Orbital Anisotropy Research Articles

X-ray absorption study of layered Co oxides with a Co-O triangular lattice

We have studied the electronic structure of the quasi-two-dimensional Co oxides ${\mathrm{NaCo}}_{2}{\mathrm{O}}_{4}({\mathrm{Na}}_{x}{\mathrm{CoO}}_{2},x\ensuremath{\sim}0.5\text{--}0.6),\phantom{\rule{0.2em}{0ex}}{\mathrm{Ca}}_{3}{\mathrm{Co}}_{4}{\mathrm{O}}_{9}$, and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{Co}}_{2}{\mathrm{O}}_{9}$ using O $1s$ and Co $2p$ x-ray absorption (XAS) spectroscopy. We found that these Co-O triangular lattice systems have in common that their ${\mathrm{Co}}^{3+}$ and ${\mathrm{Co}}^{4+}$ ions are all low-spin, supporting the Koshibae-Tsutsui-Maekawa theory to explain the enhanced thermopower at elevated temperatures. The concentration of holes in the Co $3d\phantom{\rule{0.3em}{0ex}}{t}_{2g}$ shell is estimated to be about 0.4, 0.6, and 0.33, respectively. The O $1s$ XAS spectra strongly depend on the direction of polarization vector of the incoming x-ray. The polarization dependence indicates that the ${t}_{2g}$ orbital anisotropy of ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2}$ is different from that of ${\mathrm{Ca}}_{3}{\mathrm{Co}}_{4}{\mathrm{O}}_{9}$ and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{Co}}_{2}{\mathrm{O}}_{9}$. We argue that the difference of the orbital anisotropy and hole concentration are essential to explain why ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2},\phantom{\rule{0.2em}{0ex}}{\mathrm{Ca}}_{3}{\mathrm{Co}}_{4}{\mathrm{O}}_{9}$, and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{Co}}_{2}{\mathrm{O}}_{9}$ have different electric and magnetic properties at low temperatures.

Temperature, wavelength, and polarization dependent time resolved optical spectroscopy of half-metallic CrO2

Cr O 2 is an important transition metal oxide due to its half-metallic behavior. We have performed ultrafast laser pump-probe differential transmission experiments on epitaxial CrO2(110). Polarizations parallel and perpendicular to the c axis were used, at wavelengths corresponding to important magnetic excitations: 1300 (1eV), 800 (1.5eV), and 650nm(2eV). Anisotropy is observed in the polarization-dependent measurements and is attributed to the electronic orbital anisotropy. A critical change of transient transmission is also observed at the Curie temperature of 386K. This behavior reveals the close relationship between the optical absorption and the spin dynamics of this material.

Key role of orbital anisotropy in geometrically frustrated electron system

By using the density matrix renormalization group method, we investigate ground- and excited-state properties of the e g -orbital degenerate Hubbard model at quarter filling for two kinds of lattices, zigzag chain and ladder. In the zigzag chain, the system is effectively regarded as a decoupled double chain of the S = 1 2 antiferromagnetic Heisenberg model, and the spin gap is approximately zero, similar to the case of weakly coupled Heisenberg chains. On the other hand, in the ladder, the spin correlation on the rung remains robust and the spin gap exists.

Molecular orbitals of methane: symmetry or hybridization?

Orbital electron density distributions and momentum distributions of both core and valence space of methane are studied quantum mechanically, using RHF/TZVP and B3LYP/TZVP models, respectively. The three molecular orbitals (MOs) of methane in the ground electronic state (X1A1), namely, the core MO, 1a1 and the valence MOs, i.e. 2a1 and three-fold energy degenerate MOs 1t2, are studied in both coordinate space and momentum space. They are compared with the corresponding atomic orbitals (AOs) of a ‘free’ carbon atom in its ground electronic state (3P) using configuration averaged unrestricted HF (UHF) method. The electronic structure of methane inherits that of a free single carbon atom, indicating that the symmetry of methane contributes to the equivalent orbitals and their behavior. There are no any quantitative evidences of hybridization for the MOs of methane in either coordinate space or momentum space. The core MO (1a1) of methane in momentum space is found to be nearly indistinguishable to the core AO (1s) of a free carbon atom using the same model. The net chemical bonding results as displayed in the valence MO momentum distributions have clearly retained the orbital wave function anisotropy as s-like and p-like in both methane and the free carbon atom.

