spin-orbit interaction.Related manifestations of the coupling between the spin-orbit interactions and the magnetizations are the anisotropic magneto resistance (AMR) [8,9,10,11] and the tunneling anisotropic magneto resistance (TAMR) [4,13,14]. In domain walls, some carriers are prevented by the spin-orbit interaction to adiabatically adapt to the change in the ...
We study transport in normal metals in an external magnetic field. This system exhibits an interplay between a transverse spin imbalance (spin Hall effect) caused by the spin-orbit interaction, a Hall effect via the Lorentz force, and spin precession due to the Zeeman effect. Diffusion equations for spin and charge flow are derived. The spin and charge accumulations are computed numerically in experimentally relevant thin film geometries. The out-of-plane spin Hall potential is suppressed when the Larmor frequency is larger than the spin-flip scattering rate. The in-plane spin Hall potential vanishes at zero magnetic field and attains its maximum at a finite magnetic field before spin precession starts to dominate. Spin-injection via ferromagnetic contacts creates a transverse charge Hall effect that decays in a finite magnetic field due to spin precession. 72.15.Gd,73.50.Jt, Spintronics is a new subfield of research which could provide a new class of low power and high speed electronic devices. This requires an understanding of spininjection, spin manipulation and spin detection. In many metals, spins are affected by the spin-orbit interaction which is often considered a nuisance causing a decay of the injected spin flow. However, the spin-orbit interaction can also be used to manipulate the spins in a desired way and even to cause a finite spin polarization of an initially unpolarized electron flux. This latter spin Hall effect 1,2,3,4,5,6,7,8,9,10,11,12,13 has recently attracted considerable interest.Spins are influenced by a magnetic field. A magnetic field governs the diffusion of particles via spin precession induced by the Zeeman effect 14 and via the Lorentz force. This alters the spin and charge currents and the spin and charge accumulations. There are already some theoretical works on the influence of an external magnetic field on the spin Hall effect. Refs. 15,16 discuss the influence of a magnetic field on the intrinsic 6,17 spin Hall effect. On the other hand, within our knowledge, theoretical studies of the extrinsic spin Hall effect in normal metals are limited to the regime of zero magnetic field.Recently, the first clear optical observation of the spin Hall effect in semiconductors was presented 5 . In this experiment, the dominant contribution to the spin Hall effect was extrinsic 18,19,20 and caused by spin-orbit scattering at impurities. It was also shown that an applied in-plane magnetic field causes precession and suppression of the spin accumulation via the Hanle effect. 21 We address how a magnetic field affects the extrinsic spin Hall and Hall effects in normal metals, where spin-injection and spin-detection can be done by electrical contact. 14 To this end, we study the extrinsic spin Hall effect in normal metals in a external magnetic field. We derive the diffusion equations for spin and charge flow and calculate the spin Hall and also Hall voltage as functions of magnetic field and sample geometry. We consider a normal metal thin film with weak extrinsic spin-orbit interaction. The co...
We consider spin and charge flow in normal metals. We employ the Keldysh formalism to find transport equations in the presence of spin-orbit interaction, interaction with magnetic impurities, and non-magnetic impurity scattering. Using the quasiclassical approximation, we derive diffusion equations which include contributions from skew scattering, side-jump scattering and the anomalous spin-orbit induced velocity. We compute the magnitude of various spin Hall effects in experimental relevant geometries and discuss when the different scattering mechanisms are important.Comment: 10 pages, 4 figure
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