2D ACAR Research Articles

Electron–positron momentum density distribution of Gd from 2D ACAR data via Maximum Entropy and Cormack’s methods

A successful application of the Maximum Entropy Method (MEM) to the reconstruction of electron–positron momentum density distribution in gadolinium out of the experimental of 2D ACAR data is presented. Formally, the algorithm used was prepared for two-dimensional reconstructions from line integrals. For the first time the results of MEM, applied to such data, are compared in detail with the ones obtained by means of Cormack’s method. It is also shown how the experimental uncertainties may influence the results of the latter analysis. Preliminary calculations, using WIEN2k code, of band structure and Fermi surface have been done as well.

Reconstruction of Momentum Density Distribution from 2D ACAR Data via Maximum Entropy and Cormack Methods

Novel application of Maximum Entropy method to the reconstruction of electron momentum density distribution from line projections is presented. Our new algorithm is applied to two dimensional angular correlation of annihilation radiation data in Gd. Reconstructed densities are in very good agreement with corresponding densities reconstructed by Cormack’s method.

Optimization of three-dimensional positron annihilation spectroscopy system (3DPASS) for three-dimensional momentum measurements

A three-dimensional positron annihilation spectroscopy system (3DPASS) was characterized. 3DPASS permits determination of three-dimensional electron–positron ( e −– e + ) momentum distributions by simultaneously measuring angles and energies for coincident two-gamma annihilation photons. 3DPASS collects a single dataset of correlated energies and positions for two coincident annihilation photons from a pair of solid-state double-sided strip detectors (DSSDs). Subpixel-interpolated positions are determined by transient charge analysis. 3DPASS performs simultaneous two-dimensional angular correlation of annihilation radiation (2D ACAR) and two-detector coincidence Doppler-broadening of annihilation radiation (CDBAR) measurements, which are typically collected independently. The 2D ACAR response of 3DPASS was measured for single-crystal Cu and 6H-SiC, with and without compensation for subpixel detection efficiency. Variation of efficiency across the width of DSSD charge collection electrodes was dominated by the event selection criteria required by the subpixel interpolation method. The DBAR resolution was optimized by adjusting the energy range of CDBAR events included in the Doppler-broadening (DB) lineshape. 2D ACAR and DBAR spectra from 3DPASS were compared to previously published results for single-crystal Cu and 6H-SiC. Detailed analysis of the ACAR spectra and the DB lineshapes highlighted momentum features not previously reported.

Simultaneous, coincident 2-D ACAR and DBAR using segmented HPGe detectors incorporating sub-pixel interpolation

A three-dimensional Positron Annihilation Spectrometry System (3D PASS) for determination of 3D electron-positron (e--e+) momentum densities by measuring coincident annihilation photons was designed, constructed and characterized. 3D PASS collects a single data set including correlated photon energies and coincident photon positions which are typically collected separately by two-dimensional angular correlation of annihilation radiation (2D ACAR) and two-detector coincident Doppler broadening of annihilation radiation (CDBAR) spectrometry. 3D PASS is composed of two position-sensitive, high-purity germanium (HPGe) double-sided strip detectors (DSSD(s)) linked together by a 32-channel, 50 MHz digital electronics suite. The DSSDs data were analyzed to determine location of photon detection events using an interpolation method to achieve a spatial resolution less than the 5-mm width of the DSSDs' charge collection strips. The interpolation method relies on measuring a figure-of-merit proportional to the area of the transient charges observed on both strips directly adjacent to the charge collection strip detecting the full charge deposited by the annihilation photon. This sub-pixel resolution, corresponding to the error associated with event location within a sub-pixel was measured for both DSSDs using the approach outlined in Williams et al [1] and was on the order of ± 0.20 mm (± one-standard deviation). As a result of the sub-pixel resolution, the distance between the DSSDs and material sample was reduced by a factor of five compared to what is typically required in 2D ACAR systems was necessary to achieve 0.5-mrad angular resolution. This reduction in the system's footprint decreases attenuation of the annihilation photons in the air between the material sample and the DSSDs and increases the solid angle between the sample and the DSSDs, ultimately resulting in higher system detection efficiency. 3D PASS was characterized in the same manner comparable to state-of-the-art 2D ACAR and CDBAR spectrometers. 3D PASS spectra were collected and analyzed for single-crystal copper (Cu) and silicon carbide (6H SiC) and compared with the results in the literature.