On the use of X-rays to determine dynamical properties of elliptical galaxies

The X-ray emitting interstellar medium of early type galaxies is often used as a tool to determine their total mass M and stellar orbital anisotropy beta profiles, based on the hypothesis of hydrostatic equilibrium for the hot gas. Here we investigate the effects that deviations from equilibrium have on M and beta estimates, by using simple analytical calculations and hydrodynamical simulations representative of gas rich galaxies. We show that the deviations of the X-ray determined beta^{est} and M^{est} from the true values are linked by a remarkably simple relation; in particular, M is underestimated if beta is overestimated, and more radially anisotropic orbital distributions than true are deduced in presence of gas infall velocities of the order of the local stellar velocity dispersion (as are likely in the central regions of galactic cooling flows). The results of this analysis are applied to the most thoroughly investigated bright elliptical, NGC4472. We show that beta^{est} recently derived from X-rays corresponds to a galaxy that is unstable by radial orbit instability. Then, assuming as true beta and M the optically derived values, we show that the differences beta^{est}-beta and M^{est}-M agree with the predictions found here in the case of lack of hydrostatic equilibrium, which points to the latter as a possible explanation for the discrepancies (abridged).

Molecular orbitals of methane: symmetry or hybridization?

Orbital electron density distributions and momentum distributions of both core and valence space of methane are studied quantum mechanically, using RHF/TZVP and B3LYP/TZVP models, respectively. The three molecular orbitals (MOs) of methane in the ground electronic state (X 1A 1), namely, the core MO, 1 a 1 and the valence MOs, i.e. 2 a 1 and three-fold energy degenerate MOs 1 t 2, are studied in both coordinate space and momentum space. They are compared with the corresponding atomic orbitals (AOs) of a ‘free’ carbon atom in its ground electronic state ( 3P) using configuration averaged unrestricted HF (UHF) method. The electronic structure of methane inherits that of a free single carbon atom, indicating that the symmetry of methane contributes to the equivalent orbitals and their behavior. There are no any quantitative evidences of hybridization for the MOs of methane in either coordinate space or momentum space. The core MO (1 a 1) of methane in momentum space is found to be nearly indistinguishable to the core AO (1s) of a free carbon atom using the same model. The net chemical bonding results as displayed in the valence MO momentum distributions have clearly retained the orbital wave function anisotropy as s-like and p-like in both methane and the free carbon atom.

Carrier concentration independent antiferromagnetic spin fluctuations in the electron-doped high-temperature superconducting cupratePr2−xCexCuO4

We have performed ${}^{63}\mathrm{Cu}$ NMR measurements on the electron-doped high-temperature superconducting cuprate (HTSC) ${\mathrm{Pr}}_{2\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4}$ $(x=0.10,$ 0.15, and 0.20), at 9 T, which is sufficient to suppress ${T}_{c}$ to zero. The Cu spin-lattice relaxation rate and the Cu spin-lattice relaxation rate anisotropy can be consistently interpreted in terms of coupling to antiferromagnetic spin fluctuations for temperatures as low as 6 K. We find that the spin-fluctuation spectrum probed by the Cu spin-lattice relaxation rate does not change with increasing electronic concentration, contrary to a recent theoretical predication. There is no evidence in the Cu spin-lattice relaxation rate data for a temperature-independent spin gap that is as large as theoretically predicted or as large as the normal-state pseudogap energy reported from infrared reflectance measurements on the electron-doped HTSC ${\mathrm{Nd}}_{2\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4}.$ The Cu nuclear quadrupole resonance frequency is significantly smaller than that observed in the hole doped HTSC, which implies a nearly complete cancellation of the Cu $3d,$ O $2p,$ and nuclei contributions to the electric-field gradient at the Cu nucleus. The orbital shift anisotropy is similar to that observed in the hole doped HTSC, implying a similar relative splitting of the Cu $3d$ orbitals.

