The effect of spin-orbit splitting on the valence band density of states of lead

Tight-binding calculations are reported for the valence bands of lead, with and without spin-orbit splitting in the 6p bands. The addition of spin-orbit interaction is necessary to reproduce the two-peaked structure in the 6p density of states observed in X-ray photoemission, in contrast to the assertion by Breeze that crystal-field effects alone are enough. The observed splitting is, however, only fortuitously nearly equal to the atomic spin-orbit splitting. The tight-binding band structure, with spin-orbit splitting, gives better overall agreement with optical, Fermi surface, and photoemission data than did any of the three earlier band structures.     

Unified calculations of the optical band positions and spin-Hamiltonian parameters for V2+ ions in CdCl2 crystal

The eight optical spectral band positions and three spin-Hamiltonian parameters (g factors g_//, g_⊥ and zero-field splitting D) of V²⁺ ions in trigonal CdCl₂ crystal are calculated together from the complete diagonalisation (of energy matrix) method (CDM) based on the two-spin-orbit-parameter model (also called the cluster approach). In the model, differing from the usual one-spin-orbit-parameter model in the conventional crystal-field theory (where only the contribution to spin-Hamiltonian parameters due to the spin-orbit parameter of central dⁿ ion is considered), both the contributions from the spin-orbit parameter of central dⁿ ion and that of ligand ions are taken into account. The calculated results show reasonable agreement with the experimental values. The local lattice relaxation in the vicinity of V²⁺ ion due to the introduction of V²⁺ impurity is acquired from the calculations. The calculations of spin-Hamiltonian parameters from the CDM based on the one-spin-orbit-parameter and those from the perturbation theory method based on the two-spin-orbit-parameter model are also made for comparison. The results are discussed.     

Optical properties of ZnCr<Subscript>2</Subscript>Se<Subscript>4</Subscript>

We studied the optical properties of antiferromagnetic ZnCr₂Se₄ by infrared spectroscopy up to 28,000 cm^-1 and for temperatures from 5 to 295 K. At the magnetic phase transition at 21 K, one of the four phonon modes reveals a clear splitting of 3 cm^-1 as a result of spin-phonon coupling, the other three optical eigenmodes only show shifts of the eigenfrequencies. The antiferromagnetic ordering and the concomitant splitting of the phonon mode can be suppressed in a magnetic field of 7 T. At higher energies we observed a broad excitation band which is dominated by a two-peak-structure at about 18,000 cm^-1 and 22,000 cm^-1, respectively. These energies are in good agreement with the expected spin-allowed crystal-field transitions of the Cr³⁺ ions. The unexpected strength of these transitions with d-d character is attributed to a considerable hybridization of the selenium p with the chromium d orbitals.     

Unified calculations of spin-Hamiltonian parameters and optical band positions for Ni+ ion in AgGaSe2 crystal

The complete diagonalisation (of energy matrix) method based on the two-spin-orbit-parameter model is applied to unifiedly calculate the spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants A_//, A_⊥) and optical band positions for Ni⁺ ion in silver gallium selenide (AgGaSe₂) crystal. In the model, besides the contribution due to the spin-orbit parameter of central dⁿ ion (i.e., the one-spin-orbit-parameter model in the traditional crystal-field theory), that of ligand ions are taken into account. The calculated results are reasonably consistent with the experimental values. The local structure of Ni⁺ centre in AgGaSe₂ is estimated through the calculation. The complete diagonalisation method based on the one-spin-orbit-parameter model is also applied to calculate these electron paramagnetic resonance and optical data. It is found that although the calculated optical band positions are close to those based on the two-spin-orbit-parameter model and hence to the experimental values, the calculated spin-Hamiltonian parameters (in particular, the g factors) are in disagreement with the experimental values. The latter point is further confirmed from the calculations with the perturbation method. So, for the rational calculations of spin-Hamiltonian parameters of dⁿ clusters with ligand having large spin-orbit parameter, the contributions due to spin-orbit parameters of both the central dⁿ ion and ligand ion should be contained.     

Application of the NRL tight-binding method to the heavy elements Pb and Po

We have applied the NRL tight-binding (TB) method to study the mechanical and electronic properties of the heavy elements Pb and Po. The predicted properties include ground-state structure, electronic band structure and elastic moduli. Phonon-dispersion curves at T=0 K were also determined. As demonstrated in this paper, the results are in good agreement with the full potential linearized augmented plane wave calculations and the available experimental data. In addition, we performed molecular-dynamics simulations to obtain various temperature-dependent quantities of Pb such as the atomic mean-square displacement, Debye-Waller factor and thermal expansion coefficient. With our TB we have also calculated the vacancy formation energy of Pb. Finally, we report on the effects of spin-orbit coupling, through our TB scheme, on electronic structure and energetic properties.     

