more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11

Spin Hall effect
Spin and Charge TransportThe Spin Hall effect describes the fact that a spin current may be generated across a flow of charge current due to the spinorbit interaction. The origin of the Spin Hall effect is spindependent scatterings.
The Spin Hall effect is the effect describing accumulation of the spins at a surface of a metallic wire, when an electrical current flows through the wire due to the SpinOrbit interaction.
for a Wikipedia explanation of the Spin Hall effect, click here (note: I do not agree with "intuitive" explanation given there)Explanation of the Spin Hall effect from the model of the spinup/spindown bands is here (my view)
Origin of the Spin Hall effect
The Origin of the Spin Hall effect is the scattering current. See more about the scattering current as origin of the Spin Hall effect here
Origin of the Spin Hall effect in short: The origin of the Spin Hall effect is the spindependent scattering current In order for the scattering current to flow, the electron scattering probability in one direction should be different from the scattering probability in the opposite direction (to be nonreciprocal). The spinorbit interaction makes the scatterings spindependent and nonreciprocal.
Material Parameters required for observation of the Spin Hall effect1) The scattering probability should be spindependent. That means that the scattering probability of a delocalized electron from a quantum state, in which the effective magnetic field of the spin orbitinteraction is parallel to the electron spin, to a quantum state, in which the effective magnetic field of the spin orbitinteraction is antiparallel to the electron spin, is different from probability of scattering in the opposite direction. It is not always the case!!!
In a solid there two kinds of the spinorbit interaction: 1) intrinsic. It is induced by the electric field of a nuclear. It is proportional to the orbital moment of the delocalized electrons. 2) extrinsic. It is proportional to the applied electrical field or structural electrical field (for example, the electrical field in the vicinity of the contact or QW due to a charge accumulation) . It is proportional to the speed and the movement direction of the electron. Generally the strength of the intrinsic. spinorbit interaction is larger than the extrinsic. Both types of the spinorbit interaction may contribute to the Spin Hall effect. Scatterings.When an electron is scattered from one quantum state to other quantum state, it changes its position and its wave vector ( the movement direction) The scatterings, after which the electron changes only its position, are defined as sidejump scatterings The scatterings, after which the electron changes only its movement direction, are defined as skew scatterings Both the sidejump scatterings and the skew scatterings may be spindependent and they both may contribute to the Spin Hall effect.
How the Spin Hall effect makes an electron gas to be spinpolarized?The spinorbit interaction induces a magnetic field. This magnetic field induces a spin polarization in the electron gas. (Why? See here). The electrons, which moves in opposite directions, experience the magnetic field in opposite directions. Therefore, there are two spin accumulation with opposite spin directions. Since in an electron gas, two spin accumulations of different spin directions can not coexist at same point, the spin accumulation of opposite spin directions annihilates with each other. However, because the difference of the scattering probability for electrons scattered towards the xaxis and into the opposite direction, there are more electron in one direction and even after annihilation some spin accumulation remains. This is the reason why the scattered current is the spinpolarized.
Physical mechanisms, which cause The Spin Hall Effects
1. Skew scatterings2. Sidejump scatterings3. Intrinsic. Inhomogeneous spin distribution.
Skew scatterings
the Spin Hall effect due to skew scatterings. When an electron changes its movement direction after a scattering, it may experience different the effective magnetic field of the spin orbit interaction whether it changes direction to the left or to the right. This makes different the scattering probability for an electron scattered to the left or to the right and a spin scattered current flows perpendicularly to the a charge drift current. It is a largest when (1) an electron changes its movement direction over 90 degrees. (2) the spinorbit interaction in metal is large. (3) delocalized electrons have a large orbital moment in the direction perpendicular to the direction of the drift current or (4) An electrical field induces a larger orbital moment for delocalized electrons. note: The electrical field, along which the drift current flows, itself induces Hso. It is negligibly small in a metal with high conductivity and it is larger in a metal with lower conductivity. It occurs only when (1) an electron changes its movement direction after a scattering. (2) For two opposite directions of the electron movement, the sign of the spinorbit interaction is opposite (or at least the magnitude of the spinorbit interaction is different). It is the case when the orbital moment of delocalized electrons is different in the opposite directions
A Phonon, a magnon, an impurity and a defect can be a source of a skew scattering.
Bulktype sidejump scatterings
the Spin Hall effect due to sidejump scatterings.
There is an electric field around a defect in a crustal. When a delocalized electron passes in the vicinity of the defect, it experiences an effective magnetic field of the spinorbit interaction, which is originated from this electrical field. The effective magnetic field of the spinorbit interaction opposite whether the electron passes from the left or the right side of defect. When the electron is scattered from one side to another side of the defect, the scattering probability is different whether the electron scattered from the left side to the right side of the defect or from the right to the left. This cause a flow of a spin current across the charge current.
It is a largest when 1) The defects induces a significant electrical field in the crystal lattice. 2) The density of the defects is large, but the average distance between defects is still substantially larger than the electron meanfree path
Only a sidejump scattering on crystal defect may be spindependent and contribute to the Spin Hall effect. Sidejump scatterings on phonons and magnons are spinindependent and they do not contribute to the Spin Hall effect.
When the density of defects increases, the sidejump scatterings becomes spinindependent and they do not contribute to the Spin Hall effect.
Sidejump scatterings across an interfaceThe sidejump scatterings across an interface are one of strongest contributors to the Spin Hall effect.