The stellar kinematics of the giant halos of Brightest Cluster Galaxies

We have investigated the stellar kinematics of two brightest cluster galaxies (BCGs) to large distances from the cluster centre. In both galaxies, the velocity dispersion rises with radius. Orbital anisotropy is ruled out as the cause and we conclude that the kinematics in the outer parts of BCGs are dark matter dominated. This result contrasts with the current problem for intermediate luminosity ellipticals, which appear to have less dark matter than predicted by CDM. Combining the present results with our previous work, the fraction of BCGs with outwardly rising dispersions () from the inner parts of BCGs. We argue that this phenomenon may be more common than previously thought. The agreement with radial trends expected for a smooth galaxy/cluster transition, and the lack of dependence on cD/BCG dominance and cluster environment, suggest that the outwardly rising dispersion is a genuine response of the stars to the underlying cluster potential. There is evidence that BCG in Abell 2063 is not at the centre of the cluster potential.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Generating Equilibrium Dark Matter Halos: Inadequacies of the Local Maxwellian Approximation

We describe an algorithm for constructing N-body realizations of equilibrium spherical systems. A general form for the mass density ? is used, making it possible to represent most of the popular density profiles found in the literature, including the cuspy density profiles found in high-resolution cosmological simulations. We demonstrate explicitly that our models are in equilibrium. In contrast, many existing N-body realizations of isolated systems have been constructed under the assumption that the local velocity distribution is Maxwellian. We show that a Maxwellian halo with an initial ?(r) r-1 central density cusp immediately develops a constant-density core. Moreover, after just one crossing time the orbital anisotropy has changed over the entire system, and the initially isotropic model becomes radially anisotropic. These effects have important implications for many studies, including the survival of substructure in cold dark matter (CDM) models. Comparing the evolution and mass-loss rate of isotropic Maxwellian and self-consistent Navarro, Frenk, & White (NFW), satellites orbiting inside a static host CDM potential, we find that the former are unrealistically susceptible to tidal disruption. Thus, recent studies of the mass-loss rate and disruption timescales of substructure in CDM models may be compromised by using the Maxwellian approximation. We also demonstrate that a radially anisotropic, self-consistent NFW satellite loses mass at a rate several times higher than that of its isotropic counterpart on the same external tidal field and orbit.

Orbital magnetic moments and magnetic anisotropy energy in Rh N and Co N Pd M clusters

Orbital magnetic moments and magnetic anisotropy energy in Rh N and Co N Pd M clusters

First principles determinations of magnetic anisotropy energy of Co nanoclusters

We have calculated magnetic anisotropy energies of several free standing Co nanoclusters consisting of one, two, three, and six Co atoms with the full potential linearized augmented plane wave method. The magnetic moments are found to be aligned perpendicular to the Co–Co bond. The results show that the spin magnetic moments are suppressed by roughly 10% compared to Co monolayer or Co nanowire. Orbital magnetic moments and anisotropy energies depend sensitively on the size and shape of clusters.

Orbital anisotropy of the field-induced moments in chromium and vanadium

The dependence of the cross-section for magnetic scattering of neutrons on the angleθkbetween the field direction and the scattering vector has been used to study theorbital contribution to magnetic scattering from the moments aligned bya magnetic field in chromium and vanadium. The results lend supportto band structure calculations which predict very high ratios of orbitalto spin moments. The magnetic scattering from the moments inducedin Cr and V by a 9.5 T field applied parallel to ⟨110⟩, insets of crystallographically equivalent reflections having different values of θk,has been determined from polarized neutron flipping ratio measurements. Theresults have been analysed using the tensor operator formalism. The results donot show the equatorial anisotropy predicted by a simple atomic model inwhich the orbital moment arises from mixing between empty eg and filledt2gstates. The azimuthal variation observed suggests that the major part of theorbital moment is due to 3d states with projections of angular momentum m = ±2.

