High-symmetry Positions Research Articles

Non-Fermi-liquid behavior at the onset of incommensurate2kFcharge- or spin-density wave order in two dimensions

We analyze the influence of quantum critical fluctuations on single-particle excitations at the onset of incommensurate $2k_F$ charge or spin density wave order in two-dimensional metals. The case of a single pair of hot spots at high symmetry positions on the Fermi surface needs to be distinguished from the case of two hot spot pairs. We compute the fluctuation propagator and the electronic self-energy perturbatively in leading order. The energy dependence of the single-particle decay rate at the hot spots obeys non-Fermi liquid power laws, with an exponent 2/3 in the case of a single hot spot pair, and exponent one for two hot spot pairs. The prefactors of the linear behavior obtained in the latter case are not particle-hole symmetric.

Microstrain in tetragonal lead-zirconate-titanate: the effect of pressure on the ionic displacements.

Piezoelectric materials respond to external stimuli by adjusting atomic positions. In solid-solutions, the changes occurring in atomic scale are very complex since the short- and long-range order are different. Standard methods used in diffraction data analysis fail to model the short-range order accurately. Pressure-induced cation displacements in ferroelectric Pb(Zr(0.45)Ti(0.55))O3 perovskite oxide are modeled by starting from a short-range order. We show that the model gives the average structure correctly and properly describes the local structure. The origin of the microstrain in lead zirconate titanate is the spatially varying Zr and Ti concentration and atomic distances, which is taken into account in the simulation. High-pressure neutron powder diffraction and simulation techniques are applied for the determination of atomic positions and bond-valences as a function of pressure. Under hydrostatic pressure, the material loses its piezoelectric properties far before the transition to the cubic phase takes place. The total cation valence +6 is preserved up to 3.31 GPa by compensating the increasing B-cation valence by decreasing Pb-displacement from the high-symmetry position. At 3.31 GPa, Pb-displacement is zero and the material is no more ferroelectric. This is also the pressure at which the Pb-valence is minimized. The average structure is still tetragonal. The model for microstrain predicts that the transition occurs over a finite pressure range: Pb-displacements are spatially varying and follow the distribution of Zr and Ti ions.

Chemically induced Jahn-Teller ordering on manganite surfaces.

Physical and electrochemical phenomena at the surfaces of transition metal oxides and their coupling to local functionality remains one of the enigmas of condensed matter physics. Understanding the emergent physical phenomena at surfaces requires the capability to probe the local composition, map order parameter fields and establish their coupling to electronic properties. Here we demonstrate that measuring the sub-30-pm displacements of atoms from high-symmetry positions in the atomically resolved scanning tunnelling microscopy allows the physical order parameter fields to be visualized in real space on the single-atom level. Here, this local crystallographic analysis is applied to the in-situ-grown manganite surfaces. In particular, using direct bond-angle mapping we report direct observation of structural domains on manganite surfaces, and trace their origin to surface-chemistry-induced stabilization of ordered Jahn-Teller displacements. Density functional calculations provide insight into the intriguing interplay between the various degrees of freedom now resolved on the atomic level.

Ferroelectric transitions at ferroelectric domain walls found from first principles.

We present a first-principles study of model domain walls (DWs) in prototypic ferroelectric PbTiO(3). At high temperature the DW structure is somewhat trivial, with atoms occupying high-symmetry positions. However, upon cooling the DW undergoes a symmetry-breaking transition characterized by a giant dielectric anomaly and the onset of a large and switchable polarization. Our results thus corroborate previous arguments for the occurrence of ferroic orders at structural DWs, providing a detailed atomistic picture of a temperature-driven DW-confined transformation. Beyond its relevance to the field of ferroelectrics, our results highlight the interest of these DWs in the broader areas of low-dimensional physics and phase transitions in strongly fluctuating systems.

The structure of cubic MOF [{Ca(H2O)6}{CaGd(oxydiacetate)3}2].4H2O. A comparison between structural models obtained from Rietveld refinement of conventional and synchrotron X-ray powder diffraction data and standard refinement of single-crystal X-ray diffraction data

The structure of the metal–organic framework (MOF) compound [{Ca(H2O)6}{CaGd(oxydiacetate)3}2]·4H2O was determined by single-crystal X-ray diffraction and refined using conventional single-crystal X-ray diffraction data. In addition, the structure was refined using powder diffraction data collected from two sources, a conventional X-ray diffractometer in Bragg–Brentano geometry and a 12-detector high resolution synchrotron-based diffractometer in transmission geometry. Data from the latter were processed in three different ways to account for crystalline decay or radiation damage. One dataset was obtained by averaging the multiple detector patterns, another dataset was obtained by cutting the non-overlapping portions of each detector to consider only the first few minutes of data collection and a dose-corrected dataset was obtained by fitting the independent peaks in every dataset and extrapolating the intensity and peak position to the initial time of data collection or to zero-absorbed dose. The compared structural models obtained show that special processing of powder diffraction data produced a much accurate model, close to the single-crystal-based model for this particular compound with heavy atoms in high symmetry positions that do not contribute to a significant number of diffraction intensities.

