Relativistic Band Calculations Research Articles

Intrinsic Spin Hall Effect in Platinum: First-Principles Calculations

Spin Hall effect (SHE) is studied with first-principles relativistic band calculations for platinum, which is one of the most important materials for metallic SHE and spintronics. We find that intrinsic spin Hall conductivity (SHC) is as large as approximately 2000(variant Planck's over 2 pi/e)(Omega cm)(-1) at low temperature and decreases down to approximately 200(variant Planck's over 2 pi/e)(Omega cm)(-1) at room temperature. It is due to the resonant contribution from the spin-orbit splitting of the doubly degenerated d bands at high-symmetry L and X points near the Fermi level. By modeling these near degeneracies by an effective Hamiltonian, we show that SHC has a peak near the Fermi energy and that the vertex correction due to impurity scattering vanishes. We therefore argue that the large SHE observed experimentally in platinum is of intrinsic nature.

Electronic Structure and Fermi Surface of NpGe3

Fermi surface topology of transuranium compound NpGe 3 is investigated from an itinerant 5 f picture with a relativistic band calculation in a local-density approximation (LDA), thereby analyzing the frequency branches observed by the de Haas–van Alphen (dHvA) effect. The Fermi surface volume of NpGe 3 is sensitive to the lattice constant because of its special shape. A LDA equilibrium lattice constant of NpGe 3 is determined from total-energy minimization as a function of lattice constant under the AuCu 3 -type crystal structure. The Fermi surface obtained at the LDA equilibrium can explain precisely the origin of all the dHvA frequency branches like the familiar Fermi surface of Cu. This suggests that the fermiology of Np compounds should progress on the 5 f band scheme, though Np-5 f electrons are more localized than those of a lighter actinide atom.

Fermi Surface Studies on Np115- and Related Compounds

Fermi surface studies in actinide 115-type compounds UNiGa 5 , UPtGa 5 , NpRhGa 5 and the related AuCu 3 -type compound NpGe 3 are performed with a relativistic band calculation in the local-density approximation. The recently observed de Haas–van Alphen (dHvA) frequencies are quantitatively analyzed using the obtained Fermi surfaces. In the case of the magnetic 115-compounds, especially, NpRhGa 5 the Fermi surface and the local magnetic moment, calculated in the orbital-polarized band scheme based on an itinerant 5 f picture, can give a systematic interpretation of the observed dHvA frequencies and the magnetic moment.

Fermi Surface of Heavy Fermion Compounds CeTIn5(T = Rh, Ir, and Co): Band-Calculation and Tight-Binding Approach

Electronic properties of Ce-based heavy-fermion compounds are discussed by using the relativistic band-calculation method. To seek for a route from the band calculation to a many-body Hamiitonian, which is necessary to discuss the magnetic and superconducting properties, a minimal tight-binding model is proposed for f -electron systems.

Oscillatory Magneto-Optical Effect in a Au (001) Film Deposited on Fe: Experimental Confirmation of a Spin-Polarized Quantum Size Effect

Magneto-optical response of the wedge-shaped Au ultrathin film grown on an Fe layer was investigated precisely. The magnetic circular dichroism in the reflection configuration oscillates with respect to the Au layer thickness showing superposition of several oscillations with different periods. The energy dependence of the oscillation periods is clearly explained by a concept of the spin-polarized quantum size effect in the Au layer by employing fully relativistic band calculation and electron-electron correlation.

Self-consistent relativistic band calculations and the optical conductivities of Ba and Eu

The energy band structures for BCC metals Ba and Eu are calculated by the self-consistent symmetrised relativistic APW(SRAPW) method. A one-electron potential is constructed on the basis of the local density approximation. The correlation potential for 4f electrons of Eu is separately treated so as to give the position of the 4f level expected from XPS. Non-relativistic SAPW calculations for Ba and Eu are also carried out for the purpose of comparison. The Fermi surfaces and the extremal cross sections for Ba and Eu are calculated by the SRAPW method and the results are compared with previous theoretical and experimental results. The characteristic features on the Fermi surfaces for Ba and Eu are examined and a remarkable d-like character of the Fermi surface is indicated. The results of the SAPW band calculation is applied for calculations of the optical conductivities within the random phase approximation (RPA) for Ba and Eu in the energy range 0-10.5 eV. The theoretical results are in fairly good agreement with experimental ones. In the case of Eu, it is indicated that the transitions from the 4f states are important to reproduce the experimental results in the region around 7 eV. The effects of self-energy correction on the optical conductivities are phenomenologically considered. It is shown that the different structure observed above 4.5 eV in experiments for Ba and Eu is reasonably explained, if transitions from 4f electrons in Eu are taken into account. This result supports positively the conjecture that the 4f electron levels of Eu locate at the energy region predicted from XPS.

On the axial ratio, electronic structure and magnetic moment of cobalt

Self-consistent, relativistic band calculations for cobalt are presented. These have been performed as a function of axial ratio. A minimum in total energy is found close to the experimental value of c/a. Both spin and orbital contributions to the magnetic moment have been calculated and they show excellent agreement with experiment. The role of the energy bands in determining the axial ratio and magnetic properties is discussed.

Fermi Surfaces of NbSe3

The two independent CDW transitions and the behavior of the hall constant of NbSe 3 are explained by the independent nestings of the Fermi surfaces obtained by the LCAO-Xα-SCF relativistic band calculation.

