Rigid Band Approximation Research Articles

Type-I clathrate Ba8NixSi46−x: Phase relations, crystal chemistry and thermoelectric properties

The phase relations, crystal structure and thermoelectric properties of the type-I solid solution Ba(8)Ni(x)Si(46-x) were investigated. Based on X-ray diffraction, differential thermal analysis and electron probe microanalysis data, a partial phase diagram was constructed for the Si-rich part of ternary system Ba-Ni-Si at 800 °C. The solubility range of Ni in the clathrate-I phase at 800 °C was determined (2.9 ≤x≤ 3.8) and thermoelectric properties, namely electrical resistivity, Seebeck-coefficient and thermal conductivity, were measured in the temperature range from 300 to 850 K. A shift of the thermoelectric properties from a predominantly metallic to a more semiconducting behavior was observed for an increasing Ni-content. Density functional calculations revealed a significant decrease of the gap width in the density of states induced by the incorporation of Ni. Electrical resistivity and Seebeck coefficients for Ba(8)Ni(x)Si(46-x) with 3.3 ≤x≤ 3.8 have been modeled within the rigid band approximation.

First-principles structural optimization and electronic structure of the superconductor picene for various potassium doping levels

We theoretically explore the crystal structures of K$_x$picene, for which a new aromatic superconductivity has recently been discovered for $x=3$, by systematically performing first-principles full structural optimization covering the concentration range $x=1$-4. The crystal symmetry (space group) of the pristine picene is shown to be preserved in all the optimized structures despite significant deformations of each picene molecule and vast rearrangements of herringbone array of molecules. For K$_x$picene ($x=1$-4) optimization indicates that (i) multiple structures exist in some cases, and (ii) dopants can enter not only in the interlayer region between the stack of herringbone structures, but also in the intralayer region. In the electronic structure obtained with the local density approximation for the optimized structures, the dopants are shown to affect the electronic properties not only through the rearrangement and distortion of molecules, but also molecule-metal atom hybridization. In other words, the rigid-band approximation is invalidated for multifold reasons. As a consequence the resultant Fermi surface exhibits a variety of multiband structures which take diverse topology for K$_1$picene and K$_3$picene.

Color of TiN and ZrN from first-principles calculations

The optical properties, especially the colors, of transition metal nitrides (TiN and ZrN) are studied using first-principles method. Full ab-initio procedure of color-prediction including plasma frequency is presented. The dielectric functions and reflectivity of the compounds are calculated including both intraband and interband transitions. The color of the compounds is then produced by calculating the red-green-blue color codes through the convolution of color matching functions and the calculated reflectivity. Calculated colors and screened plasma frequency for the materials are in good agreement with measurement. The color variation due to chemical doping is also studied within the rigid band approximation.

Scaffolding, Ladders, Chains, and Rare Ferrimagnetism in Intermetallic Borides: Electronic Structure Calculations and Magnetic Ordering

The electronic structures of "Ti(9-n)Fe(2+n)Ru(18)B(8)" (n=0, 0.5, 1, 2, 3), in connection to the recently synthesized Ti(9-n)Fe(2+n)Ru(18)B(8) (n=1, 2), have been investigated and analyzed using LSDA tight-binding calculations to elucidate the distribution of Fe and Ti, to determine the maximum Fe content, and to explore possible magnetic structures to interpret experimental magnetization results. Through a combination of calculations on specific models and using the rigid band approximation, which is validated by the DOS curves for "Ti(9-n)Fe(2+n)Ru(18)B(8)" (n=0, 0.5, 1, 2, 3), mixing of Fe and Ti is anticipated at both the 2b- and 4h-chain sites. The model "Ti(8.5)Fe(2.5)Ru(18)B(8)" (n=0.5) revealed that both Brewer-type Ti-Ru interactions as well as ligand field splitting of the Fe 3d orbitals regulated the observed valence electron counts between 220 and 228 electrons/formula unit. Finally, models of magnetic structures were created using "Ti(6)Fe(5)Ru(18)B(8)" (n=3). A rigid band analysis of the LSDA DOS curves concluded preferred ferromagnetic ordering at low Fe content (n≤0.75) and ferrimagnetic ordering at higher Fe content (n>0.75). Ferrimagnetism arises from antiferromagnetic exchange coupling in the scaffold of Fe1-ladder and 4h-chain sites.