The sidejump scatterings across an interface can be: 1) extrinsic. It occurs because of a charge accumulation at the interface between two metals. 1) intrinsic. It occurs because of the deformation of the orbital of electrons moving in the vicinity of the interface (See here). Extrinsic contribution to the spindependent sidejump scatterings The contact interface between two metals are charged. The charge may be accumulated because of the difference of the metal work functions. The charge accumulation at Schottky contact and the charge accumulation at sides of a pnjunction are the examples. The electrons, which move along different sides of the contact, experience different direction of the electrical field from the accumulated charge. Because of the opposite electrical field, the electrons at different sides of the contact experience the opposite effective magnetic field of the spin  orbit interaction. Therefore, the probabilities of the sidejump scatterings across interface is different whether the electron scattered from left side of the contact to the right side or in the opposite direction. Because of this difference, a spin current flows across the contact interface when a charge current flows along the contact. In the case when there is a tunnel contact, the charge accumulation can be changed significantly by applying a voltage to the contact. By this method the magnitude of the spinorbit interaction can be modulated and the magnitude of the Spin Hall effect can be modulated as well. Since the electrical field at the contact interface may be significant, this contribution to the Spin Hall effect may be large.
Intrinsic contribution to the spindependent sidejump scatterings. In the vicinity of an interface the electron orbital deforms. It causes a substantial magnetic field of the spinorbit interaction. Mainly this effective magnetic field acts on the localized delectrons. However, the delocalized electrons, which moves along the contact interface, also may experience a significant effective magnetic field. On each side of the contact, the effective magnetic field is in opposite directions. It makes the scattering across the contact interface to become spindependent (See Fig.10) The effective magnetic field of the spinorbit interaction for localized delectrons in the vicinity of an interface may be very large. It may reach 130 kOe and larger. The effective magnetic field for the delocalized electrons is smaller, but still it may be very large. Therefore, in the vicinity of the interface the Spin Hall effect can be substantial.
Intrinsic contribution to the Spin Hall effect.
This contribution is defined as a contribution, which electron gains not during a scattering, but during the movement between scatterings. Because of its relativistic nature, the spinorbit interaction can not change a trajectory of an electron.
Incorrect interpretation of the intrinsic. contribution to the Spin Hall effect: When an electron moves perpendicularly to an electrical field, it experiences the effective magnetic field due to the effect of the spinorbit interaction, which direction is perpendicular to the electron movement direction. When an an electron moves perpendicularly to an electrical field, it experiences the Lorentz force. It is easy to assume that the effective magnetic field of the spinorbit interaction may induce the Lorentz force or that it may induce the ordinary Hall effect. It is very incorrect.
It is important!!!!The effective magnetic field of the spinorbit interaction does not induce the Lorentz force and it can not be a cause the ordinary Hall effect. The effective magnetic field of the spinorbit interaction only affects the electron spin and it can not change the electron trajectory.
Explanation why the spinorbit interaction can not cause the ordinary Hall effect When an is moving in a static electric field, in the coordinate system moving together with the electron, the static electric field is relativistically transformed into the effective electric field and the effective magnetic field. The effective magnetic field is called the effective magnetic field of the spinorbitinteraction. In the coordinate system, which moves together with the electron, obviously the electron does not move. The effective magnetic field does not induce the Lorentz force on a stationary particle. Therefore, the spinorbit interaction can not cause the ordinary Hall effect.
Since the spinorbit interaction can not change an electron trajectory, what is the intrinsic contribution to the Spin Hall effect???
Two mechanisms for the intrinsic contribution to the Spin Hall effect (1) The spin polarization induced by the effective magnetic field of the spinorbit interaction (See Fig. 30) (2) Inhomogeneous spin distribution
Detailed explanation of this Figure is here
Effects often confused with the Spin Hall effect.
effect 1: Ordinary Hall effecteffect 2: Spin polarization induced by the Oersted magnetic field of electrical current (the Ampere's law)
effect 3: Spin detection
effect 1: Ordinary Hall effectThe spin accumulation generated by the ordinary Hall effect is often wrongly assigned to the Spin Hall Effect
The Hall effect is very effective to enlarge the spin accumulation at one side of the sample. How to distinguish between effects?? The Spin Hall effect =====> the spin accumulation at two opposite edges of the sample The ordinary Hall effect =========> the spin accumulation at one edge of the sample
effect 2: Spin polarization induced by the Oersted magnetic field of electrical current (the Ampere's law)The spin accumulation generated by the Oersted field is often wrongly assigned to the Spin Hall Effect
Figure 6 shows a film of a nonmagnetic material, in which an electrical current flows under an applied voltage. A magnetic field (blue circles) is generated around the current (the Ampere's law). The magnetic field is small at the center of film, but it is large at the edges.
effect 3: Spin DetectionThe charge current, which flow along an AC spin current, is often wrongly assigned to the Inverse Spin Hall Effect
When is nonzero in a material, the charge is accumulated along a spin diffusion and the spin current can be detected. When the spin current is modulated in time, the distribution of the charge accumulation becomes modulated as well. The change of the charge distribution requires a charge current. This means that along an AC spin current flows a AC charge current. The amplitude of this AC charge current may be significant and it is proportional to the amplitude of the AC spin current.
This AC charge current usually surpasses significantly the current induced by the Inverse Spin Hall Effect
For this reason, AC charge current, which is induced due to the spin detection effect, is often wrongly assigned to the Inverse Spin Hall Effect.
How to distinguish between effects?? The magnitude of the Spin Hall effect and the Inverse Spin Hall Effect should be the same for DC and AC currents!!!!

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