Zur anschaulichen Diskussion der qualitativen Eigenschaften der galvanomagnetischen Koeffizienten

The dependence of the different components of the conductivity resp. the resistivity tensor upon the strength and direction of an external magnetic field is discussed qualitatively. — In metals, in which the Fermi surface is simply closed, the changes in longitudinal and transversal resistance and the Hall coefficients are large if the anisotropies of the Fermi surface resp. of the scattering mechanism in the planes perpendicular to magnetic field direction are large, and vice versa. In fields, in which this effect already clearly is marked, the changes in transversal resistance in addition increase with increasing anisotropies ink-space perpendicular to Hall field direction, whereas by equal set in of current and Hall field direction the Hall coefficients now show a tendency to decrease with increasing anisotropies perpendicular to magnetic field direction. The order of Hall coefficients may change in high magnetic fields. In contrast to the changes in resistance the Hall coefficients decrease with increasing strength of magnetic field. — In the presence of open Fermi surfaces the transversal resistance doesn't saturate in the direction of the open orbits. If open orbits exist in more than one direction, saturation returns and the Hall coefficients now vanish proportional to 1/B ². In considering open Fermi surfaces it is not allowed to neglect scattering in strong magnetic fields.     

Motion of Charged Particle in Electric and Magnetic Fields in 3D Noncommutative Spaces and Related Problems

In three-dimensional noncommutative phase space, the energy spectrum and wave functions for the motion of a charged particle in a magnetic field are derived. Due to the momentum–momentum noncommutativity, the particle feels an effective magnetic field in a new direction. When an external electric field perpendicular to this effective magnetic field is applied, the Hall conductivity can be calculated. To get the Hall conductivity, one should define the electric currents from the probability currents in quantum mechanics rather than extending the classical electric currents to quantum mechanics directly. When the electric field is not perpendicular to the effective magnetic field, it is difficult to define the Hall conductivity.     

Effect of Hall Current on the Magnetogravitational Instability of Anisotropic Plasma with Generalized Polytrope Law

The effect of Hall current on the propagation of small perturbations through self gravitating anisotropic collisionless pressure plasma with generalized polytrope law is investigated. The poly-trope law for pressure components parallel and perpendicular to the direction of magnetic field is utilized in the analysis. The effect of Hall current and finite conductivity is introduced in the generalized Ohm's law. Using the polytrope law and Ohm's law dispersion relations are obtained from linearized perturbation equations for wave propagation along and perpendicular to the direction of magnetic field. The dispersion relations incorporating polytrope indices are able to represent the Chew, Goldberger and Low approximation with double adiabatic equation of state for the anisotropic pressure and the magnetohydrodynamic set of equations with isothermal equation of state for the isotropic pressure. The effect of Hall current, finite conductivity and polytrope indices is discussed on the well known hose and gravitational instability. It is found that Jeans' criterion depends on polytrope indices and the condition of gravitational instability is determined for different special cases of interest.     

Mutual rectification of alternating currents in graphene in the field of two electromagnetic waves

For graphene placed in a dc magnetic field and exposed to two electromagnetic waves of the same polarization but different frequencies, an expression for the direct current density in a direction perpendicular to the polarization plane of the waves is derived. The direct current component is nonzero for the wave frequency ratio equal to two; it is proportional to the magnetic field strength, the electric field strength of the higher-frequency wave, and the squared electric field strength of the lower-frequency wave. The physical mechanism of the current generation is similar to the Hall effect.     

The Effect of Finite Larmor Radius on Gravitational Instability of a Finitely Conducting Magnetised Hall Medium in Presence of Suspended Particles

The problem of stability of a self-gravitating, infinite homogeneous gas in the presence of suspended particles is investigated. The medium is assumed conducting and effect of external magnetic field, Hall current and finite Larmor radius corrections are also considered. The equations of the problem are linearized and from linearized equations a general dispersion relation for a dusty gas-particle medium is obtained. The dispersion relation is reduced for two special cases of wave propagations: Parallel and perpendicular to the direction of uniform magnetic field. The effect of suspended particles on the medium is investigated in both the cases. It is found that in the presence of finite Larmor radius corrections and suspended particles the condition of instability is determined by Jeans's criterion for a self gravitating finitely conducting magnetised Hall medium.     