Toward Simultaneous 2D ACAR and 2D DBAR: Sub-Pixel Spatial Characterization of a Segmented HPGe Detector Using Transient Charges

Sub-pixel spatial characterization of an Ortec HPGe double-sided strip detector was measured in preparation for its planned use in a positron annihilation spectrometer (PAS) to simultaneously measure the two-dimensional Angular Correlation (2D ACAR) and Doppler Broadening (2D DBAR) of Annihilation Radiation. Sr-85 514-keV photons were finely collimated onto the center of 25, equally spaced sub-pixels within a single 5-mm by 5-mm intrinsic pixel, using a collimator with an aperture diameter of 0.15 ± 0.05 mm. The location of each full-energy recorded event was determined by analyzing the relative sizes of coincident transient charges on charge collection strips adjacent to the strip recording full-energy events. Interpolation, using ratios of the coincident transient charge sizes, was used to determine two-dimensional locations of full-energy events. Radial location data was fit to a function which describes a Gaussian point spread function uniformly distributed over a circular aperture. The standard deviation of the point spread function, 0.22 mm, is a measure of the spatial resolution of this detector system. The relative efficiency for detection of 514-keV photons across the intrinsic pixel was also measured.

Many body effects seen in the positron annihilation experiment

AbstractThe electron‐positron (e‐p) momentum density in p‐space for copper, magnesium, cadmium and yttrium, calculated by using various theoretical approaches, are compared with corresponding densities reconstructed from two‐dimensional angular correlation of annihilation radiation (2D ACAR) experimental spectra. We demonstrate that (at least for positrons in metals) strong electron‐electron (e‐e) correlations are clearly visible not only in the Compton scattering but also in positron annihilation experiments. Moreover, a proper description of e‐p correlations needs to include the lattice‐periodical crystal potential. In case of strong lattice effects, the increase of the e‐p enhancement with increasing momentum ‐ the so‐called Kahana‐like enhancement, is vanishing. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electronic structure of rare‐earth compounds TmGa3, ErGa3, and CeIn3 studied by positrons

AbstractThe electronic structure of the isostructural rare‐earth systems TmGa3, ErGa3, and CeIn3 has recently been investigated by measurements of two‐dimensional angular correlations of annihilation radiation (2D ACAR). We employ different tomography techniques to reconstruct electron‐positron (e‐p) momentum density ρ (p) from its line projections. In all these compounds we get very specific shape of ρ (p). In order to draw the Fermi surface (FS), we perform conversion from the extended p to reduced k space. In the case of TmGa3 and ErGa3 a nesting feature of the FS consistent with the antiferromagnetic structure is observed. On the other hand, in CeIn3 we cannot detect any link between the FS topology and the vector of the magnetic propagation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of experimental noise on densities reconstructed from line projections

AbstractThe influence of experimental noise on densities ρ(p) reconstructed by the Cormack method from their line projections, e.g. 2D ACAR spectra, is investigated. Simulations of statistical noise are performed for various sets of 2D spectra for two model ρ(p) having the cubic symmetry. For the reconstructed densities propagation of the statistical error in terms of standard deviations, σ[ρ(p)], is estimated. We observe that the distribution of σ[ρ(p)] has its extremes along the main symmetry directions and also a tendency to accumulate for small p. Moreover, the more density components, ρn(p), have to be taken to description of ρ(p) the less anisotropic is the distribution of σ[ρ(p)]. Additionally, the error generated by the reconstruction method itself is discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Self-Energy Correction to Momentum-Density Distribution of Positron-Electron Pairs

Positron two-dimensional angular correlation of annihilation radiation (2D ACAR), i.e., the 2D projection of the electron momentum densities sampled by positron, in Si is employed to verify the prediction of the density functional theory within the local-density approximation (LDA). Carefully conducted test shows that the LDA introduces small but definite discrepancies to the 2D-ACAR anisotropies. Self-energy calculation using the GW method indicates that density-fluctuation contributes anisotropic momentum-density correction and thus improves the agreement between theory and experiment. These results provide valuable annotations to the arguments concerning the accuracy and validity of the LDA and GW schemes.