Strong Coulomb correlation effects in ZnO

The electronic structure, band parameters, and optical spectra of wurtzite-type ZnO were studied by first-principles calculations within different approximations of the density functional theory. The local-density approximation underestimates the band gap, the energy levels of the Zn-3d states, the band dispersion, the crystal-field splitting, the spin-orbit interaction, and location of peaks in the optical spectra. The generalized-gradient approximation slightly corrects the discrepancies with the experimental findings and it shows good agreement for the optical spectra with experimental data at energies 10-20 eV for E⊥c. Studies within the local-density approximation with the multiorbital mean-field Hubbard potential show that strong Coulomb correlations are in operation. From effective mass calculations it is found that holes are much heavier and more anisotropic than the conduction-band electrons in ZnO.     

Electronic structures of the zinc-blende GaN/Ga1−xAlxN compressively strained superlattices and quantum wells

The electronic structures of the zinc-blende GaN/Ga_0.85Al_0.15N compressively strained superlattices and quantum wells are investigated using a 6×6 Hamiltonian model (including the heavy hole, light hole and spin-orbit splitting band). The energy bands, wavefunctions and optical transition matrix elements are calculated. It is found that the light hole couples with the spin-orbit splitting state even at thek=0 point, resulting in the hybrid states. The heavy hole remains a pure heavy hole state atk=0. The optical transitions from the hybrid valence states to the conduction states are determined by the transitions of the light hole and spin-orbit splitting states to the conduction states. The transitions from the heavy hole, light hole and spin-orbit splitting states to the conduction states obey the selection rule Δn=0. The band structures obtained in this work will be valuable in designing GaN/GaAlN based optoelectronic devices.     

闪锌矿结构CdTe和ZnTe能带结构和有效质量的第一性原理计算

基于第一性原理全电子势线性缀加平面波方法(FPLAPW)，计算了闪锌矿结构半导体材料ZnTe，CdTe的能带结构.结合闪锌矿对称化合物的有效质量近似理论，对第一性原理的计算结果进行拟合后，得到了ZnTe，CdTe在带隙附近的电子结构.此外还讨论了晶体场分裂能、自旋-轨道相互作用的分裂能和电子、空穴的有效质量及相应的Luttinger参数，结果与实验值相符合. 关键词： FLAPW 电子结构 有效质量     

Quantum theory of the magneto-optical effect and magnetization of Nd-substituted yttrium iron garnet

The magneto-optical and magnetic properties of Nd ³⁺ ions in Y ₃Fe ₅O ₁₂ garnet are analyzed by using quantum theory. In the spontaneous state, the magneto-optical effects originate mainly from the intra-ionic electric dipole transitions between the 4 f ³ and 4 f ²5d states split by the spin-orbit, crystal field, and superexchange interactions. For the excited configuration, the coupling scheme of Yanase is extended to the Nd ³⁺ ion. The magneto-optical resonance frequencies are mainly determined by the splitting of the 5d states induced by the crystal field. The theoretical results of both Nd magnetization and Faraday rotation are in good agreement with experiments. The observed Faraday rotation is proved to be of the paramagnetic type. Although the value of the magneto-optical resonance frequency derived from a macroscopic analysis is approximately confirmed by our theoretical study, a new assignment about the transitions associated with this resonance is unambiguously determined. The spin-orbit coupling of the ground configuration has a great influence on both the Faraday rotation and magnetization, but, unlike the theoretical results obtained in some metals and alloys, the relation between the Faraday rotation and the spin-orbit coupling strength is more complex than a linear one. The magnitude of the magneto-optical coefficient increases as the spin-orbit interaction strength of the ground configuration decreases when the strength is not very weak. Finally, the temperature dependence of the magneto-optical coefficient and the effect of the mixing of different ground-term multiplets induced by the crystal field are analyzed. Received 8 November 2000     

Spin–orbit coupling in bulk GaAs

We study the spin–orbit coupling in the whole Brillouin zone for GaAs using both the sp³s^*d⁵ and sp³s^* nearest-neighbor tight-binding models. In the Γ-valley, the spin splitting obtained is in good agreement with experimental data. We then further explicitly present the coefficients of the spin splitting in GaAs L- and X-valleys. These results are important to the realization of spintronic device and the investigation of spin dynamics far away from equilibrium.     

