Self-consistent Energy Band Calculations Research Articles

Rare-earth transition-metal intermetallics

The combination of itinerant transition metal (M = Fe) and localized rare-earth (R = Gd-Y) magnetism in RFe 2 compounds has been investigated in self-consistent energy band calculations. The computed and measured total moments are in good agreement for all cases where single crystal data are available. We find, however, that there is a significant contribution to the moment from the R-5d partial moments coupled antiparallel to the Fe-3d moment which results from 3d–5d hybridization. The R-4f moments interact with the conduction band system solely by local exchange interactions, which are calculated ab initio from density functional theory. A sum rule for the total 3d + 5d moment is shown to be obeyed and the effective ferrimagnetic exchange interaction between rare-earth and transition-metal moments is discussed. Finally, the spin wave spectra of these materials are evaluated in terms of a model arising from these calculations.

Magnetism of RFe2 compounds

The combination of itinerant transition metal (M=Fe) and localized rare earth (R=Gd-Yb) magnetism in RFe2 compounds has been investigated in self-consistent energy band calculations. The computed and measured total moments are in good agreement. We find, however, that there is a significant contribution to the moment from the R-5d partial moments coupled antiparallel to the Fe-3d moment which results from 3d-5d hybridization. The R-4f moments interact with the conduction band system solely by local exchange interactions which are calculated ab initio from density functional theory. A sum rule for the total 3d+5d moment is shown to be obeyed and an expression for the effective ferrimagnetic exchange interaction between 3d and 4f electrons is derived.

Photoreflectance studies of GaAs containing a Si-δ-doping layer

The electronic structure of several n-type GaAs samples containing ‘‘δ-doping’’ layers of Si have been studied using photoreflectance (PR) spectroscopy. Well-defined oscillatory features due to electronic transitions well above the band gap are observed at 300 K and identified as Franz–Keldysh oscillations. The energy spacing and the intensity of the oscillations decrease with decreasing temperature as a consequence, we believe, of changes in the electric field due to the surface charges. Self-consistent energy-band calculations support the interpretation that the oscillatory structure is due to Franz–Keldysh effects. The imposition of magnetic fields up to 15 even at room temperature has a pronounced influence on the PR spectrum. Parallel fields suppress the oscillatory structure but cause a large increase in the PR peaks near the GaAs energy gap. At 4.2 K Landau-like spectral features are observed for fields applied perpendicular to the doping layer.

Non-collinear itinerant magnetism: the case of Mn3Sn

Spin-density functional theory is applied to describe non-collinear itinerantmagnetism. For this the theory is formulated and a new implementation is given. Itserves to perform self-consistent energy-band calculations for the compound Mn3Sn whichpossesses a triangular magnetic structure. Our results are discussed in detail and comparedwith experimental data.

3d-5d band magnetism in rare earth transition metal intermetallics: LuFe2

Self-consistent energy band calculations for LuFe2 are reported. LuFe2 is found to order magnetically according to the Stoner criterion and the calculated moment is 2.85 mu B/formula unit in agreement with experiment. Spin-orbit coupling was included in the calculation and the spin and induced orbital contributions to the moment at the Fe site also found to be in agreement with experiment. The total moment is calculated to include a contribution of -0.41 mu B at the Lu site, which as yet has not been observed. The mechanism responsible for the ferrimagnetic alignment of the 3d and 5d spin densities is investigated in detail, and the Lu-5d moment related to 3d-5d hybridisation.

Electronic structure of the pseudobinary U(Rh1-yPdy

Self-consistent energy band calculations have been made for URh/sub 3/ and UPd/sub 3/ and the fictitious compounds URh/sub 2/Pd and URhPd/sub 2/. The calculated electronic structures of these ordered compounds are used to estimate the critical concentration for the onset of ferromagnetism in the pseudobinary U(Rh/sub 1-//sub y/Pd/sub y/)/sub 3/ alloys. Calculations based on the virtual crystal approximation give results very similar to those for the ordered compounds. An explanation of the anomalous volume dependence of the alloys upon y, involving a Mott transition of the 5f electrons, is presented.

Electronic structure of rhodium.

Local-density, all-electron, self-consistent energy-band calculations are reported for face-centered-cubic rhodium. The Fermi surface is obtained; charge form factors, the Compton profile, and the optical conductivity are determined. Results are compared with other calculations and with experiment where these exist. A possible ferromagnetic state is found for an increased lattice constant with a moment developing at about a=8.17 a.u.

4f-band magnetism in CeFe2.

