ROTATIONAL ENERGY LEVELS OF STATES AND INTENSITIES IN TRANSITIONS: APPLICATIONS TO SOME HEAVIER HYDRIDES

1967 ◽  
Vol 45 (8) ◽  
pp. 2581-2596 ◽  
Author(s):  
I. Kopp ◽  
J. T. Hougen
Keyword(s):  
Energy Levels ◽  
Relative Size ◽  
Orbit Interaction ◽  
Spin Splitting ◽  
Energy Separation ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
First Approximation ◽  
Coupling Case ◽  
Π State

Three topics concerning [Formula: see text] states are discussed: (1) The magnitude of the Ω-type splitting in a [Formula: see text] state arising from a Σ state of even multiplicity has been considered and is found to be given to a first approximation by [Formula: see text]. This result leads to the introduction and discussion of a coupling case (a′) for Σ states. (2) Expressions for the Λ-type splitting in a 2Π state and the spin splitting in a 2Σ state (caused by their mutual interaction via spin-orbit coupling) are derived. These expressions are valid when the rotational intervals are small compared to both the spin-orbit interaction and the 2Π−2Σ energy separation, but do not place any restriction on the relative size of the latter two quantities. (3) Branch intensity expressions are presented which apply to any [Formula: see text] transition in which the [Formula: see text] states are not contaminated (due to uncoupling phenomena) by states having a different value of Ω.

Ground configuration splitting in UCl5

1977 ◽  
Vol 55 (10) ◽  
pp. 937-942 ◽  
Author(s):  
A. F. Leung ◽  
Ying-Ming Poon
Keyword(s):  
Crystal Field ◽  
Energy Levels ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Point Charge Model ◽  
X Ray Crystallography ◽  
Charge Model ◽  
Crystal Field Parameters

The absorption spectra of UCl5 single crystal were observed in the region between 0.6 and 2.4 μm at room, 77, and 4.2 K temperatures. Five pure electronic transitions were assigned at 11 665, 9772, 8950, 6643, and 4300 cm−1. The energy levels associated with these transitions were identified as the splittings of the 5f1 ground configuration under the influence of the spin–orbit coupling and a crystal field of C2v symmetry. The number of crystal field parameters was reduced by assuming the point-charge model where the positions of the ions were determined by X-ray crystallography. Then, the crystal field parameters and the spin–orbit coupling constant were calculated to be [Formula: see text],[Formula: see text], [Formula: see text], and ξ = 1760 cm−1. The vibronic analysis showed that the 90, 200, and 320 cm−1 modes were similar to the T2u(v6), T1u(v4), and T1u(v3) of an UCl6− octahedron, respectively.

scholarly journals Layer- and gate-tunable spin-orbit coupling in a high-mobility few-layer semiconductor

2021 ◽  
Vol 7 (5) ◽  
pp. eabe2892
Author(s):  
Dmitry Shcherbakov ◽  
Petr Stepanov ◽  
Shahriar Memaran ◽  
Yaxian Wang ◽  
Yan Xin ◽  
...  
Keyword(s):  
Electric Field ◽  
High Mobility ◽  
Orbit Coupling ◽  
Spin Splitting ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Quantum Oscillations ◽  
Out Of Plane ◽  
Order Of Magnitude ◽  
Spin Degeneracy

Spin-orbit coupling (SOC) is a relativistic effect, where an electron moving in an electric field experiences an effective magnetic field in its rest frame. In crystals without inversion symmetry, it lifts the spin degeneracy and leads to many magnetic, spintronic, and topological phenomena and applications. In bulk materials, SOC strength is a constant. Here, we demonstrate SOC and intrinsic spin splitting in atomically thin InSe, which can be modified over a broad range. From quantum oscillations, we establish that the SOC parameter α is thickness dependent; it can be continuously modulated by an out-of-plane electric field, achieving intrinsic spin splitting tunable between 0 and 20 meV. Unexpectedly, α could be enhanced by an order of magnitude in some devices, suggesting that SOC can be further manipulated. Our work highlights the extraordinary tunability of SOC in 2D materials, which can be harnessed for in operando spintronic and topological devices and applications.

Ligand Field-Spin Orbit Energy Levels in the d4 and d6 Electron Configurations of Octahedral and Tetrahedral Symmetry

1974 ◽  
Vol 29 (1) ◽  
pp. 31-41 ◽  
Author(s):  
E. König ◽  
S. Kremer
Keyword(s):  
Strong Field ◽  
Energy Levels ◽  
Coulomb Repulsion ◽  
Orbit Interaction ◽  
Complete Agreement ◽  
Ligand Field ◽  
Spin Orbit ◽  
Tetrahedral Symmetry ◽  
Spin Orbit Interaction ◽  
Orbit Perturbation

The complete ligand field -Coulomb repulsion -spin orbit interaction matrices have been derived for the d4 and d6 electron configurations within octahedral (Oh) and tetrahedral (Td) symmetry. The calculations were perform ed in both the weak-field and strong-field coupling schemes and complete agreement of the results was achieved. The energy matrices are parametrically dependent on ligand field (Dq), Coulomb repulsion (B, C) and spin-orbit interaction (ζ). Correct energy diagrams are presentend which display the splittings by spin-orbit perturbation as well as the effect of configuration mixing. Applications to the interpretation of optical spectral data, to the detailed behavior at the crossover of ground terms, and to complete studies in magnetism are pointed out.