Spectral signatures of hyperfine and isotopic effects and of Tm-Tm pairs in LiYF4:Tm

We report on the high-resolution optical Fourier-transform spectroscopy of the LiYF₄:Tm³⁺ crystals. Splitting of several lines in the optical low-temperature polarized spectra was observed. We show that these splittings are caused by (i) the hyperfine interaction, (ii) the isotopic disorder in the lithium sublattice, and (iii) the interionic interaction between neighboring Tm ions. It is the first observation of the hyperfine splitting in the spectra of the Tm³⁺ ions in crystals. From the experimentally measured hyperfine splitting we evaluate the magnetic field at the thulium nucleus and calculate the magnetic g-factors of the excited crystal-field levels.     

Positioning photonic crystal cavities to single InAs quantum dots

We have investigated the optical properties of planar photonic crystal cavities formed by removing a single hole from a two-dimensional square lattice of air holes etched through a thin GaAs slab. We have demonstrated cavity resonances with quality factors (Q’s) as high as 8500, using an internal light source provided by an ensemble of InAs quantum dots (QDs) grown by molecular beam epitaxy (MBE). The high-Q modes are confined to a very small mode volume, V = 0.7(λ/n)³, making them attractive to study in the context of cavity quantum electrodynamics with single QDs, where a high is needed to observe the strong coupling between an electronic state of the dot and the optical cavity mode. To this end, we have developed an accurate and robust alignment technique that positions a photonic crystal cavity to a single QD with 25 nm resolution. We present the details of this new technology and demonstrate its effectiveness by strategically positioning a number of QDs within photonic crystal cavities at points where the electric field intensity is high.     

Interpretation of the excitation spectrum of Cr2+(d 4) ions in ZnS crystals

The excitation spectrum of Cr²⁺ in ZnS is interpreted on the base of classical crystal field theory with a modification accounting for the dependence of one-electron energies on spin orientation. In a treatment starting from the relevant free-ion terms, values of the crystal-field splitting parameterDq, the Racah parameterB and the spin-polarisation energyE _p are derived. Implications of spin-orbit interaction and Jahn-Teller effect are discussed.     

Mössbauer,magnetic susceptibility,EPR, and EXAFS investigations of the vibrationally-induced low-spin/high-spin transition in a biomimetic Fe(III) complex

Magnetic susceptibility measurements from 2 to 520 K, Mössbauer measurements from 1.2 to 450 K, and EPR measurements at 10 K have been performed on the monomeric Fe^III complex (1,4,7-tris(4-tert-butyl-2-mercaptobenzyl)-1,4,7-triaza-cyclononan)Fe. The complex exhibits a low-spin/high-spin transition at temperatures above 250 K. This behavior is quantitatively explained on the basis of a crystal-field model, which explicitly includes the vibrational properties of iron ligands. The EPR spectrum at 10 K yields a pure Fe^III low-spin signal withg values 2.58(5), 2.12(5), 1.45(5). The values are consistently described by a crystal-field model, which explicitly includes spin-orbit coupling within the t_2g subspace. The temperature dependence of the quadrupole splitting indicates a phase transition at approximately 100 K. The existence of the phase transition is corroborated by the temperature dependence of the effective thickness. The observation of only one quadrupole doublet up to 450 K indicates that the relaxation time between the high-spin and the low-spin configurations is shorter than the quadrupole precession time. X-ray structure analysis on single crystals at RT and temperature-dependent EXAFS investigation of powder material between 30 and 200 K indicate that the observed phase transition induces only changes of bond angles, while the low-spin/high-spin transition most likely induces changes of metal-ligand bond distances.     

自旋轨道耦合作用对碳纳米管电子能带结构的影响

本文考虑自旋轨道耦合作用的情况下,采用紧束缚近似螺旋对称模型计算了单壁碳纳米管的电子能带结构.研究发现:对于Armchair型单壁碳纳米管,自旋轨道耦合作用和弯曲效应共同导致了费米面Dirac点附近电子能带结构的能隙;对于Zigzag型和手性单壁碳纳米管,自旋轨道耦合作用使得电子最高占据态和最低未占据态产生能级劈裂,能级劈裂的大小不但与碳纳米管的直径和手性角密切相关,而且相对于费米面是不对称的;根据指数(n,m)可以将Zigzag型和手性单壁碳纳米管分为金属性碳纳米管(ν=0) 关键词： 单壁碳纳米管 自旋轨道耦合 紧束缚近似螺旋对称模型     