Clustering and magnetic anisotropy of Fe adatoms on graphene

Single Fe adatoms and clusters of Fe adatoms on graphene are studied through first-principles calculations using density functional theory (DFT) and spin density functional theory (sDFT). First, we consider computational cells containing various numbers of C atoms and one Fe adatom. We calculate the binding energy, adatom height, and magnetic moment of the adatom above a few high-symmetry positions in the cell. In all cases, the binding energy increases with decreasing cell size, suggesting that clustering of the Fe adatoms is energetically favored. We also calculate the energy of various clusters of two to four Fe atoms on graphene in computational cells of various sizes, using both DFT and sDFT. These calculations again show that, both in DFT and sDFT, the Fe adatoms strongly prefer to form clusters. The energy barrier for an isolated Fe adatom to diffuse from the center of one graphene hexagon is calculated to be 0.49 eV. This barrier is reduced for an Fe atom which is one of a pair of neighboring adatoms. Finally, by including spin-orbit interactions within sDFT, we calculate the magnetic anisotropy energy of a single Fe adatom on graphene. We find that the in-plane anisotropy energy is close to zero, while the out-of-plane anisotropy energy is $\ensuremath{\sim}$$D{S}^{2}{\mathrm{cos}}^{2}\ensuremath{\theta}$ where $S\ensuremath{\sim}2.0$, $\ensuremath{\theta}$ is the angle between the magnetic moment and the perpendicular to the graphene plane, and $D\ensuremath{\sim}0.25$ meV.

Ferromagnetically Coupled Shastry-Sutherland Quantum Spin Singlets in(CuCl)LaNb2O7

A thorough crystal structure determination at very low temperature of (CuCl)LaNb₂O₇, originally proposed as a spin-1/2 square-lattice antiferromagnet, is reported thanks to the use of single-crystal x-ray diffraction and powder neutron diffraction. State-of-the-art calculations (maximum entropy method) reveal that (CuCl)LaNb₂O₇ is orthorhombic with Pbam symmetry. First-principles calculations demonstrate that the dominant magnetic interactions are antiferromagnetic between fourth nearest neighbors with a Cu-Cl-Cl-Cu exchange path, which lead to the formation of spin singlets. The two strongest interactions between the singlets are ferromagnetic, which makes (CuCl)LaNb₂O₇ the first system of ferromagnetically coupled Shastry-Sutherland quantum spin singlets.

Orbitally controlled Kondo effect of Co adatoms on graphene

Based on ab-initio calculations we identify possible scenarios for the Kondo effect due to Co ad-atoms on graphene. General symmetry arguments show that for magnetic atoms in high-symmetry positions, the Kondo effect in graphene is controlled not only by the spin but also by the orbital degree of freedom. For a Co atom absorbed on top of a carbon atom, the Kondo effect is quenched by spin-orbit coupling below an energy scale of $\sim 15$\,K. For Co with spin $S=1/2$ located in the center of a hexagon, an SU(4) Kondo model describes the entanglement of orbital moment and spin at higher energies, while below \sim 60$\,meV spin-orbit coupling leads to a more conventional SU(2) Kondo effect. The interplay of the orbital Co physics and the peculiar band-structure of graphene is directly accessible in Fourier transform tunneling spectroscopy or in the gate-voltage dependence of the Kondo temperature displaying a very strong, characteristic particle-hole asymmetry.

Elastic relaxations associated with the – transition in LaAlO3: IV. An incipient instability below room temperature

Resonant ultrasound spectroscopy has been used to characterize elastic softeningand acoustic dissipation behaviour in single crystal and ceramic samples ofLaAlO3 between 10 and 300 K. For the twinned single crystals, average values of the cubic elastic moduli and C44 were followed while the ceramic sample provided data for the bulk and shear moduli. ADebye-like dissipation peak occurs in the vicinity of 250 K, from which an activation energy of43 ± 6 kJ mol−1 has been obtained. The mechanism for this is not known, but it is associated withC44 and therefore could be related in some way to the transition at ∼817 K. Slight softening in the temperature interval K of resonance peaks determined by shear elastic moduli hints at an incipientEg ferroelasticinstability in LaAlO3. The softening interval ends with a further dissipation peak at∼60 K, the origin of which is discussed in terms of freezing of atomic motions of La and/or Alaway from their high symmetry positions in the structure. LaAlO3 thus shows evidence of incipient structural instability at low temperatureswhich is potentially analogous with the phenomenologically rich behaviour ofSrTiO3.