Electron Excitation Energies in the Rare Earth and Actinide Metals

Calculations of various electronic excitation energies for the rare earth and actinide metals are discussed. Relativistic Hartree-Fock computations for atomic configurations most closely approximating those of the metal are initially performed, and crystal potentials are constructed by means of the renormalized atom method. Relativistic band calculations are iterated to crude self-consistency, and excitation energies derive from differences between total band energies. Results include (1) occupied and unoccupied 4f level positions in the lanthanide metals and associated values of the 4f coulomb interaction energy, U; (2) 3d levels in the rare earths; and (3) 5f excitation energies and coulomb terms for the actinide metals. There is excellent agreement between these results and X-ray photoemission and bremsstrahlung isochromat spectroscopy measurements for the rare earths, while corresponding experimental information for the actinides is as yet unavailable.

4fexcitation energies in rare-earth metals: Relativistic calculations

We describe calculations of $4f$ electron binding energies for the rare-earth metals. Relativistic Hartree-Fock calculations for atomic configurations most closely approximating those of the metals are initially performed, and crystal potentials are constructed by means of the renormalized-atom method. Relativistic band calculations are iterated to crude self-consistency and total band energies obtained. Correlation effects identical to those in the free atoms are assumed. Within the assumption of a completely screened final state, in which the atomic site having the $4f$ hole is electrically neutral, $4f$ binding energies are estimated which are in at least as good agreement with experiment as previous, less complete calculations. The impact of the complete screening approximation is assessed by estimating the binding energies corresponding to atomic sites which are ionized in their final states; we find that the presence of an additional screening electron lowers the $4f$ binding energy by 4-6 eV.

Relativistic Band Calculation and the Optical Properties of Gold

The energy band structure of gold is calculated by the relativistic augmented-plane-wave (RAPW) method. A nonrelativistic calculation is also presented, and a comparison between this and the RAPW results demonstrates that the shifts and splittings due to relativistic effects are of the same order of magnitude as the gaps (approximately 1 eV). Various integrated functions, density of states, joint density of states, and energy distributions of joint density of states are derived from the RAPW calculation. These functions are used in an interpretation of photoemission and static reflectance measurements. It is shown that the photoemission results are extremely well described in terms of a model assuming all transitions to be direct whereas a nondirect model fails. The ${\ensuremath{\epsilon}}_{2}$ profile calculated in a crude model assuming constant matrix elements matches well the corresponding experimental results. The calculated interband edge ($\ensuremath{\hbar}{\ensuremath{\omega}}_{i}=2.38$ eV) agrees with experimental values, and the absorption tail below the interband edge which is found in experimental traces is also contained in the theoretical curve. By means of a calculation of the Fermi surface and the constant-energy-difference surfaces it has been possible to trace out the regions in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space where the edge and tail transitions occur. It is demonstrated that structure in the static reflection curves are not related to critical points in the band structure. The arguments are supported by calculations of temperature shifts of the critical-point energies and comparison to the observed temperature shifts of the elements of structure in the experimental ${\ensuremath{\epsilon}}_{2}$ function. Such structure may originate in extended rather than localized regions of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space. In contrast, critical-point transitions show up clearly in modulated reflectance spectra, and all elements of structure are fully accounted for by our band model. The temperature and strain responses in the band structure are determined by performing the RAPW calculation with two lattice constants and estimating the effects of the lattice vibrations by means of an OPW-LCAO (linear combination of atomic orbitals) scheme with pseudopotential Fourier constants reduced by the appropriate Debye-Waller factors. The phonon spectrum has been calculated for the latter purpose.

Relativistic band calculation and the optical properties of gold

A relativistic band structure calculation for gold is presented. Its band separations at critical points agree well with structure in Δϵ 2 as derived from modulated reflectance spectra. The static spectrum cannot be interpreted in terms of critical points, but matches well the joint density-of-states function calculated on the basis of direct transitions with constant matrix elements.

Energy Bands of Hexagonal II-VI Semiconductors

Energy bands for hexagonal ZnO and ZnS have been calculated along the main symmetry axes of the hexagonal Brillouin zone with the relativistic mass velocity and Darwin correction considered. The band structure of ZnO differs from the ZnS band structure in that $d$ bands occur closely below the upper valence bands, and $p$-like conduction bands lie 17 eV above the valence bands. Thus, the ZnO band structure exhibits a very broad lowest conduction band. For hexagonal ZnS, the relativistic corrections increase the separation between $p$-like valence and conduction bands. This effect is discussed in connection with relativistic band calculations for cubic ZnS along the $\ensuremath{\Lambda}$ axis, and a revised interpretation of higher interband transitions is given. At k = 0, full relativistic calculations yielded good agreement with experimental values for crystal-field and spin-orbit splittings for ZnS, CdS, and CdSe, and gave a negative spin-orbit splitting for ZnO. Deformation potentials for CdS were calculated in good accord with experiment.

The de Haas-van Alphen effect and the fermi surface of tungsten

The de Haas-van Alphen effect in tungsten has been studied in detail using large impulsive magnetic fields, and the frequencies have been determined to high accuracy with the aid of digital data recording, digital analysis and dynamic calibration of the entire apparatus. These improvements in experimental technique have resulted in the detection of several new frequency branches which have not been previously reported. A quantitative description of all sheets of the Fermi surface is given in terms of simple analytical functions, and this geometrical model is in excellent agreement with the observed angular variations of the de Haas-van Alphen frequencies. In most respects, the model surface is found to be quite similar to that deduced by Loucks from first-principles relativistic band calculations, and the predictions of the empirical model are compared with the results of other experiments relating to the Fermi surface.