Theoretical investigation of the thermoelectric transport properties of BaSi2

The full-potential linear augmented plane wave method based on density functional theory is employed to investigate the electronic structure of BaSi2. With the constant relaxation time and rigid band approximation, the electrical conductivity, Seebeck coefficient and figure of merit are calculated by using Boltzmann transport theory, further evaluated as a function of carrier concentration. We find that the Seebeck coefficient is more anisotropic than electrical conductivity. The figure of merit of BaSi2 is predicted to be quite high at room temperature, implying that optimal doping may be an effective way to improve thermoelectric properties.

Effects of magnetism and doping on the electron-phonon coupling inBaFe2As2

We calculate the effect of local magnetic moments on the electron-phonon coupling in doped ${\text{BaFe}}_{2}{\text{As}}_{2}$ using the density-functional perturbation theory. We show that the magnetism enhances the total electron-phonon coupling by $\ensuremath{\sim}50\mathrm{%}$, up to $\ensuremath{\lambda}\ensuremath{\lesssim}0.35$, still not enough to explain the high critical temperature, but strong enough to have a non-negligible effect on superconductivity, for instance, by frustrating the coupling with spin fluctuations and inducing order-parameter nodes. The enhancement comes not from the phonon softening but mostly from a renormalization of the electron-phonon matrix elements. We also investigate, in the rigid band approximation, the effect of doping, and find that $\ensuremath{\lambda}$ versus doping does not mirror the behavior of the density of states; while the latter decreases upon electron doping, the former does not, and even increases slightly.

Comment on “Doping Driven (π, 0) Nesting and Magnetic Properties ofFe1+xTeSuperconductors”

In this Comment, using Korringa-Kohn-Rostoker coherent-potential approximation method in the atomic-sphere approximation (KKR-ASA CPA) to describe the effects of disorder due to excess Fe in FeTe alloys, we show that (i) the rigid-band approximation is inadequate to describe the effects of disorder and its application leads to an incorrect description of the underlying physics, (ii) the rigid-band energy shift of ~0.76 eV for going from FeTe to Fe_{1.068}Te (or Fe_{1.063}Te), as obtained by Han and Savrasov (Phys. Rev. Lett. 103, 067001(2009)), is inconsistent with our FP-LMTO as well as the KKR-ASA results, and thus the FS of Fe_{1.063}Te shown in Fig. 3(b) of their paper is not correct.

Theoretical study of the electronic structure and the totally symmetric vibrations of selected CoMoCat carbon nanotubes

AbstractIn situ Raman spectroelectrochemical studies of CoMo‐Cat single‐walled carbon nanotubes enriched in (6,5) tubes have been carried out recently. We performed calculations on the density functional level using local density approximation for the electronic and vibrational properties of the most abundant tubes in these samples. The following chiral semiconducting tubes were investigated: (6,4), (7,3), (6,5), (9,1), (8,3) and (7,5). The calculated and the measured frequencies of the RBM and G– modes agree within several wave numbers. The calculated E11, E22 transition energies ‐after 30% and 20% upscaling, respectively‐ are comparable with the experimental values. The quenching of the RBM band with p‐ and n‐doping can be interpreted within the rigid band approximation. The validity of the rigid band approximation was shown by calculating the density of states for neutral and charged tubes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Magnetic Properties of (Sm$scriptstyle_0.4$Pr$scriptstyle_0.6$)$scriptstyle_3$(Fe$scriptstyle_1-rm x$Co$scriptstyle_rm x$)$scriptstyle_27.5$Ti$scriptstyle_1.5$$[rm x = 0.1, 0.2, 0.3, 0.4