Band structure ofLaB6by an algorithm for filtering reconstructed electron-positron momentum densities

A new method (NM) for filtering three-dimensional reconstructed densities is proposed. The algorithm is tested with simulated spectra and employed to study the electronic structure of the rare-earth compound LaB6. For this system, momentum densities are reconstructed from theoretical and experimental two-dimensional angular correlation of electron-positron annihilation radiation (2D ACAR) spectra. The experimental results are in good agreement with the band structure calculated with the full-potential linearized augmented-plane-wave (FLAPW) method within the local-density approximation (LDA), apart from the detection of small electron pockets in the 15th band. It is also shown that, unlike the electron-positron enhancement, the electron-electron correlations affect noticeably the momentum density.

Fermi surface nesting and magnetic structure ofErGa3

A three dimensional mapping of the Fermi Surface (FS) of the rare-earth compound ErGa3 was determined via measurements of the angular correlation of the electron-positron annihilation radiation. The topology of the electronlike FS does show nesting properties which are consistent with the modulated antiferromagnetic structure of the system. We determine the density of states at the Fermi energy N(EF) and the electronic contribution to the gamma constant to be N(EF)=16 states/Ryd/cell and gamma=2.7 (mJ/mole K^2), respectively. Densities rho(k) of ErGa3 and TmGa3 in the kz=0 and kz=pi/a plane of the Brillouin zone reconstructed from 2D ACAR data. The arrow highlights the nesting feature attributed to TmGa3 and ErGa3 (left and right sides, respectivelty).

Positron annihilation study of the electronic structure of CeCu6 and LaCu6

The results of a prelimianry study of the electronic structure of the heavy-fermion system CeCu6 via the two-dimensional angular correlation of electron-positron annihilation radiation (2D ACAR) technique were compared with those obtained for the isostructural reference non-f-electron material LaCu6. The spectra relating to the 2 compounds displayed extremely similar anisotropic structures, with features related to the symmetry of the Brillouin zone. At present, these structures cannot however be attributed to Fermi-surface or positron wave function effects or to anisotropies of some full valence band. In the case of LaCu6, data processing prior to the LCW procedure via new filtering techniques revealed a reasonably good agreement between the LCW data and LAPW Fermi-surface calculations while in the case of CeCu6 it appeared difficult to relate the results, still of controversial interpretation, to any theoretical model.

Positron annihilation study of the electronic structure of CeB 6, CeCu 6 and LaCu 6

The two-dimensional angular correlation of electron-positron annihilation eradiation (2D-ACAR) from the heavy-fermion dense Kondo system CeB 6 was measured. The use of a recently developed filter procedure, designed to remove characteristic positron-induced long range distortions that are frequently superimposed on the Fermi breaks, provided a good description of the Fermi surface features. Further, the results of a preliminary 2D ACAR study of the electronic structure of the heavy-fermion system CeCu 6 are shown and compared with those obtained for the reference non-f-electron material LaCu 6.

The enhancement of Fermi-surface images in positron ACAR spectra

This paper describes a frequency-limited derivative technique that has dramatically increased our ability to resolve Fermi-surface discontinuities in our 2D ACAR spectra. The performance of the technique, which involves minimal CPU time, is demonstrated with example applications to both simulated and real 2D ACAR spectra.