scholarly journals Ligand-Field Spin-Orbit Energy Levels in the d5 Electron Configuration of Octahedral and Tetrahedral Symmetry

1974 ◽  
Vol 29 (3) ◽  
pp. 419-428 ◽  
Author(s):  
E. König ◽  
R. Schnakig ◽  
S. Kremer
Keyword(s):  
Strong Field ◽  
Energy Levels ◽  
Orbit Interaction ◽  
Complete Agreement ◽  
Ligand Field ◽  
Electron Configuration ◽  
Spin Orbit ◽  
Tetrahedral Symmetry ◽  
Spin Orbit Interaction ◽  
Orbit Perturbation

The complete ligand-field, Coulomb interelectronic repulsion, and spin-orbit interaction matrices have been derived for the d5 electron configuration within octahedral (Oh) and tetrahedral (Td) symmetry. The calculations were performed in both the weak-field and strong-field coupling schemes and complete agreement of the results was achieved. The energy matrices are parametrically dependent on ligand field (Dq), Coulomb repulsion (B, C), and spin-orbit interaction (ζ). Correct energy diagrams are presented which display the splittings by spin-orbit perturbation as well as the effect of configuration mixing. Applications to the interpretation of electronic spectra, and to complete studies in magnetism are pointed out. The detailed behavior at the crossover of ground terms is considered

scholarly journals Absence of the Rashba Splitting of Au(111) Surface Bands

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
I. N. Yakovkin
Keyword(s):  
Electronic Structure ◽  
Dft Calculations ◽  
Surface States ◽  
Orbit Coupling ◽  
Spin Splitting ◽  
Inversion Symmetry ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Relativistic Approximation ◽  
Photoemission Experiment

The electronic structure of Au(111) films is studied by means of relativistic DFT calculations. It is found that the twinning of the surface bands, observed in photoemission experiment, does not necessarily correspond to the spin-splitting of the surface states caused by the break of the inversion symmetry at the surface. The twinning of the bands of clean Au(111) films can be obtained within nonrelativistic or scalar-relativistic approximation, so that it is not a result of spin-orbit coupling. However, the spin-orbit coupling does not lead to the spin-splitting of the surface bands. This result is explained by Kramers’ degeneracy, which means that the existence of a surface itself does not destroy the inversion symmetry of the system. The inversion symmetry of the Au(111) film can be broken, for example, by means of adsorption, and a hydrogen monolayer deposited on one face of the film indeed leads to the appearance of the spin-splitting of the bands.

ELECTRONIC PROPERTIES OF A HYDROGENIC IMPURITY IN A QUANTUM WIRE WITH V-SHAPED CROSS-SECTION: SPIN-ORBIT COUPLING, RELATIVISTIC CORRECTION AND CONDUCTANCE

2013 ◽  
Vol 24 (07) ◽  
pp. 1350041 ◽  
Author(s):  
R. KHORDAD ◽  
H. BAHRAMIYAN
Keyword(s):  
Cross Section ◽  
Quantum Wire ◽  
Energy Levels ◽  
Relativistic Correction ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Hydrogenic Impurity ◽  
Mass Approximation ◽  
Shaped Cross Section

The effects of spin-orbit coupling (SOC) and relativistic correction (RC) on the energy levels of a hydrogenic impurity in a GaAs/Ga 1-x Al x As quantum wire are studied. The quantum wire has a V-shaped cross-section and the impurity located in its center. Our numerical calculations have done using a variational procedure within the effective mass approximation. Our results show that (i) the splitting due to the SOC decreases with increasing the wire width, (ii) the SOC and RC increase when the concentration increases, (iii) the SOC is zero for l = 0 (l is angular momentum) and nonzero for l ≠ 0, (iv) for a given wire width, the RC is different for l = 0 and l = 1 due to expectation values of [Formula: see text] and [Formula: see text] (r is distance between the electron and impurity). We also computed the conductance of the quantum wire with and without impurity.

Spin-Orbit Coupling and Zero-Field Electron Spin Splitting in AlGaN/AlN/GaN Heterostructures with a Polarization Induced Two-Dimensional Electron Gas

2006 ◽  
Vol 955 ◽  
Author(s):  
Ç. Kurdak ◽  
N. Biyikli ◽  
H. Cheng ◽  
U. Ozgur ◽  
H. Morkoç ◽  
...  
Keyword(s):  
Electron Spin ◽  
Orbit Coupling ◽  
Spin Splitting ◽  
Zero Field ◽  
Material System ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Weak Antilocalization ◽  
High Carrier ◽  
Dimensional Electron Gas

ABSTRACTWe studied spin-orbit coupling in wurtzite AlxGa1−xN/AlN/GaN heterostructures with different Al concentrations using weak antilocalization measurements at 1.6 K. Using the persistent photoconductivity effect we change the carrier density in controllable manner. We find that the electron spin splitting energies does not scale linearly with the Fermi wavevector at high carrier densities. From this deviation, for the first time, we are able to extract the cubic spin-orbit parameter for this material system.

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