Anomalous Hall effect in the phonon thermal conductivity of paramagnetic dielectrics

A theory of the phonon Hall effect during heat transfer in a paramagnetic dielectric discovered by Strohm et al. [Phys. Rev. 95, 155901 (2005)] is developed. The heat flux emerging in the direction perpendicular to the magnetic field and to the temperature gradient is associated with the interaction of magnetic ions with the oscillating crystal field. In crystals with an arbitrary phonon spectrum, this interaction induces elliptic polarization of phonons. On the other hand, for any type of scattering, the temperature gradient forms part of the phonon density matrix, which is nondiagonal in modes. The combined action of these factors leads to the anomalous Hall effect.     

Finite-temperature density instability at high landau level occupancy

We study here the onset of charge density wave instabilities in quantum Hall systems at finite temperature for Landau level filling nu>4. Specific emphasis is placed on the role of disorder as well as on an in-plane magnetic field. Beyond some critical value, disorder is observed to suppress the charge density wave melting temperature to zero. In addition, we find that a transition from perpendicular to parallel stripes (relative to the in-plane magnetic field) exists when the electron gas thickness exceeds approximately 60 A. The perpendicular alignment of the stripes is in agreement with the experimental finding that the easy conduction direction is perpendicular to the in-plane field.     

Phenomenological evidence for the phonon Hall effect

In the electrical Hall effect, a magnetic field, applied perpendicular to an electrical current, induces through the Lorentz force a voltage perpendicular to the field and the current. It is generally assumed that an analogous effect cannot exist in the phonon thermal conductivity, as there is no charge transport associated with phonon propagation. In this Letter, we argue that such a magnetotransverse thermal effect should exist and experimentally demonstrate this "phonon Hall effect" in Tb3Ga5O12.     

Anomalous Hall effect in magnetic sandwiches with a dielectric spacer

Quantum-statistical calculations are presented for the anomalous Hall effect in a magnetic sandwich with a tunnel junction across a thin dielectric spacer. The tunneling current flows across the junction perpendicular to the plane of the layers while the Hall component of the current lies in this plane. The Kubo formalism and the Green’s functions are used to calculate the contribution of skew scattering to the Hall conductivity. The classical size effect in the Hall conductivity of this structure is studied and two new effects are observed. One is associated with the dependence of the effective electric field in the magnet on the transparency of the dielectric potential barrier for electrons when the current flows perpendicular to the layers of the structure and may be called “ geometric”. The other occurs as a result of the influence of the strong electric field in the dielectric on the electron motion in the adjacent magnetic layers.     

Planar hall effect in ferromagnets

The planar Hall effect in a ferromagnetic conductor is considered within a simple two-liquid hydro-dynamic model. It is shown that, even in the simple case of an isotropic Fermi surface in the absence of thermal spread, the magnitude of the Hall effect is comparable to that in semiconductors because of the presence of two groups of conduction electrons with their spins parallel and perpendicular to the quantization axis, respectively. In addition to the planar Hall field, a spin flux parallel to this field arises, with the consequence that the extent of spin polarization of the conduction electrons varies along the Hall field direction (planar spin Hall effect).     

Lattice electrons on a cylinder surface in the presence of rational magnetic flux and disorder

We consider a disordered two-dimensional system of independent lattice electrons in a perpendicular magnetic field with rigid confinement in one direction and generalized periodic boundary conditions (GPBC) in the other direction. The objects investigated numerically are the orbits in the plane spanned by the energy eigenvalues and the corresponding center of mass coordinate in the confined direction, parameterized by the phase characterizing the GPBC. The Kubo Hall conductivity is expressed in terms of the winding numbers of these orbits. For vanishing disorder the spectrum of the system consists of Harper bands with energy levels corresponding to the edge states within the band gaps. Disorder leads to broadening of the bands. For sufficiently large systems localized states occur in the band tails. We find that within the mobility gaps of bulk states the Diophantine equation determines the value of the Hall conductivity as known for systems with torus geometry (PBCs in both directions). Within the spectral bands of extended states the Hall conductivity fluctuates strongly. For sufficiently large systems the generic behavior of localization-delocalization transitions characteristic for the quantum Hall effect are recovered.     