The structural and magnetic properties of Co substituted (Sm0.4Pr0.6)3(Fe1-xCox )27.5Ti1.5 [x=0.1,0.2,0.3,0.4] compounds have been studied through powder X-ray diffraction (XRD) and magnetization measurements. All the compounds have formed in monoclinic R3(Fe,M)29 phase with A2/m space group. The unit cell volume decreases with Co concentration in accordance with its size. The magnetization at room temperature increases with Co substitution and is qualitatively explained on the basis of rigid band approximation. Curie temperature is also found to increase with Co concentration. XRD patterns on the magnetically oriented samples reveal that nearly axial anisotropy is obtained for the x=0.4 compound and that the easy magnetization direction (EMD) is along [2 0 4]

Anisotropic normal-state properties of theMgB2 superconductor

Based on the experimentally-found existence of two superconducting gaps inMgB2 (one gap associated tothe boron σ-states andthe other to the boron π-states), the different contributions to the transport properties, electrical conductivity andHall coefficient were studied using the full potential-linearized augmented plane wavemethod and the generalized gradient approximation. Four different relaxation times wereneeded to adjust the electrical conductivity and Hall coefficient to experimental values.MgB2 doping was analysed in the rigid band approximation; this permitted adetailed study of the partial substitution of magnesium for aluminium(Mg1−xAlxB2). Other substitutionssuch as AB2 (A = Be, Sc, Zr, Nb and Ta) are also discussed. TheMgB2 σ-bands(boron σ-states), which are associated to the large gap, are very anisotropic atEF, whilethe π bands have very little anisotropic character. InMg1−xAlxB2,Tc diminishes with Al content; the other compounds are not superconductors or have a lowTc. In this work it was found that with electron doping, such as Al substitution, theσ-band conductivity decreases and the corresponding bands become less anisotropic. Theσ-bandcontribution for BeB2 and ScB2 at EF is very small and the anisotropy is much lower. For Zr, Nb and Ta there are noσ-bandsat EF. These results give a clear connection between superconductivity and the character of theσ-band, band conductivity, and band anisotropy. This gives a plausible explanation for the diminution ofTc with differentdoping of MgB2.

Coherence scale of the two-dimensional Kondo lattice model

A doped hole in the two-dimensional half-filled Kondo lattice model with exchange $J$ and hopping $t$ has momentum $(\ensuremath{\pi},\ensuremath{\pi})$ irrespective of the coupling $J∕t$. The quasiparticle residue of the doped hole, ${Z}_{(\ensuremath{\pi},\ensuremath{\pi})}$, tracks the Kondo scale, ${T}_{K}$, of the corresponding single impurity model. Those results stem from high precision quantum Monte Carlo simulations on lattices up to $12\ifmmode\times\else\texttimes\fi{}12$. Accounting for small dopings away from half-filling within a rigid band approximation, this result implies that the effective mass of the charge carriers at the Fermi level tracks $1∕{T}_{K}$ or equivalently that the coherence temperature ${T}_{\mathrm{coh}}\ensuremath{\propto}{T}_{K}$. This results is consistent with the large-N saddle point of the $SU(N)$ symmetric Kondo lattice model.

Ab Initio Study of Structural and Electronic Properties of Hole-Doped Fullerenes: Enhancement of Tc

An ab initio study of the structural and electronic properties of the hole-doped C60 has been made by using pseudopotential method in density functional theory in local density approximation. The halogen-doped fullerenes (C60Br3 and C60Cl3) are found to be as stable as the realized alkali-doped fullerenes. The results for the electron density of states (DOS) for pure C60 at Fermi level (EF) containing either holes or electrons calculated in the rigid band approximation are seen to be quite low as compared to those of the self-consistently calculated halogen-doped C60. The present results for DOS for the alkali-doped fullerenes are very close to the other workers. The DOS for the halogen-doped fullerenes is seen to be about 2–3 times higher than those for the electron-doped systems. Experimental efforts are needed to obtain the halogen-doped systems to achieve high value of Tc.