Effect of impurities in high-symmetry lattice positions on the local density of states and conductivity of graphene

Motivated by quantum chemistry calculations, showing that molecular adsorption in graphene takes place on preferential sites of the honeycomb lattice, we study the effect of an isolated impurity on the local electronic properties of a graphene monolayer, when the impurity is located on a sitelike, bondlike, or hollowlike position. We evaluate the local density of states (LDOS) as a function of energy on the impurity and on its neighboring sites, as well as in reciprocal space, at an energy corresponding to a bound state, in the three cases of interest. The latter study may be relevant to interpret the results of Fourier-transformed scanning tunneling spectroscopy, as they show which states mostly contribute to impurity-induced variations in the LDOS. We also estimate, semianalytically, the dependence of the condition for having a low-energy bound state on the impurity potential strength and width. Such results are then exploited to obtain the quasiparticle lifetime and the static conductivity in graphene in the dilute impurity limit. In particular, we recover a sublinear dependence of the conductivity on the carrier concentration as a generic impurity effect.

Hydrogen Embrittlement of High Strength Steels

Hydrogen embrittlement is believed to be one of the main reasons for cracking of structures under stress. High strength steels in these structures often include a ferritic core made of alpha-iron (body centered cubic lattice). We compute the interaction of atomic hydrogen with iron using first principles. The interstitial hydrogen can be placed in two high symmetry positions: octahedral and tetrahedral sites. Our calculations provide diffusion barriers between these sites. These barriers have been analyzed to understand the propagation of hydrogen through the iron lattice. We analyze how these barriers can be modified by the hydrogen concentration. The results show the main site for high and low hydrogen density and they show the diffusion coefficient variation by the hydrogen density.

Neutron powder diffraction and magnetic study of perovskites Pb(Mn 1/2Nb 1/2)O 3 and Pb(Mn 1/4Fe 1/4Nb 1/2)O 3

The structural and magnetic properties of the complex metal oxides Pb(Mn 1/2Nb 1/2)O 3 (PMNO) and Pb(Mn 1/4Fe 1/4Nb 1/2)O 3 (PMFNO), which belong to a class of disordered perovskites have been studied. The magnetic susceptibilities of PMNO showed hysteresis between field cooled and zero-field cooled conditions below the transition of 15 K, suggesting that the material has a spin-glass feature. Neutron diffraction patterns of PMNO showed no evidence of a long-range magnetic ordering at 1.5 K, which is consistent with spin-glass behavior. Rietveld refinements of neutron powder diffraction data collected at different temperatures between 1.5 and 700 K have been carried out in order to extract structural information. The crystal structure of this compound is cubic (space group Pm 3 ¯ m) within the whole temperature interval. The Mn and Nb ions were found to be disordered over the perovskite B-sites. The main feature of this structure is the positional disorder at the Pb site, the importance of which in connection with the ferroic transitions is briefly discussed. The Pb cations show a positional disorder shifting from their high-symmetry positions along the [1 1 1] direction. The effect of Fe-doping on PMNO has been studied. The substitution of Fe at the Mn site in PMFNO results in a small changes of the magnetic properties without significant differences in the crystal structures. The factors governing the observed structural and magnetic properties of PMNO and PMFNO are discussed and compared with those of other quaternary Mn-containing perovskites. For the PbB 3+ 1/2Nb 1/2O 3 series with the isomorphous substitution B 3+, graphs of average lattice parameters of the perovskite phase and the temperatures of ferroelectric and magnetic phase transitions as functions of the B 3+ cation radius were constructed and are discussed. Influence of A-cation sublattice on magnetic properties is also considered.