Elektrische Leitungsphänomene in anisotropen Medien. III

In lattices, in which the Fermi surface is simply closed, the saturation values of the electrical resistivities in longitudinal/transversal magnetic fields are equal to the approximate values for the resistivities, obtained from the variational method of Kohler using rotation symetrical trial functions/constant relaxion times. — Depending upon the magnetic field direction the changes of the longitudinal and transversal resistance and of the Hall coefficient are proportional to the anisotropies ink-space perpendicular to the magnetic field direction. Depending upon the current direction the change of the transversal resistance is larger in the direction perpendicular to the smaller anisotropy. — By generalization of the results of part II of this paper (concerning special elliptic models) one can conclude, that the saturation of the transversal resistance vanishes in the direction of the axis in presence of cylindrical dispersion surfaces and perpendicular to the open orbits in presense of open oblate Fermi surfaces.     

Antisymmetric magnetoresistance in magnetic multilayers with perpendicular anisotropy

While magnetoresistance (MR) has generally been found to be symmetric in applied field in nonmagnetic or magnetic metals, we have observed antisymmetric MR in Co/Pt multilayers. Simultaneous domain imaging and transport measurements show that the antisymmetric MR is due to the appearance of domain walls that run perpendicular to both the magnetization and the current, a geometry existing only in materials with perpendicular magnetic anisotropy. As a result, the extraordinary Hall effect gives rise to circulating currents in the vicinity of the domain walls that contributes to the MR. The antisymmetric MR and extraordinary Hall effect have been quantitatively accounted for by a theoretical model.     

Effects of electric and magnetic fields on electronic states and transport of a Hall bar

We study the edge-state band and transport property for a HgTe/CdTe quantum well Hall bar under the combined coupling of a transverse electric field and a perpendicular magnetic field. It is demonstrated that a weak magnetic field can protect one of the two edge states, open or enlarge a gap of the other edge state in the Hall bar. However, an appropriate electric field can remove the gap, restoring the quantum spin Hall effect. Using the scattering matrix method, we study the electronic transport of the system. We find that the electric field can not only make the switch from pure spin-up to spin-down current, but also open or close the edge-state channels in a narrow Hall bar under a weak magnetic field, which provides us with a new way to construct a topological insulator-based spin switch and charge switch.     

Anomalous Hall effect in perpendicular CoFeB thin films

Our recent research achievements in the perpendicular magnetic anisotropy （PMA） properties of the CoFeB sand- wiched by MgO and tantalum layers are summarized. We found that the PMA behaviors of Ta/CoFeB/MgO and MgO/CoFeB/Ta thin films are different. The larger PMA in the latter film is related to the lower magnetization of CoFeB deposited on MgO. Furthermore, we have demonstrated a large anomalous Hall effect in perpendicular CoFeB thin fihn. Our results show large anomalous Hall resistivity, large longitudinal resistivity, and low switching field can be achieved, all at the same time, in the perpendicular CoFeB thin film. Anomalous Hall effect with high and linear sensitivity is also found in an MgO/CoFeBFFa thin film with a thick MgO layer, which opens a door tbr future device applications of perpendicular ferromagnetic thin films.     