Structural properties, electronic structure, Fermi surface, and mechanical behavior of bcc Cr-Re alloys

The electronic structure and ground-state properties (lattice parameter, cohesive energy, bulk and tetragonal shear moduli) were calculated for bcc Cr and Cr-Re alloys over a wide range of Re concentration by the full-potential linear muffin-tin orbital method (FLMTO) with generalized gradient approximation (GGA). We show that the GGA predicts the commensurate antiferromagnetic Cr state as a ground state for the experimental volume with a small lower energy compared with the nonmagnetic state, but gives a large moment of $0.92{\ensuremath{\mu}}_{B}.$ In the Cr-Re system the magnetism becomes weak with Re concentration and for 25% Re the mean Cr moment is about $0.05{\ensuremath{\mu}}_{B}.$ Examining the Fermi surface of Cr-Re alloys within the modified rigid-band approximation, the electronic topological transition (ETT) is found to occur for 6% Re. A weakening of the Cr-Cr bonds near this ETT is considered as a possible microscopic reason for the ``small'' rhenium effect---the ductility enhancement in Cr(Mo,W)-Re alloys with small Re additions. As the mechanism for the ``large'' rhenium effect (near 25--35% Re) the formation of Cr-Re close-packed particles should play an important role together with the significantly weakened Cr-Cr bonding.

Magnetic anisotropy inNi2MnGa

We study here, within the density-functional theory, the magnetic anisotropy energy (MAE) in ${\mathrm{Ni}}_{2}\mathrm{MnGa}$ which is a prototype of a magnetic shape-memory alloy. We calculate the MAE, which is a key property for the magnetic shape-memory effect, for tetragonal structure with different ratios of the c and a lattice constants, reproducing the experimental easy axes both in compression and elongation of the structure. Good agreement between the theory and the experiments in the actual values of the MAE is also found when the nonstoichiometry of the experimental samples is modeled with a simple rigid band approximation. In addition, we estimate the magnetostriction coefficient, confirming the difference between the ordinary magnetostriction and the magnetic shape-memory effect. Equally important, we study the microscopic origin of the MAE in ${\mathrm{Ni}}_{2}\mathrm{MnGa}$ with the spin density and the orbital moment anisotropy and extend the analysis of the orbital moment anisotropy to the ternary compounds. These results show that the largest contribution to the MAE comes from Ni, in spite of the larger magnetic moment in the Mn sites.

Electronic and magnetic properties of layered colossal magnetoresistive oxides:La1+2xSr2−2xMn2O7

The electronic and magnetic properties of double-layered Roddlesdon-Popper compounds, La{sub 1+2x}Sr{sub 2-2x}Mn{sub 2}O{sub 7} with different doping x from 0.0 to 0.2 have been calculated using the full-potential linear muffin-tin orbital method. The total energies, band structures, densities of states, and Fermi surfaces were investigated by means of the virtual crystal approximation. The band structure of La{sub 1+2x}Sr{sub 2-2x}Mn{sub 2}O{sub 7} is found to be that of a half-metallic ferromagnet, in agreement with experiment. The density of states shows that La and Sr act solely as electron donors and have almost no states at or below the Fermi level, and therefore a rigid band approximation can be considered as a good approximation to describe the effects of doping. The calculated Mn magnetic moments increase from 3.09{mu}{sub B} to 3.24{mu}{sub B} when the doping increases from 0.0 to 0.2, which is in qualitative agreement with experiment. The calculated Fermi surface shows pronounced nesting features along the {Gamma}-X directions in the undoped case, which implies a possible charge- or spin-density wave instability in this material.

Predictions of magnetism in transition metal aluminides

The Stoner Model has been used to investigate the stability of ferromagnetism in FeAl and the analogous series 3d transition metal aluminide compounds. Stoner factors, N(EF)I, were calculated from augmented plane wave (APW) electronic structure calculations based on local density approximation (LDA), using the Janak formalism. The Stoner criteria [N(EF)I>1] predicts ferromagnetism in FeAl for lattice parameters larger than 5.44 a.u., which is less than the experimental lattice constant of 5.50 a.u., but greater than the APW–LDA minimum energy lattice constant. The Stoner factors for ordered transition metal aluminides in the B2 (CsCl) structure agree reasonably well with those calculated using a rigid band approach, starting from FeAl and shifting EF to simulate the remainder of the series. These Stoner factors predict ferromagnetism for CrAl and MnAl and, assuming the rigid band approximation, for FeAl alloyed with Cr and Mn to the level of Fe0.8Cr0.2Al and Fe0.6Mn0.4Al.