Ba 2In 2O 4(OH) 2: Proton sites, disorder and vibrational properties

The structure of Ba 2In 2O 4(OH) 2 is analysed by the explicit full optimization of a large number of possible proton arrangements using periodic density functional theory. It is shown that the experimental assignments in which protons appear to be located at high symmetry positions with unphysical bond lengths do not correspond to minima on the potential energy hypersurface. The apparent sites are averages of a number of possible proton locations involving a set of possible local structural environments in which the internuclear separations are more realistic. Such problems with structural refinements are common where profile refinement programs place the atoms at the average position due to dynamic and/or static disorder. Thus while the calculations support a previous neutron diffraction analysis of the structure in that the average structure contains two different proton sites, they also reveal substantial information about the local environments of the protons. In all optimizations, the protons moved from the average positions suggested in the neutron diffraction study with calculated O–H and OH⋯O distances consistent with those observed in other oxides. The energies of different proton distributions vary significantly so the protons are not randomly distributed. We also present an analysis of the vibrational properties of the O–H bonds. Since the strength of the hydrogen bonds is closely related to the local structural environments of the protons, a range of vibrational frequencies is obtained providing a prediction of the vibrational spectra. In O–H⋯O linkages, O–H stretching modes soften with increasing H⋯O hydrogen bond strength, while the in-plane and out-of-plane bending or libration modes stiffen. Together, our results show how modern theoretical methods can provide a clearer understanding of the structure and dynamics of a complex inorganic material.

Contrasting oxide crystal chemistry of Nb and Ta:: The structures of the hexagonal bronzes BaTa 2O 6 and Ba 0.93Nb 2.03O 6

The high-temperature hexagonal forms of BaTa 2O 6 and Ba 0.93Nb 2.03O 6 have P6 /mmm symmetry with unit-cell parameters a=21.116(1) Å, c=3.9157(2) Å and a=21.0174(3) Å, c=3.9732(1) Å, respectively. Single crystal X-ray structure refinements for both phases are generally consistent with a previously proposed model, except for displacements of some Ba atoms from high-symmetry positions. The structures are based on a framework of corner- and edge-connected Nb/Ta-centred octahedra, with barium atoms occupying sites in four different types of [0 0 1] channels with hexagonal, triangular, rectangular and pentagonal cross-sections. The refinements showed that the non-stoichiometry in the niobate phase is due to barium atom vacancies in the pentagonal channels and to extra niobium atoms occupying interstitial sites with tri-capped trigonal prismatic coordination. The origin of the non-stoichiometry is attributed to minimisation of non-bonded Ba–Ba repulsions. The hexagonal structure is related to the structures of the low-temperature forms of BaNb 2O 6 and BaTa 2O 6, through a 30° rotation of the hexagonal rings of octahedra centred at the origin.

Cesium adsorption on the β2-GaAs(001) surface

The results of first-principles calculations of the cesium adsorption energy on the β2-GaAs(001) surface performed within approaches of the density functional theory are presented for two possible terminations of the surface. It is shown that, among the considered high-symmetry positions, the energy-preferred position for cesium is position T 3 when the surface layer contains arsenic and position T 4 for gallium terminated surface. Cesium introduces insignificant perturbations in the positions of surface-layer atoms, and surface dimers do not break even in the case of adsorption at the dimer bridge and top positions. It is shown that cesium bonding to the GaAs (001) substrate can be explained by sp hybridization of arsenic and gallium orbitals as well as by formation of cesium states mixed with delocalized states of a clean surface. At low coverage, more preferable adsorbate sites are those with nearest neighbor arsenic atoms for both surface terminations.

Structural, magnetic and Mössbauer spectroscopic investigations of the magnetoelectric relaxor Pb(Fe 0.6W 0.2Nb 0.2)O 3

The complex perovskite lead iron tungsten niobium oxide, Pb(Fe 0.6W 0.2Nb 0.2)O 3 (PFWN) which belongs to the class of disordered magnetoelectrics, has been studied by X-ray and neutron powder diffraction, magnetic and Mössbauer spectroscopic measurements. Structural, dielectric and magnetic properties of PFWN are presented and reviewed. Magnetic measurements indicate that the most important interactions are of antiferromagnetic nature yielding T N = 300 K, however, with indications of a reentrant spin glass behaviour below 20 K. The parameters of Mössbauer spectra also support the existence of the magnetic order and are consistent with the presence of high-spin Fe 3+ cations located in the octahedral B-site. Rietveld refinements of diffraction data at different temperatures between 10 and 700 K have been carried out. The long-range structure of PFWN is cubic (space group Pm−3 m) over the whole temperature interval. The Fe, W and Nb cations were found to be disordered over the perovskite B-sites. The Pb cations show a position disorder along the 〈111〉 direction shifting from their high-symmetry position. At the temperatures below T N, an antiferromagnetic arrangement of the magnetic moments of Fe 3+ cations in the B-site is proposed in accordance with the antiferromagnetic properties of PFWN. The factors governing the observed nuclear and magnetic structures of PFWN are discussed and compared with those of pure Pb(Fe 0.67W 0.33)O 3, Pb(Fe 0.5Nb 0.5)O 3 and other quaternary Pb-based perovskites containing iron.

