# Spin-Orbit Coupling

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## spin-orbit coupling

[′spin ¦ȯr·bət ‚kəp·liŋ]
(quantum mechanics)
The interaction between a particle's spin and its orbital angular momentum.

## Spin-Orbit Coupling

an interaction of particles that depends on the values and mutual orientations of the particles’ orbital and spin angular momenta and that leads to the fine-structure splitting of the system’s energy levels. Spin-orbit coupling is a relativistic effect. Formally, it is obtained if the energy of particles moving rapidly in an external field is found with an accuracy of v2/c2, where v is the speed of the particle and c is the speed of light.

A simple physical interpretation of spin-orbit coupling can be obtained by considering, for example, the motion of an electron in a hydrogen atom. We shall use here a semiclassical model wherein the electron is viewed as moving around the nucleus along some “orbit.” The electron has an intrinsic angular momentum, or spin, which is responsible for the existence of the electron’s spin magnetic moment. The electric charge of the nucleus generates a Coulomb electric field that should affect the spin magnetic moment of the electron moving along its orbit. This situation can be easily understood if we imagine the frame of reference where the electron is at rest—that is, the frame of reference moves with the electron. For this stationary electron, the nucleus will appear as moving, and, like any moving charge, it will produce a magnetic field H. The magnetic field will affect the magnetic moment H. of the electron. The contribution thereby made to the electron energy depends on the orientation of µ, and H and is equal to – µH = – µ.HH. Since the projection µ,H of the magnetic moment µ, on the vector of the field H can assume two values (±ℏ/2, where is Planck’s constant), the spin-orbit coupling leads to the splitting of energy levels in the hydrogen atom and in hydrogen-like atoms into two close-lying sublevéis (a doublet structure). For atoms with more than one electron, a complicated multiplet splitting of energy levels occurs. It may be noted that the atoms of alkali metals, whose total electron spin is ℏ/2, also have levels of doublet structure.

Spin-orbit coupling is also found for neutral particles, such as neutrons, that have both orbital and spin angular momenta. The spin-orbit coupling of nucleons (protons and neutrons) in atomic nuclei is of great importance, since its contribution to the total interaction energy reaches 10 percent.

V. I. GRIGOREV’EV

References in periodicals archive ?
Concretely the project aims at using spin-orbit interaction present in the valence band of silicon to drive ultra-fast and ultra-coherent hole spin quantum bits (qubits).
Still, the research could help scientists understand the spin-orbit interaction, the interplay between a proton's angular momentum in its orbital and its intrinsic angular momentum, or spin.
Their topics include self-organizing carbon structures: tight binding molecular dynamics calculations, effects of spin-orbit interaction on optical properties for quantum dots and quantum wires, up-converting nanoparticles as promising markers for biomedical applications, graphene and fullerene clusters: molecular polarization and ion-di/graphene associations, and some scientific and ethical issues around developing sustainability.
The reason for the synchronous spin motion is a carefully engineered spin-orbit interaction, a physical mechanism that couples the spin with the motion of the electron.
Time Reversal Aharonov-Casher Effect Using Rashba Spin-Orbit Interaction.
In materials where the spin-orbit interaction is strong, a spin-up electron will be deflected in one direction on encountering a nuclear magnetic field, while a spin-down nucleus will be deflected in the opposite direction - an effect dubbed the quantum spin Hall effect.
The results show that relative spin-orbit interaction effect is insignificant according to Rashba effect for thin layer Pb/Si(III) empirical results contrary to high atomic number of zinc.
Other topics include semiconductor QDs based on spin-orbit interaction, Wigner crystallization in a few-electronic circular QD, and a progress report on research in II-IV QDs.
ground] plus a spin-orbit interaction that results from the presence of the excited Na 3[P.
As wide bandgap III-nitride nanostructures are relatively new materials, he pays special attention to comparing zinc-blend gallium-arsenic with wurtzite gallium-nitrogen-based structures where the Rashba spin-orbit interaction plays a crucial role in voltage-controlled spin engineering.
Except for the quantum numbers, Eisberg and Resnick [6, Example 8-3] find a similar result for the energy due to spin-orbit interaction.

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