Crystal-field calculations with trigonal bipyramidal symmetry potential. 2. Weak-field matrices at nonzero spin-orbit coupling for a d3,7 configuration

1978 ◽  
Vol 82 (7) ◽  
pp. 825-829 ◽  
Author(s):  
F. Palacio
Keyword(s):  
Crystal Field ◽  
Weak Field ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Symmetry Potential ◽  
Trigonal Bipyramidal ◽  
Nonzero Spin

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.

Determination of the spin orbit coupling and crystal field splitting in wurtzite InP by polarization resolved photoluminescence

2018 ◽  
Vol 112 (7) ◽  
pp. 071903 ◽  
Author(s):  
Nicolas Chauvin ◽  
Amaury Mavel ◽  
Ali Jaffal ◽  
Gilles Patriarche ◽  
Michel Gendry
Keyword(s):  
Crystal Field ◽  
Orbit Coupling ◽  
Crystal Field Splitting ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Field Splitting

Space-group operations and time-reversal for a Dirac electron in a crystal field

1958 ◽  
Vol 243 (1235) ◽  
pp. 546-554 ◽  
Keyword(s):  
Dirac Equation ◽  
Crystal Field ◽  
Time Reversal ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Band Theory ◽  
Space Group ◽  
Basic Formalism ◽  
Dirac Electron

It is shown in the first part how the basic formalism of the theory of spin-orbit coupling in the band theory of crystals can be deduced at once from the Dirac equation without the usual ambiguities over improper rotations associated with the formalism based on the Pauli-Schrödinger equation. In the second part it is shown that the original proofs of the time-reversal theorems given by Wigner are unnecessarily complicated.

On the magnetic anisotropy and susceptibility of Fe(NH 4 SO 4 ) 2 , 6H 2 O

1961 ◽  
Vol 261 (1305) ◽  
pp. 207-214 ◽  
Keyword(s):  
Thermal Expansion ◽  
Magnetic Anisotropy ◽  
Crystal Lattice ◽  
Crystal Field ◽  
Coupling Coefficient ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Anisotropic Part ◽  
Free Ion

The theory of magnetic anisotropy and susceptibility of Fe 2+ in Tutton salts has been worked out on the basis of Abragam & Pryce’s method. It is found that the anisotropic part of the crystal field changes with temperature owing to the thermal expansion of the crystal lattice. The spin-orbit coupling coefficient has to be decreased by ~ 20 % from its free ion value of - 103 cm -1 which indicates some amount of overlap between the 3 d -Fe 2+ and 8 - and p -O 2- charge clouds. The agreement of the theoretical values with the experiment is good within the limitations of the approximations involved.

The spectrum of Tm III in CaF 2

1964 ◽  
Vol 277 (1370) ◽  
pp. 289-296 ◽  
Keyword(s):  
Crystal Field ◽  
Coupling Parameter ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Paramagnetic Resonance ◽  
Hyperfine Constant ◽  
Charge Model ◽  
Resonance Data ◽  
Atomic Beams

The crystal field of CaF 2 is evaluated on a point-charge model, and from comparison with the crystal field constants derived from the optical spectrum (Kiss 1962) of Tm III in CaF 2 , empirical values of < r 4 >= 4.3 a.u., < r 6 > = 36 a.u. are found. These are considerably larger than the estimates of Freeman & Watson (1962). The crystal field data reveal a small discrepancy with the paramagnetic resonance data of Hayes & Twidell (1961), which can be resolved by the introduction of an orbital k -factor which is slightly less than unity (1 — k — 0009 ± 0-001). Comparison with the spectrum of Tm I measured by atomic beams (Ritter 1962) shows that the magnetic hyperfine constant for a free Tm III ion is (2.2 ± 0.5 )% greater, while the spin-orbit coupling is 1.2% greater, assuming a core polarization correction of the same magnitude as that measured for Eu III in CaF 2 . Similar effects are shown to occur for Ho III in CaF 2 . The results suggest that the values of < r -3 > and the spin-orbit coupling parameter ζ are only about 1 to 2 % greater for the free divalent 4 f ions than for the atoms.

scholarly journals Excitonic magnetism at the intersection of spin-orbit coupling and crystal-field splitting

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Teresa Feldmaier ◽  
Pascal Strobel ◽  
Michael Schmid ◽  
Philipp Hansmann ◽  
Maria Daghofer
Keyword(s):  
Crystal Field ◽  
Orbit Coupling ◽  
Crystal Field Splitting ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Field Splitting

Investigation of the multiplet structures and crystal field effects of a TiO6 3d 1 cluster based on configuration interaction calculations

2017 ◽  
Vol 50 (2) ◽  
pp. 576-584 ◽  
Author(s):  
Meng Wu ◽  
Jin-Cheng Zheng ◽  
Hui-Qiong Wang
Keyword(s):  
Charge Transfer ◽  
Crystal Field ◽  
Configuration Interaction ◽  
Local Density ◽  
Orbit Coupling ◽  
Crystal Field Splitting ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Transfer Energy ◽  
Field Splitting

Configuration interaction cluster calculation can effectively reproduce the experimentally measured Ti L 23-edge absorption spectrum for the TiO6 cluster LaTiO3. A further investigation of the hybridization strength and charge-transfer energy effects on the multiplet structures suggests that LaTiO3 should be classified as an intermediate state between the charge-transfer and Mott–Hubbard regimes. Detailed temperature-dependent simulations of absorption spectra support the lifting of Ti t 2g orbital degeneracy and crystal field splitting. The spin–orbit coupling scenario is ruled out, even though 3d spin–orbit coupling can reproduce the experimental spectrum without including temperature. A combined polarization- and crystal-field-splitting-dependent analysis indicates asymmetric ΔCF–orbital interactions for the TiO6 cluster [Ti3+:3d 1(t 2g 1)], different from the orbital–lattice interactions reported for the NiO6 cluster [Ni3+:3d 7(t 2g 6 eg 1)]. The orbital polarization is defined in terms of the normalized electron occupancies in orbitals with xy and xz(yz) symmetries, and nearly complete orbital polarization (more than 75%) is observed, indicating strongly reduced orbital fluctuations due to the correlation effects. This is consistent with the density of states for titanates based on local density approximation plus dynamical mean-field theory calculations.

scholarly journals Crystal-field effects in graphene with interface-induced spin-orbit coupling

2018 ◽  
Vol 98 (4) ◽  
Author(s):  
Tarik P. Cysne ◽  
Aires Ferreira ◽  
Tatiana G. Rappoport
Keyword(s):  
Crystal Field ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Field Effects
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