We explain the anomaly in the lattice constants of the series Ce${\mathrm{Fe}}_{2}$-Ce${\mathrm{Ni}}_{2}$ quantitatively in terms of $3d\ensuremath{-}4f$ hybridization rather than a valence change. Ce${\mathrm{Fe}}_{2}$ is calculated to be magnetic and is the first Ce compound for which self-consistent energy-band calculations yield the correct total moment (${2.4}_{\mathrm{\ensuremath{\mu}}\mathrm{B}}$/formula unit) including a contribution of ${\ensuremath{-}0.4}_{\mathrm{\ensuremath{\mu}}\mathrm{B}}$ from the $4f$ electrons. The calculated magnetization density and spin-resolved density of states, which are unique to itinerant-electron theory, may be verified in detail by magnetic form-factor and spin-polarized photoemission measurements.

Local spin-density functional theory of noncollinear magnetism (invited)

We apply spin-density functional theory (SDF) to describe noncollinear magnetism; i.e., self-consistent energy-band calculations based on the local approximation to SDF theory are presented in which the magnetization associated with different atoms in a unit cell is allowed to point along different, noncollinear directions. In contrast to older work (e.g., by You and Heine and by Oguchi, Terakura, and Hamada) the present calculations are (1) self-consistent, (2) provide the total energy, and (3) provide the spin-quantization axes. In our applications we deal with noncollinear antiferromagnets γ-FeMn and perovskites Mn3GaN and show that their total energies are minimized in tetrahedral and triangular magnetic structures, respectively, first proposed by Kouvel and Kasper.

Chemical bonding and magnetism in 3d-5f intermetallics

The authors report self-consistent energy band calculations for UFe2 and UCo2 in four approximations: both semi-relativistic and fully relativistic for the paramagnetic ground states; both spin-polarised and spin-polarised with spin-orbit coupling included self consistently for the ferromagnetic ground state of UFe2. They compare ab initio calculated and measured lattice constants, bulk moduli, linear specific heat coefficients, pressure dependence of the magnetic moment and magnetic form factor. UCo2 is found to be an enhanced paramagnet and UFe2 an itinerant ferromagnet with a magnetic moment due mainly to the iron moments. However, the magnetism on the uranium sites is unusual in that they calculate both spin and orbital contributions to the moment that are large, antiparallel and almost equal.

Self-consistent calculations using canonical scaling in the linearized atomic-cell orbital method: Energy bands of fcc Cu.

The linearized atomic-cell orbital (LACO) method is used for self-consistent calculations of energy bands of fcc Cu. This method eliminates the local-sphere approximation while retaining much of the efficient computational organization of earlier linear methods. Large effects of this approximation are not expected for a close-packed metal, but the present calculations serve to calibrate the LACO method against earlier self-consistent results. General close agreement is found. Formalism for canonical scaling is developed appropriate to a nonspherical atomic cell, and is applied to a given density-of-states function in an inner self-consistency loop.

PuS, PuSe, PuTe: Relativistic Semiconductors

The band structures of PuS, PuSe and PuTe were calculated from self-consistent energy band calculations in a number of ways: (1) With 5f electrons treated as localized and Pu divalent. In this case insulators were obtained which would have non-magnetic J = 0 ground states, in agreement with experiment. However the calculated lattice constants were far too large. (2) With 5f electrons treated as localized and Pu trivalent. Metals were obtained, and trivalent Pu systems are normally magnetic. In addition the calculated lattice constants were too large. (3) With 5f-electrons treated as itinerant but with spin-orbit coupling neglected. All three systems were found to be metallic and the Stoner criterion for ferromagnetism was easily satisfied although experimentally no moment has been observed in these systems. The calculated lattice parameters were also too small. (4) With 5f-electrons treated as itinerant and fully relativistically. In this case all three systems were found to be semiconductors with calculated lattice constants in agreement with experiment and band gaps of between 0.2-0.4 eV.

Momentum density distributions in Ni3Ga

Self-consistent energy band calculations of Ni3Ga are carried out by the symmetrised augmented plane wave (SAPW) method. In the construction of a one-electron potential, the local-density approximation is used. Momentum density distributions determined by Compton scattering and positron annihilation are calculated by the SAPW method. These anisotropies are due not only to the partially occupied bands but also to the fully occupied ones. The calculated anisotropy in angular correlation curves of positron annihilation radiation is in good agreement with the recent experimental result. The corresponding calculated result in the Compton profile is also in good agreement with the recent experimental result. However, in contrast to the case of elemental transition metals, the calculated Compton profiles and angular correlation curves of positron annihilation radiation show anisotropies of different structures. It is shown that this feature originates from the localised d electron states of Ni3Ga.