Calculated trends of the magnetostriction coefficient of 3d alloys from first principles

The general behavior of the magnetostriction coefficients for Fe, Co, and Ni and their alloys is reproduced by first-principles theory. It is shown that the low magnetostriction coefficient of soft magnetic materials, observed for specific alloy concentrations, such as permalloy, can be explained theoretically by employing relativistic first-principles calculations in combination with the rigid-band approximation. The connection between magnetostriction and magnetocrystalline anisotropy is discussed as well as the physical mechanisms behind soft magnetic materials. Theory is hence demonstrated to have the ability of predicting values of the magnetostriction coefficient of any alloy, and a microscopic understanding of this entity is starting to emerge.

Effect of intercalation on structural instability and superconductivity of layered 2H-type NbSe2 and NbS2

Abstract Effects of intercalation on the lattice instability and the superconductivity of NbSe2 and NbS2 are studied in the framework of the rigid band approximation. In the case of doping acceptor-type intercalants into NbSe2, the point of lattice instability in q-space is moved to q = Γ M from q = 2 3 ΓM . Further, the frequency renormalization is enhanced and the CDW transition temperature is expected to increase. In the case of doping donor-type intercalants, on the other hand, the frequency renormalization is weakened and the lattice instability is suppressed. The same tendency is found also in NbS2. The effect of intercalation on the superconducting transition temperature Tc of NbS2 is investigated by calculating the functional derivative of Tc with respect to the spectral function. The donor-type intercalant lowers Tc as observed in the case of alkali-metal doping. On the other hand, the acceptor-type intercalant raises Tc as long as the lattice instability does not take place.

Van Hove singularities in the parent superconductor Ca 1 − xSr xCuO 2

We have investigated for the first time the electronic structure and the van Hove singularities of the ordered Ca 1 − x Sr x CuO 2 structures for five values of the concentration x = 0.0, 0.25, 0.50, 0.75 and 1.0 by employing a first-principles full potential self-consistent linear muffin tin orbital (LMTO) method without invoking any rigid-band approximation. The scalar relativistic effects have been considered. We observed that the vHs peak at the Λ point shows a shifting towards the Fermi energy with the Sr concentration and is closest to the Fermi energy for the ordered structure CaSr 3Cu 4O 8 in agreement with the experimentally observed maximum value for T c.

Photoemission study of valence electrons in La(Co1-xFex)13 (x=0,0.2).

The electronic structure of La(Co{sub 1{minus}{ital x}}Fe{sub {ital x}}){sub 13} ({ital x}=0,0.2) has been investigated by using photoemission spectroscopy. The La 5{ital d} and {ital T} 3{ital d} ({ital T}=Fe,Co) partial spectral weights (PSW`s) are extracted and compared with the calculated angular momentum projected densities of states (PLDOS`s). No Co 3{ital d} satellite is observed, impling a weak Co 3{ital d} Coulmb correlation in this system. La 5{ital d} emissions exhibit a weak enhancement near the La 4{ital d} absorption edge, from which the La 5{ital d} PSW`s of La(Co{sub 1{minus}{ital x}}Fe{sub {ital x}}){sub 13} ({ital x}=0,0.2) have been extracted. For a given {ital x} in La(Co{sub 1{minus}{ital x}}Fe{sub {ital x}}){sub 13}, the overall features of the La 5{ital d} PSW, such as bandwidths and long tails, are rather similar to those of the {ital T} 3{ital d} PSW, indicating a large hybridization between the {ital T} 3{ital d} and La 5{ital d} states. The experimental Co 3{ital d} and La 5{ital d} PSW`s of LaCo{sub 13} show a large disagreement with the calculated PLDOS`s. With a substitution of Fe for Co, the PSW`s of La(Co{sub 1{minus}{ital x}}Fe{sub {ital x}}){sub 13} remain nearly unchanged between {ital x}=0 and 0.2, whichmore » is contradictory to the predicted changes in the PLDOS`s obtained in the rigid-band scheme. This finding suggests a breakdown of a simple rigid-band approximation in La(Co{sub 1{minus}{ital x}}Fe{sub {ital x}}){sub 13}, which is probably due to a large hybridization bonding between Co and Fe 3{ital d} electrons.« less