scholarly journals Short Communications Crystal Field Theory and Magnetic Groups: Spin?Orbit Coupling

1967 ◽  
Vol 20 (2) ◽  
pp. 189 ◽  
Author(s):  
AP Cracknell
Keyword(s):  
Field Theory ◽  
Energy Levels ◽  
Unitary Groups ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Crystal Field Theory ◽  
Crystalline Field ◽  
Initial Work ◽  
Point Groups ◽  
Atomic Energy Levels

Some initial work has recently been done (Cracknell 1966a) on the applicationof the theory of the corepresentations of non-unitary groups to the consideration ofthe splitting of atomic energy levels in a crystalline field possessing the mmetryof one of the magnetic point groups, or Shubnikov point groups. In that work onlythe situation of a strong rystalline field in the complete absence of spin

scholarly journals Crystal Field Theory And Magnetic Point Groups

1966 ◽  
Vol 19 (4) ◽  
pp. 519 ◽  
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Crystal Field ◽  
Energy Levels ◽  
Unitary Groups ◽  
Crystal Field Theory ◽  
Symmetry Properties ◽  
Point Groups

The author's previous work on the application of Wigner's theory of the coreps of non-unitary groups to the Shubnikov groups (magnetic groups) is here considered in relation to crystal field theory. Both the splitting of the energy levels and the symmetry properties of the wave function are considered in magnetic point groups. Examples of 4'mm' and 4m'm' are studied.

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.

Pentavalent iridium pyrochlore Cd2Ir2O7 : A prototype material system for competing crystalline field and spin-orbit coupling

2018 ◽  
Vol 97 (8) ◽  
Author(s):  
Jianhong Dai ◽  
Yunyu Yin ◽  
Xiao Wang ◽  
Xudong Shen ◽  
Zhehong Liu ◽  
...  
Keyword(s):  
Orbit Coupling ◽  
Material System ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Crystalline Field

Elektronische und Resonanz-Raman-Spektren der Chloro-Bromo-Ruthenate(IV), [RuClnBr6-n]2-, n = 0 ... 6

1987 ◽  
Vol 42 (6) ◽  
pp. 597-602
Author(s):  
H. N. v. Allwörden ◽  
W. Preetz
Keyword(s):  
Fine Structure ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Tetraalkylammonium Salts ◽  
Ground Term ◽  
Point Groups ◽  
Resonance Raman Spectra ◽  
And Shifts ◽  
Electronic Resonance ◽  
Polarisation Measurements

The vibrational and electronic resonance Raman spectra of the solid tetraalkylammonium salts of [RuClnBr6-n]2-, n = 0 . . . 6, are measured at 80 K. The observed electronic Raman bands in the regions of 640-740 cm-1 and 1560-1790 cm-1 are assigned to the intraconfigurational transitions Γ1 → Γ4 and Γ1 → Γ3, Γ5 within the 3T1g(Oh) ground term. The observed splittings and shifts, due to spin orbit coupling and lowered symmetry, are interpreted qualitatively according to the point groups D4h, C4V, C3V and C2V. The O-O-transitions are deduced from vibrational fine structure. The electronic Raman bands of [RuCl6]2- and [RuBr6]2- are assigned in detail by polarisation measurements.

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.

CRYSTALLINE FIELD THEORY OF Ni2+ COMPLEXES

1967 ◽  
Vol 45 (6) ◽  
pp. 2121-2131 ◽  
Author(s):  
R. Chatterjee
Keyword(s):  
Optical Absorption ◽  
Absorption Spectra ◽  
Energy Levels ◽  
Spin Orbit Coupling ◽  
Optical Absorption Spectra ◽  
Crystalline Electric Field ◽  
Crystalline Field ◽  
Racah Parameters ◽  
Tetrahedral Complexes ◽  
Experimental Values

The energy levels of the octahedrally and the tetrahedrally coordinated 3d8 Ni2+ complexes have been calculated using the Racah formalism (1942), taking account of both the crystalline electric field and the spin-orbit coupling. The predicted optical absorption spectra are in satisfactory agreement with the observed spectra in the octahedral complexes by Hartmann and Müller (1958) and in the tetrahedral complexes by Cotton et al. (1961). The magnetic susceptibility calculated using these energy levels agrees with the experimental values. It is found that the Racah parameters must be reduced by 55% from the free ion values in order to explain the optical absorption spectra in tetrahedral complexes.

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.

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