Download Citation on ResearchGate | Etude du couplage spin-orbite dans les metaux de transition. Application au platine | The effect of spin-orbit coupling on. Download Table | 1 -Intégrales de Slater et paramètres de couplage spin-orbite ( eV) pour Co 2+ pour les quatre configurations considérées. from publication. Spin-orbit coupling in Wien2k. Robert Laskowski [email protected] Institute of High Performance Computing. Singapore.

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In quantum physicsthe 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—orbit interaction leading to shifts in an electron ‘s atomic energy levelsdue to electromagnetic interaction between the electron’s magnetic dipoleits orbital motion, and the electrostatic field of the positively charged nucleus.

This phenomenon is detectable as a splitting of spectral lineswhich can be thought of as a Zeeman effect product of two relativistic effects: A similar effect, due to the relationship between angular momentum and the strong nuclear forceoccurs for protons and neutrons moving inside the nucleus, leading to a shift in their energy levels in the nucleus shell model.

In the field of spintronicsspin—orbit effects for electrons in semiconductors and other materials are explored for technological applications.

The spin—orbit interaction is one cause of magnetocrystalline anisotropy and the spin Hall effect. For atoms, energy level split produced by the spin-orbit interaction is usually of the same order in size to the relativistic corrections to the kinetic energy and the zitterbewegung effect. The addition of these three corrections is coulpage as the fine structure.

Note that the spin-orbit effect is due to the electrostatic field of the electron and not the magnetic field created by its orbit. The interaction between the magnetic field created by the electron and the magnetic moment of the nucleus is a slighter correction to the energy levels known as the hyperfine structure. This section presents a relatively simple and quantitative description of the spin—orbit interaction for an electron bound to a hydrogen-like atomup to first order in perturbation theoryusing some semiclassical electrodynamics and non-relativistic coullage mechanics.

This gives results that agree reasonably sipn with observations. Couplave rigorous calculation of the same result would use relativistic quantum mechanicsusing Dirac equationand would include many-body interactions.

Achieving an even more precise result would involve calculating small corrections from quantum electrodynamics.

We shall deal with the magnetic field first. Although in the rest frame of the nucleus, there is no magnetic field acting on the electron, there is one in the rest frame of the electron see classical electromagnetism and special relativity.

Ignoring for now that this frame is not inertialin SI units we end up with the equation. Substituting this in and changing the order of the cross product gives. Here we make the central field approximationthat is, that the electrostatic potential is spherically symmetric, so is only a function of radius. This approximation is exact for hydrogen and hydrogen-like systems. Now we can say that. Putting it all together, we get.

It is important to note at this point that B is a positive number multiplied by Lmeaning that the magnetic field is parallel to the orbital angular momentum of the particle, which is itself perpendicular to the particle’s velocity. The magnetic moment of the electron is. The spin—orbit potential consists of two parts.

The Larmor part is connected to the interaction of the magnetic moment of the electron with the magnetic field of the nucleus in the co-moving frame of the electron. The second contribution is related to Thomas precession. Substituting in this equation expressions for the magnetic moment and the magnetic field, one gets. Now we have to take into account Thomas precession correction for the electron’s curved trajectory.

In Llewellyn Thomas relativistically recomputed the doublet separation in the fine structure of the atom. Thanks to all the above approximations, we can now evaluate the detailed energy shift in this model. Note that L z and S z are no longer conserved quantities. To find out what basis this is, we first define the total angular momentum operator.

Therefore, the basis we were looking for is the simultaneous eigenbasis of these five operators i. Elements of this basis have the five quantum numbers: For the exact relativistic result, see the solutions to the Dirac equation for a hydrogen-like atom.

A crystalline solid semiconductor, metal etc. The bands of interest can be then described by various effective models, usually based on some perturbative approach. An example of how the atomic spin—orbit interaction influences the band structure of a crystal is explained in the article about Rashba and Dresselhaus interactions. In crystalline solid contained paramagnetic ions, e.

For rare-earth ions the spin—orbit interactions are much stronger than the CEF interactions. The SL and J of the ground multiplet are determined by Hund’s rules. CEF interactions and magnetic interactions resemble, somehow, Stark and Zeeman effect known from atomic physics.

### Spin-orbit coupling

The fine electronic structure can be directly detected by many different spectroscopic methods, including the inelastic neutron scattering INS experiments. The case of strong cubic CEF [8] [9] for 3 d transition-metal ions interactions form group of levels e. T 2 gA 2 gwhich are partially split by spin—orbit interactions and if occur lower-symmetry CEF interactions.

It allows evaluate the total, spin and orbital moments. Taking into consideration the thermal population of states, the thermal evolution of the single-ion properties of the compound is established. This technique is based on the equivalent operator theory [10] defined as the CEF widened by thermodynamic and analytical calculations defined as the supplement of the CEF theory by including thermodynamic and analytical calculations.

In combination with magnetization, this type of spin—orbit interaction will distort the electronic bands depending on the magnetization direction, thereby causing magnetocrystalline anisotropy a special type of magnetic anisotropy. If the semiconductor moreover lacks the inversion symmetry, the hole bands will exhibit cubic Dresselhaus splitting. Within the four bands light and heavy holesthe dominant term is. Two-dimensional electron gas in an asymmetric quantum well or heterostructure will feel the Rashba interaction.

The appropriate two-band effective Hamiltonian is. Electric dipole spin resonance EDSR is the coupling of the electron spin with an oscillating electric field. Similar to the electron spin resonance ESR in which electrons can be excited with an electromagnetic wave with the energy given by the Zeeman effectin EDSR the resonance can be achieved if the frequency is related to the energy band split given by the spin-orbit coupling in solids.

While in ESR the coupling is obtained via the magnetic part of the EM wave with the electron magnetic moment, the ESDR is the coupling of the electric part with the spin and motion of the electrons. This mechanism has been proposed for controlling the spin of electrons in quantum dots and other mesoscopic systems.

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## Spin–orbit interaction

Electron Paramagnetic Resonance of Transition Ions. The Theory of Transition Metal Ions. The effective crystal field potential. Operator methods in ligand field theory. Sheka, Electric-Dipole Spin-Resonances, in: Retrieved from ” https: Atomic physics Magnetism Spintronics.

### Spin–orbit interaction – Wikipedia

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