The spin Hall effect (SHE) is a transport phenomenon predicted by Russian physicists Mikhail I. Dyakonov and Vladimir I. Perel in 1971. It consists of the appearance of

spin Spin or spinning most often refers to: * Spin (physics) or particle spin, a fundamental property of elementary particles * Spin quantum number, a number which defines the value of a particle's spin * Spinning (textiles), the creation of yarn or thr ...

accumulation on the lateral surfaces of an

electric current An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...

-carrying sample, the signs of the spin directions being opposite on the opposing boundaries. In a cylindrical wire, the current-induced surface spins will wind around the wire. When the current direction is reversed, the directions of spin orientation is also reversed.

Definition

The spin Hall effect is a transport phenomenon consisting of the appearance of spin accumulation on the lateral surfaces of a sample carrying electric current. The opposing surface boundaries will have spins of opposite sign. It is analogous to the classical

Hall effect The Hall effect is the production of a voltage, potential difference (the Hall voltage) across an electrical conductor that is wikt:transverse, transverse to an electric current in the conductor and to an applied magnetic field wikt:perpendicul ...

, where ''charges'' of opposite sign appear on the opposing lateral surfaces in an electric-current carrying sample in a

magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

. In the case of the classical Hall effect the charge build up at the boundaries is in compensation for the

Lorentz force In electromagnetism, the Lorentz force is the force exerted on a charged particle by electric and magnetic fields. It determines how charged particles move in electromagnetic environments and underlies many physical phenomena, from the operation ...

acting on the charge carriers in the sample due to the magnetic field. No magnetic field is needed for the spin Hall effect which is a purely

-based phenomenon. The spin Hall effect belongs to the same family as the anomalous Hall effect, known for a long time in

ferromagnet Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromag ...

s, which also originates from

spin–orbit interaction In quantum mechanics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion inside a potential. A key example of this phenomenon is the spin– ...

History

The spin Hall effect (direct and inverse) was predicted by Russian physicists Mikhail I. Dyakonov and Vladimir I. Perel in 1971. They also introduced for the first time the notion of ''spin current''. In 1983 Averkiev and Dyakonov proposed a way to measure the inverse spin Hall effect under optical spin orientation in semiconductors. The first experimental demonstration of the inverse spin Hall effect, based on this idea, was performed by Bakun et al. in 1984. The term "spin Hall effect" was introduced by Hirsch who re-predicted this effect in 1999. Experimentally, the (direct) spin Hall effect was observed in

semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...

s more than 30 years after the original prediction.

Physical origin

Two possible mechanisms give origin to the spin Hall effect, in which an

(composed of moving charges) transforms into a spin current (a current of moving spins without charge flow). The original (extrinsic) mechanism devised by Dyakonov and Perel consisted of spin-dependent

Mott scattering In physics, Mott scattering is elastic electron scattering from nuclei. It is a form of Coulomb scattering that requires treatment of spin-coupling. It is named after Nevill Francis Mott, who first developed the theory in 1929. Mott scattering ...

, where carriers with opposite spin diffuse in opposite directions when colliding with impurities in the material. The second mechanism is due to intrinsic properties of the material, where the carrier's trajectories are distorted due to

as a consequence of the asymmetries in the material. One can intuitively picture the intrinsic effect by using the classical analogy between an electron and a spinning tennis ball. The tennis ball deviates from its straight path in air in a direction depending on the sense of rotation, also known as the

Magnus effect The Magnus effect is a phenomenon that occurs when a spin (geometry), spinning Object (physics), object is moving through a fluid. A lift (force), lift force acts on the spinning object and its path may be deflected in a manner not present when ...

. In a solid, the air is replaced by an effective electric field due to asymmetries in the material, the relative motion between the magnetic moment (associated to the spin) and the electric field creates a coupling that distorts the motion of the electrons. Similar to the standard Hall effect, both the extrinsic and the intrinsic mechanisms lead to an accumulation of spins of opposite signs on opposing lateral boundaries.

Mathematical description

The spin current is described by a second-rank ''tensor'' , where the first index refers to the direction of flow, and the second one to the spin component that is flowing. Thus denotes the flow density of the ''y''-component of spin in the ''x''-direction. Introduce also the ''vector'' ''q''_''i'' of charge flow density (which is related to the normal current density j=''e''q), where ''e'' is the elementary charge. The coupling between spin and charge currents is due to spin-orbit interaction. It may be described in a very simple way by introducing a single dimensionless coupling parameter ''ʏ''.

Spin Hall magnetoresistance

is needed for spin Hall effect. However, if a strong enough magnetic field is applied in the direction perpendicular to the orientation of the spins at the surfaces, spins will

precess Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In ot ...

around the direction of the magnetic field and the spin Hall effect will disappear. Thus in the presence of magnetic field, the combined action of the direct and inverse spin Hall effect leads to a change of the sample resistance, an effect that is of second order in spin-orbit interaction. This was noted by Dyakonov and Perel already in 1971 and later elaborated in more detail by Dyakonov. In recent years, the spin Hall magnetoresistance was extensively studied experimentally both in magnetic and non-magnetic materials (heavy metals, such as Pt, Ta, Pd, where the spin-orbit interaction is strong).

Swapping spin currents

A transformation of spin currents consisting in interchanging (''swapping'') of the spin and flow directions (''q''_''ij'' → ''q''_''ji'') was predicted by Lifshits and Dyakonov. Thus a flow in the ''x''-direction of spins polarized along ''y'' is transformed to a flow in the ''y''-direction of spins polarized along ''x''. This prediction has yet not been confirmed experimentally.

Optical monitoring

The direct and inverse spin Hall effect can be monitored by optical means. The spin accumulation induces

circular polarization In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to ...

of the emitted

light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...

, as well as the

Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English chemist and physicist who contributed to the study of electrochemistry and electromagnetism. His main discoveries include the principles underlying electromagnetic inducti ...

(or

Kerr Kerr may refer to: People *Kerr (surname) *Kerr (given name) Places ;United States *Kerr Township, Champaign County, Illinois *Kerr, Montana, A US census-designated place *Kerr, Ohio, an unincorporated community *Kerr County, Texas Kerr Co ...

) polarization rotation of the transmitted (or reflected) light. Observing the polarization of emitted light allows the spin Hall effect to be observed. More recently, the existence of both direct and inverse effects was demonstrated not only in

s, but also in

metal A metal () is a material that, when polished or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, electricity and thermal conductivity, heat relatively well. These properties are all associated wit ...

Applications

The spin Hall effect can be used to manipulate electron spins electrically. For example, in combination with the electric stirring effect, the spin Hall effect leads to spin polarization in a localized conducting region.

References

{{Authority control Hall effect Condensed matter physics Spintronics