Optical properties of semiconducting carbon nanotubes under axial magnetic field

The linear polarizability absorption spectra of semiconducting carbon nanotubes under axial magnetic field (B) have been calculated by the π-orbital tight-binding model and sum-over-state method. We have found that the optical spectra are split by the B-induced symmetry breaking and the amount of splitting increases with increase of magnetic field. Although the results are obtained within the noninteracting tight-binding model, the amount of splitting is still consistent with the experimental observation, offering a fast estimation of the B-induced splitting. Our numerical results also indicate that the splitting amounts of the second and third absorption peaks are close to that of the first one, which may be observed by the future experiments.     

Ground state properties of CsCoCl3

The electronic spectra of CsCoCl₃ are fit to a Hamiltonian that includes terms for interelectron repulsion, octahedral and trigonal crystal fields, and spin-orbit coupling. The fit adequately accounts for both the optical spectrum and the electronic Raman spectrum. The fitted parameters give empirical estimates of the radial expectation values 〈r^?1〉 and 〈r^?3〉 as well as the charge on the cobalt. The ground state wave functions generated from the fit are used to calculate the following properties: parallel and perpendicular g factors, Co hyperfine field, ⁵⁹Co quadrupole splitting, anisotropy of magnetic exchange, the magnetic moment of Co²⁺, and the spin flop field. The agreement between calculated values and observed values for this variety of independently obtained properties is reasonable in all cases.     

Perturbative Handling of the Renner-Teller Effect and Spin-Orbit Coupling in Π Electronic States of Triatomic and Tetra-atomic Molecules

Second-order perturbative formulae for handling the Renner-Teller effect combined with the spin-orbit coupling in Π electronic states of triatomic and symmetric (ABBA-type) tetra-atomic molecules with linear equilibrium geometry are derived. Two schemes for partition of the model Hamiltonian are employed: In the first the spin-orbit coupling term is treated as a perturbation, in the second it is included in the zeroth-order Hamiltonian. It is demonstrated that both approaches lead to the same results when the spin-orbit coupling constant is small compared to the bending frequency, but much larger than the splitting of potential surfaces upon bending. The perturbative formulae derived for tetra-atomic molecules are used to compute the spectrum of the X²Π_u state of the acetylene ion, employing the parameters obtained in ab initio calculations. The results are compared with those generated in corresponding variational computations.     

Electron transport through SWNT/<Emphasis Type="Italic">trans</Emphasis>-PA/SWNT structure (the role of solitons): A t-matrix technique

Using a tight-binding model and a transfer-matrix technique, we numerically investigate the effects of the coupling strength and the role of solitons on the electronic transmission through a system in which trans-polyacetylene (trans-PA) molecule is sandwiched between two semi-infinite single-walled carbon nanotubes (SWNT). We rely on Landauer formalism as the basis for studying the conductance properties of this system. Our calculations show that the solitons play an important role in the response of this system causing a large enhancement in the conductance. Also our results suggest that the conductance is sensitive to the CNT/molecule coupling strength.      

A comprehensive study of the effect of <Emphasis Type="Italic">in situ</Emphasis> annealing at high growth temperature on the morphological and optical properties of self-assembled InAs/GaAs QDs

We investigate the effect of in situ annealing during growth pause on the morphological and optical properties of self-assembled InAs/GaAs quantum dots (QDs). The islands were grown at different growth rates and having different monolayer coverage. The results were explained on the basis of atomic force microscopy (AFM) and photo-luminescence (PL) measurements. The studies show the occurrence of ripening-like phenomenon, observed in strained semiconductor system. Agglomeration of the self-assembled QDs takes place during dot pause leading to an equilibrium size distribution. The PL properties of the QDs are affected by the Indium desorption from the surface of the QDs during dot pause annealing at high growth temperature (520°C) subsiding the effect of the narrowing of the dot size distribution with growth pause. The samples having high monolayer coverage (3.4 ML) and grown at a slower growth rate (0.032 ML s⁻¹) manifested two different QD families. Among the islands the smaller are coherent defect-free in nature, whereas the larger dots are plastically relaxed and hence optically inactive. Indium desorption from the island surface during the in situ annealing and inhomogeneous morphology as the dots agglomerate during the growth pause, also affects the PL emission from these dot assemblies.