Dynamics of magnetic vortices

The canonical conservation laws of linear and angular momentum in the ferromagnetic continuum have been known to be plagued by certain ambiguities which are resolved in this paper by constructing conservation laws as suitable moments of a topological density. The resulting canonical structure is then shown to be analogous to that encountered in the familiar Hall effect and explains the unusual features of the dynamics of magnetic vortices without resorting to a detailed solution of the underlying nonlinear equations. Thus, in the absence of external magnetic fields, a magnetic vortex is shown to be spontaneously pinned around a fixed guiding center. The guiding center would drift in a direction perpendicular to an applied magnetic field gradient, provided that dissipation can be neglected, with a Hall velocity that is calculated explicitly in terms of the initial configuration of the vortex. In the presence of dissipation, the vortex undergoes skew deflection at an angle δ ≠ 90° with respect to the applied field gradient. The angle δ is related to the winding number of the vortex according to the well-known golden rule of bubble dynamics.     

Interplay of Rashba effect and spin Hall effect in perpendicular Pt/Co/MgO magnetic multilayers

The interplay of the Rashba effect and the spin Hall effect originating from current induced spin–orbit coupling was investigated in the as-deposited and annealed Pt/Co/MgO stacks with perpendicular magnetic anisotropy. The above two effects were analyzed based on Hall measurements under external magnetic fields longitudinal and vertical to dc current,respectively. The coercive field as a function of dc current in vertical mode with only the Rashba effect involved decreases due to thermal annealing. Meanwhile, spin orbit torques calculated from Hall resistance with only the spin Hall effect involved in the longitudinal mode decrease in the annealed sample. The experimental results prove that the bottom Pt/Co interface rather than the Co/MgO top one plays a more critical role in both Rashba effect and spin Hall effect.     

Anfachung und Dämpfung magneto-akustischer Wellen in MHD-Kanälen und ihr Einfluß auf die mittlere Stromdichte und die mittlere Hall-Feldstärke

Magneto-acoustic waves generated by fluctuations in the Hall parameter, the electric conductivity and the stream velocity are theoretically investigated in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both magnetic field and stream velocity. The investigations hold for seeded rare gas plasmas at any degree of seed ionization but are resticted to waves propagating in parallel or antiparallel direction to the current density vector and in parallel or antiparallel direction to the stream velocity vector and to wave lengths which are small in comparsion to the interaction length which occurs as a characteristic wave length. The influence of these waves on the mean current density and the mean Hall field intensity is calculated in case of small amplitudes and low degree of seed ionization up to second order terms. Omitting Ohmic heating the dispersion equation can be solved exactly. A phase shift exists between the fluctuations in gas density and gas velocity. The phase velocity and the amplification rate depend on the wave length. Typical results are represented in a diagram. For both types of waves the phase velocity slightly rises with increasing wave length, while the amplification rate decreases. Waves propagating in opposite direction to the current density vector are amplified, if the electron velocity exceeds a critical value. They reduce the mean current density and the mean Hall field intensity. Waves propagating in opposite direction to the stream velocity vector are also amplified except for very high degrees of seed ionization. The threshold current density is greater than that for the waves of the first type approximately by the Hall parameter as factor. At extremely high degree of seed ionization the phase velocity is directed opposite to the direction occuring at weakly ionized seed. Waves of the second type decrease the mean current density, but increase the mean Hall field intensity.     

Magnetic field induced multi-component QED3 and quantum Hall effect

Dynamics of two dimensional electrons under the strong perpendicular magnetic field is shown to be described by a multi-component fermion theory. The electric conductance has a remarkable property known as the quantum Hall effect. The Hall conductance is quantized in units ofe ²/h in the gap region and in the localized state region. The proof of exactness is presented in general cases using quantum field theory.     

Probing the onset of strong localization and electron–electron interactions with the presence of a direct insulator–quantum Hall transition

We have performed low-temperature transport measurements on a disordered two-dimensional electron system (2DES). Features of the strong localization leading to the quantum Hall effect are observed after the 2DES undergoes a direct insulator–quantum Hall transition on increasing the perpendicular magnetic field. However, such a transition does not correspond to the onset of strong localization. The temperature dependences of the Hall resistivity and Hall conductivity reveal the importance of the electron–electron interaction effects for the observed transition in our study.