Disorder of Pb Atom in Cubic Structure of Pb(Zn1/3Nb2/3)O3–PbTiO3 System

The crystal structures of (1-x)Pb(Zn1/3Nb2/3)O3–xPbTiO3 (PZN–PT: 0≤x≤0.3) in the cubic phase at 650 K have been investigated by analyzing the high-energy synchrotron-radiation (SR) powder diffraction data using the Rietveld method. It is found that the Pb atom does not settle at the ideal high-symmetry position with a harmonic thermal parameter. The split-atom method reveals that the Pb atom in the cubic phase is disordered and settles randomly at crystallographically equivalent positions slightly off-center of the cubic-corner site. The disordered directions of the Pb atom are significantly changed at the concentration x∼0.15. This structural boundary found in the cubic phase is related to the appearance of the morphotropic phase boundary (MPB).

Crystal structure and lattice dynamics of high-pressure scandium trihydride

Powder samples of hcp $\mathrm{Sc}{\mathrm{H}}_{2.9}$ and $\mathrm{Sc}{\mathrm{D}}_{2.9}$ have been synthesized under a $1\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ pressure of gaseous hydrogen or deuterium and studied at ambient pressure and $95\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ by neutron diffraction. A profile analysis of the diffraction patterns indicated a crystal structure with $P{6}_{3}∕mmc$ symmetry that differs from the structures of hcp trihydrides of yttrium and rare-earth metals by the absence of long-range order in the displacements of hydrogen atoms from high-symmetry positions. The lattice dynamics of scandium trihydride and, for comparison, yttrium trihydride were studied by inelastic neutron scattering at $20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in the range of energy transfers $4--250\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. The spectra of optical H vibrations in these two trihydrides proved to be similar, suggesting similar arrangements of hydrogen atoms on a short-range scale.

Ab initiostudy of icosahedral Al-Pd-Mn quasicrystals: Structural model, electric field gradients, and negative valence of Mn

The atomic and electronic structures of the Quandt-Elser model of $i\text{\ensuremath{-}}{\mathrm{Al}}_{70.8}{\mathrm{Pd}}_{21.5}{\mathrm{Mn}}_{7.7}$ [A. Quandt and V. Elser, Phys. Rev. B 61, 9336 (2000)] are studied by pseudopotential and full-potential linear augmented plane-wave methods. A model with a lower total energy than the original Quandt-Elser model ($\ensuremath{\Delta}E=\ensuremath{-}0.03\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$/atom) is obtained by moving one of the Al atoms on a cube in the Mackay void away from its high symmetry position and by performing a subsequent structural relaxation. The electronic density of states of this modified Quandt-Elser model is found to be similar to that of the model of Katz and Gratias, but with a more pronounced pseudogap near the Fermi energy. Good agreement is obtained with an available photoemission spectrum, but calculated electric field gradients do not reproduce the angular dependence of a $^{27}\mathrm{Al}$ nuclear magnetic resonance spectrum. By introducing vacancies at Mn sites and by comparing the filling of bands near the Fermi energy for the models with and without a vacancy, it is found that the Mn atoms have an apparent negative number of $\ensuremath{-}3.2$ valence electrons independent of the Mn site. It is argued that this apparent negative number of valence electrons is due to the filling of $\mathrm{Mn}\text{\ensuremath{-}}d$ states below the Fermi energy.

Linear combination of atomic orbitals calculation of the Auger neutralization rate ofHe+on Al(111), (100), and (110) surfaces

We develop a theory of the Auger neutralization rate of ions on solid surfaces in which the matrix elements for the transition are calculated by means of a linear combination of atomic orbitals technique. We apply the theory to the calculation of the Auger rate of ${\mathrm{He}}^{+}$ on unreconstructed Al(111), (100), and (110) surfaces, assuming ${\mathrm{He}}^{+}$ to approach these surfaces on high symmetry positions and compare them with the results of the jellium model. Although there are substantial differences between the Auger rates calculated with both kinds of approaches, those differences tend to compensate when evaluating the integral along the ion trajectory and, consequently, are of minor influence in some physical magnitudes like the ion survival probability for perpendicular energies larger than $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. We find that many atoms contribute to the Auger process and small effects of lateral corrugation are registered.