In-plane magnetocrystalline anisotropy observed on Fe/Cu(111) nanostructures grown on stepped surfaces

Magnetic in-plane and out-of-plane anisotropies measured by angle dependent x-ray magnetic circular dichroism (XMCD) on fcc Fe nanostructures are discussed and compared with fcc FeNi nanostructures. All studies were performed using XMCD at the Fe ${L}_{2,3}$ edges for Fe grown on a Cu(111) vicinal vic surface. The step induced in-plane anisotropy in the step decoration regime is analyzed by measuring the orbital magnetic moment dependence as a function of the in-plane azimuth and out-of-plane incidence angles. In the one-dimensional limit where the out-of-plane magnetic easy axis dominates, Fe/Cu(111) shows a large in-plane orbital magnetic moment anisotropy leading to a magnetocrystalline anisotropy energy of 0.4 meV/atom and an in-plane magnetic easy axis perpendicular to the steps. In the nanometer scale the aspect ratio of the elongated rectangular Fe stripes are found to be responsible for the in-plane and out-of-plane anisotropy. This is coherent with previous findings where the circular shaped fcc ${\mathrm{Fe}}_{0.65}{\mathrm{Ni}}_{0.35}$ nanostructures do not show any in-plane anisotropy. The three-dimensional nanostructures are characterized by magnetic orbital moments connected with the number of broken bonds in the direction of the quantization axis defined by the direction of the saturation field. The microscopic origin of the in-plane large orbital magnetic moment anisotropy is attributed to the nanometer size of the structures perpendicular to the steps and to the asymmetry of the number of broken bonds in the plane.

Radial orbital anisotropy and the Fundamental Plane of elliptical galaxies

The existence of the Fundamental Plane imposes strong constraints on the structure and dynamics of elliptical galaxies, and thus contains important information on the processes of their formation and evolution. Here we focus on the relations between the Fundamental Plane thinness and tilt and the amount of radial orbital anisotropy: in fact, the problem of the compatibility between the observed thinness of the Fundamental Plane and the wide spread of orbital anisotropy admitted by galaxy models has often been raised. By using N-body simulations of galaxy models characterized by observationally motivated density profiles, and also allowing for the presence of live, massive dark matter haloes, we explore the impact of radial orbital anisotropy and instability on the Fundamental Plane properties. The numerical results confirm a previous semi-analytical finding (based on a different class of one-component galaxy models): the requirement of stability matches almost exactly the thinness of the Fundamental Plane. In other words, galaxy models that are radially anisotropic enough to be found outside the observed Fundamental Plane (with their isotropic parent models lying on the Fundamental Plane) are unstable, and their end-products fall back on the Fundamental Plane itself. We also find that a systematic increase of radial orbit anisotropy with galaxy luminosity cannot explain by itself the whole tilt of the Fundamental Plane, the galaxy models becoming unstable at moderately high luminosities: at variance with the previous case, their end-products are found well outside the Fundamental Plane itself. Some physical implications of these findings are discussed in detail.

Doping dependence of the exchange energies in bilayer manganites: Role of orbital degrees of freedom

Recently, an intriguing doping dependence of the exchange energies in the bilayer manganites $La_{2-2x}Sr_{1+2x}Mn_2O_7$ has been observed in the neutron scattering experiments. The intra-layer exchange only weakly changed with doping while the inter-layer one drastically decreased. Here we propose a theory which accounts for these experimental findings. We argue, that the observed striking doping dependence of the exchange energies can be attributed to the evaluation of the orbital level splitting with doping. The latter is handled by the interplay between Jahn-Teller effect (supporting an axial orbital) and the orbital anisotropy of the electronic band in the bilayer structure (promoting an in-plane orbital), which is monitored by the Coulomb repulsion. The presented theory, while being a mean-field type, describes well the experimental data and also gives the estimates of the several interesting energy scales involved in the problem.

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.