Positron Annihilation Study of the Electronic Structure of CeCu<sub>6</sub> and LaCu<sub>6</sub>

The results of a prelimianry study of the electronic structure of the heavy-fermion system CeCu6 via the two-dimensional angular correlation of electron-positron annihilation radiation (2D ACAR) technique were compared with those obtained for the isostructural reference non-f-electron material LaCu6. The spectra relating to the 2 compounds displayed extremely similar anisotropic structures, with features related to the symmetry of the Brillouin zone. At present, these structures cannot however be attributed to Fermi-surface or positron wave function effects or to anisotropies of some full valence band. In the case of LaCu6, data processing prior to the LCW procedure via new filtering techniques revealed a reasonably good agreement between the LCW data and LAPW Fermi-surface calculations while in the case of CeCu6 it appeared difficult to relate the results, still of controversial interpretation, to any theoretical model.

A positron-annihilation study of the electronic structure of CeB6

The two-dimensional angular correlation of electron-positron annihilation radiation (2D ACAR) from the heavy-fermion dense Kondo system CeB6 was measured. The anisotropies of the measured momentum spectra were in reasonable agreement with those of model spectra based on the Fermi-surface topology suggested by band-structure calculations and de Haas-van Alphen measurements. However, the related k-space densities, obtained by an LCW analysis, were far removed from those expected from the Fermi-surface topology. The use of a recently developed filter procedure, designed to remove the characteristic long-range distortions that are frequently encountered in such LCW spectra, provided a much improved image of the Fermi-surface features.

Spin-Polarized 2D ACAR in Nickel Across the Curie Temperature

We present two-dimensional angular correlation of (polarized positrons) annihil- ation radiation (20 ACAR) results measured on a single crystal of Ni in the (100) plane below andabove the Curie temperature (at4.2,300, M10and640 K).The rxperimentaldistributions (total momentum density) measured at different temperatures do not exhibit any significant differences, in contradiction to the one-dimensional (non-spin-polarized) results of Kon- trym-Smajd et al. We conclude that the Fermi surface topology of Ni essentially does not change between 4.2 and 600 K. This can be related to the fact that the exchange splitting. A. remainsalmostmnstant up to thecurie temperature. This wouldconfirm thespin-polarized electron-energy-loss spectroscopy results of Kinchner and Langenbach.

Spin-polarized 2D ACAR in nickel across the Curie temperature

The authors present two-dimensional angular correlation of (polarized positrons) annihilation radiation (2D ACAR) results measured on a single crystal of Ni in the (100) plane below and above the Curie temperature (at 4.2, 300, 600 and 660 K). The experimental distributions (total momentum density) measured at different temperatures do not exhibit any significant differences, in contradiction to the one-dimensional (non-spin-polarized) results of Kontrym-Sznajd et al. They conclude that the Fermi surface topology of Ni essentially does not change between 4.2 and 600 K. This can be related to the fact that the exchange splitting Delta , remains almost constant up to the Curie temperature. This would confirm the spin-polarized electron-energy-loss spectroscopy results of Kirschner and Langenbach.

Positron-electron product wavefunction calculation of angular correlation in silicon

Using a novel formalism in which the positron-electron product (PEP) wavefunction is obtained directly from a Schrödinger like wave equation, we have calculated the two dimensional angular correlation of 2γ annihilation radiation (2D ACAR) of electron-positron states in silicon. We are able to remove two significant discrepancies between earlier theoretical calculations and experimental data and our new results are in good general agreement with presently available experiments.

Positron annihilation in high critical temperature superconductors

Two dimensional angular correlation of electron-positron annihilation radiation (2D ACAR) experiments are discussed in terms of calculated positron wavefunctions and ACAR spectra for high critical temperature superconductors. It is emphasized that positron wavefunction effects are larger in these materials than, for example, the previous class of A15 superconductors. Calculations indicate that the chain derived ridge section and the S centered hole pocket may be observable in YBa 2Cu 3O 7, in agreement with recent experiments. The plane derived Fermi surfaces are expected to be extremely difficult to observe in this material. On the other hand, calculations show that positrons are a good probe of the Cu-O layers in Tl 2CaCu 2O 2.