PuS, PuSe, PuTe: Relativistic semiconductors

The equations of state of PuS, PuSe and PuTe were calculated from self-consistent energy band calculations in a number of ways: (1) With 5f electrons treated as localized and Pu divalent. In this case insulators were obtained which would have non-magnetic J = 0 ground states, in agreement with experiment. However, the calculated lattice constants were far too large. (2) With 5f electrons treated as localized and Pu trivalent. Metals were obtained, and trivalent Pu systems are normally magnetic. In addition the calculated lattice constants were too large. (3) With 5f-electrons treated as itinerant but with spin-orbit coupling neglected. All three systems were found to be metallic and the Stoner criterion for ferromagnetism was easily satisfied although experimentally no moment has been observed in these systems. The calculated lattice parameters were also too small. (4) With 5f-electrons treated as itinerant and fully relativistically. In this case all three systems were found to be semiconductors with calculated lattice constants in agreement with experiment and band gaps of between 0.2–0.4 eV.

Electronic structure of unoccupied states of stoichiometric ZrN, NbC and NbN As determined by high energy electron energy loss spectroscopy

Abstract The nonmetal K-absorption edges of ZrN, NbC and NbN have been studied using high-energy-electron-energy-loss-spectroscopy. These spectra reflect the densities of unoccupied states. They are compared to total densities of states which are calculated by the linearized augmented planewave (LAPW) method using results of previous self-consistent APW energy band calculations. Except for one peak in ZrN good agreement between theory and experiment is observed especially in peak position.

Binding mechanism and itinerant magnetism of ZrFe 2 and YFe 2

Self-consistent spin-polarized energy band calculations for the two Laves phases show that a ferrimagnetic state is more stable than the paramagnetic one, but at a slightly larger volume. For ZrFe 2 the interaction between the low lying Zr and the exchange-split Fe states leads to covalent magnetism which is discussed using site- and spin-projected densities of states. The different interaction between Fe and Zr for majority and minority spin is responsible for the ferrimagnetic ordering which is analyzed in terms of spin densities. The resulting magnetic moment of about 1.9 μ B for Fe is spatially localized near the Fe site, while around Zr a small but extended negative spin density causes (through the large volume) a moment of about -0.56 μ B a prediction which should be verified experimentally. YFe 2 is qualitatively similar, but contrasts YCo 2 which is near a possible metamagnetic transition.

Electronic structure of actinide hydrides

We report self-consistent LMTO, spin-polarized LMTO, and RLMTO energy band calculations for ThH 2 and PuH 2 in which the zero temperature equations of state were calculated. For ThH 2 the calculated lattice constant, bulk modulus and cohesive energies are 5.397 Å, 99 GPa and 342 kcal/mol, respectively. For PuH 2 the calculated lattice parameters were 4.74 Å (LMTO), 4.89 Å (RLMTO), 4.98 Å (spin-polarized LMTO) compared with a measured value of 5.395 Å. It is deduced that the 5f electrons in PuH 2 are localized.

First-principles calculation of the electric field gradient of Li3N.

The electric field gradient can be obtained from self-consistent energy-band calculations by the linearized-augmented-plane-wave method provided that a general potential is used. This first-principles method, which does not rely on any Sternheimer antishielding factor, is tested for ${\mathrm{Li}}_{3}$N and yields electric field gradients for Li(1), Li(2), and N in excellent agreement with NMR experiments. The electric field gradient is mainly determined by local distortions of the electronic charge density, especially in the case of the polarizable ${\mathrm{N}}^{3\ensuremath{-}}$ ion.

Calculated electronic structure of CeN

Self-consistent LMTO-ASA and RLMTO-ASA energy band calculations for CeN, in which the equation of state was determined, are reported. The calculated lattice constant is 2% less than is measured. The number of 4f and 2p electrons are 1.02 and 3.25, respectively.

Itinerant metamagnetism in YCO2

The cubic Laves phase of YCo2 is near a transition from a paramagnetic to a magnetically ordered state. Self-consistent energy-band calculations yield the total energy and the magnetic moment as functions of volume. The new fixed spin-moment (FSM) method, which allows one to calculate the total energy as an explicit function of the magnetisation, is introduced. At the theoretical equilibrium volume YCo2 is found to be a strongly enhanced Pauli paramagnet, but at a slightly larger lattice constant a metamagnetic transition seems possible. Its occurrence can be understood on the basis of a double minimum in the total energy obtained from the present FSM calculations, which lead to an estimated critical field of about 350 T. In the magnetic state the Y moment is coupled antiferromagnetically to the Co moment.