Magnetic properties of a Co/Cu/Ni trilayer on the Cu(100) surface

The present thesis concerns applications of first principles electronic structure calculations in conjunction with methods of statistical mechanics for simulations of transition metal alloys both in the bulk and at surfaces.A fully relativistic generalization of the exact muffin-tin orbitals (EMTO) method has been developed. The method accurately takes into account spin-orbit coupling and allows one to calculate orbital polarization and magneto-crystalline anisotropy in magnetic systems as well as increasing the range of applicability of the EMTO method to heavy elements. A new direct-exchange Monte Carlo (DEMC) method has been proposed, which is capable to tackling effectively statistical simulations of surface segregations in disordered and ordered alloys.The applications of relativistic methods include calculations of spin and orbital magnetization in iron-cobalt disordered and partially ordered alloys, as well as computation of the core-level shifts (CLS) in transition metal alloys. It has been found, that relativistic corrections are important for CLS calculations in 5-d metal alloys. Properties of a Ni monolayer deposited on a Cu surface have been studied. The monolayer is found to be unstable in the top layer, and its magnetization depends greatly on the surface orientation. Two distinct energy levels have been found to exist Co/Cu/Ni trilayers deposited on the (100) Cu surface, which correspond to a completely paramagnetic trilayer and the case when only Ni is paramagnetic.Vacancy ordering in substoichometric titanium carbides TiCx have been simulated. Existence of three ordered phases in the range of carbon concentration x=0.5 ÷1.0 has been revealed and a theoretical phase diagram has been proposed. Surface segregations have been calculated in disordered Ni50Pt50 and Ni50Pd50 as well as in ordered NiPt alloys. Segregation reversal has been observed in the Ni50Pt50 alloy with Pt segregation at the (111) surface and Ni segregation at the (110). In the ordered NiPt alloys segregation behaviour is found to be affected greatly by small deviations from the exact stoichiometric composition in bulk. Surface magnetization in PdV and MoV bcc alloys have been studied. It has been found, that in PdV alloys surface segregations suppress magnetic order at the surface, while in MoV alloys magnetization is substantially enhanced due to the segregation.

Step-induced in-plane orbital anisotropy in FeNi films on Cu(111) probed by magnetic circular x-ray dichroism

The effects of nanostructured magnetic ${\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35}$ films deposited on a vicinal Cu(111) single-crystal surface on the magnetic anisotropy have been studied using magnetic circular x-ray dichroism (MCXD) at the Fe ${L}_{2,3}$ edges. In the one-dimensional (1D) limit a large dipolar out-of-plane anisotropy is evidenced with in-plane isotropic magnetic moments. After the 1D coalescence the orbital moment shows a more complex behavior depending on the in-plane direction of saturation. We show that MCXD is strongly sensitive to in-plane orbital anisotropy for the 1D stripes. We demonstrate the importance of the step induced in-plane anisotropy by measuring the orbital magnetic moment dependence as a function of the in-plane azimuth angle. In the submonolayer regime an in-plane magnetic anisotropy is observed related to the step decoration growth mode. In the thickness range of 2--4 equivalent monolayers, 2D coalescence induces a strong in-plane magnetic anisotropy of the magnetic orbital moment. The microscopic origin of the strong in-plane variation of ${M}_{L}$ has been attributed to magnetocrystalline effects. Strained films give rise to an in-plane magnetic anisotropy energy up to 2 meV/at., which is larger than those measured out of the plane (0--1 meV/at.).

Spin-orbit coupling in the Mott insulator Ca(2)RuO(4).

O 1s x-ray absorption study of the Mott insulator Ca(2)RuO(4) shows that the orbital population of the 4d t(2g) band dramatically changes with temperature. In addition, spin-resolved circularly polarized photoemission study of Ca(2)RuO(4) shows that a substantial orbital angular momentum is induced in the Ru 4d t(2g) band. Based on the experimental results and model Hartree-Fock calculations, we argue that the cooperation between the strong spin-orbit coupling in the Ru 4d t(2g) band and the small distortion of the RuO(6) octahedra causes the interesting changeover of the spin and orbital anisotropy as a function of temperature.

In-plane orbital moment anisotropy in fcc Fe 0.65Ni 0.35 ultrathin films grown on stepped Cu(1 1 1) surfaces

Fe 0.65Ni 0.35 ultrathin films 3.5 monolayer thick have been grown on a vicinal Cu(1 1 1) surface in order to correlate the in-plane step-induced magnetic anisotropy deduced from X-ray magnetic circular dichroism (XMCD) to the crystal structure and morphology of the films obtained by scanning tunneling microscopy and surface extended X-ray absorption spectroscopy. Magnetic moments are derived by applying the well-known sum rules to XMCD data and their anisotropies are determined by measurements obtained through various geometric conditions implying different polar and azimuth angles. The results for 3.5 ML alloy films show that the orbital moment M L depends strongly on the azimuth angles while the effective spin moment M eff S is found nearly isotropic. We explain the strong in-plane orbital moment anisotropy in the light of the structural in-plane strains induced by the steps, the growth mode and the lattice parameter relaxation in this thickness range.