G. Kontrym-Sznajd

Observation of a Strongly Nested Fermi Surface in the Shape-Memory Alloy Ni 0.62 Al 0.38

The Fermi surface topology of the shape-memory alloy Ni0.62Al0.38 has been determined using Compton scattering. A large area of this Fermi surface can be made to nest with other areas by translation through a vector of approximately 0.18[1,1,0](2pi/a), which corresponds to the wave vector associated with martensitic precursor phenomena such as phonon softening and diffuse streaking in electron diffraction patterns. This observation is compelling evidence that these phenomena are driven by the enhanced electron-lattice coupling due to the Fermi surface nesting.

Special directions in the Brillouin zone

Abstract.Rules are given for determining special directions in the Brillouin zone which optimize the description of various physical quantities with Γ1-type symmetry. We consider the cubic, hexagonal, tetragonal and trigonal (e.g. Bi) lattice. These rules allow us to construct, in all of momentum space, quantities which have the full symmetry of the Brillouin zone such as the Fermi surface, momentum density and others, from the knowledge of these quantities for a limited number of special directions. These results can also be used for determining the projections which should be measured either in Compton scattering or in positron-annihilation experiments in order to reconstruct properly the electron-momentum density. Such a treatment is approximately equivalent to applying Gaussian quadrature in calculations of the radial functions that occur in the expansion of data into lattice harmonics.

Band structure of LaB6 by an algorithm for filtering reconstructed electron-positron momentum densities

A new method 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 LaB{sub 6}. 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 of Mg and Cd

We present three-dimensional (3D) electron-positron momentum densities in Mg and Cd, reconstructed from 2D angular correlation of annihilation radiation data. By folding densities from the extended momentum space into the first Brillouin zone, we separated Fermi surfaces in various bands. Our results are in good agreement with band structure LMTO calculations. In order to examine how many 1D profiles give us a possibility to reproduce the same details of the Fermi surfaces and Umklapp components of electron densities, various sets of 1D spectra were created for special directions in the Brillouin zone. Finally, corresponding 3D densities were reconstructed to show how many details one can get depending on the number of 1D profiles.

Different ways of dealing with Compton scattering and positron annihilation experimental data

AbstractDifferent ways of dealing with one-dimensional (1D) spectra, measured e.g., in the Compton scattering or angular correlation of positron annihilation radiation (ACAR) experiments, are presented. Using the example of divalent hexagonal close packed metals, we show what kind of information on the electronic structure one can get from 1D profiles interpreted in terms of either 2D or 3D momentum densities.2D and 3D densities are reconstructed from merely two and seven 1D profiles, respectively. Applied reconstruction techniques are particular solutions of the Radon transform in terms of orthogonal Gegenabauer polynomials. We propose their modification connected with so-called two-step reconstruction.The analysis is performed both in the extended p and reduced k zone schemes. It is demonstrated that if the positron wave function or many-body effects are strongly momentum dependent, analysis of 2D densities folded into k space may lead to wrong conclusions concerning the Fermi surface. In the case of 2D ACAR data in Mg, we found very strong many-body effects.

Fermi surface of ErGa3

We discuss an efficiency of various band structure algorithms in determining the Fermi surface (FS) of the paramagnetic ErGa3. The linear muffin-tin orbital (LMTO) in the atomic sphere approximation (ASA) method and three full potential (FP) codes: FP-LMTO, FP linear augmented plane wave (FLAPW), and FP local orbitals (FPLO) methods are employed. Results are compared with electron-positron (e-p) momentum densities reconstructed from two dimensional angular correlation of annihilation radiation (2D ACAR). Unexpectedly, none of used modern FP codes is able to give satisfying description of the experimental data that are in perfect agreement with LMTO-ASA results. We suspect that it can be connected with a different choice of the linearization energy.

The influence of a positron on electron–positron momentum densities in metallic materials

General properties of the electron?positron (e?p) momentum densities were investigated in the extended momentum space (Kontrym-Sznajd et al 2012 Phys. Rev. B 85 245104). In this paper, a small selection of numerical tests of our theory is presented for the independent particle model in the simple and the transition metals. It is confirmed that the intensity of the Umklapp components of the electron densities is generally reduced by a positron. Nevertheless, some of them may be enlarged, provided the fulfilment of certain conditions which are discussed in detail. On the example of yttrium it is also demonstrated how the positron influences the electron momentum densities in the reduced zone. Our considerations are given for both the independent particle model and after including the e?p correlations within the local density approach.

How to estimate isotropic distributions and mean values in crystalline solids.

The concept of special directions in the Brillouin zone and the applicability of Houstons formula (or its extended versions) to both theoretical and experimental investigations are discussed. We propose some expressions to describe the isotropic component in systems having both cubic and non-cubic symmetry. The results presented have implications for both experimentalists who want to obtain average properties from a small number of measurements on single crystals, and for theoretical calculations which are to be compared with isotropic experimental measurements, for example coming from investigations of polycrystalline or powder samples. As George Orwell might have put it: all directions are equal, but some directions are more equal than others.

Isotropic distributions in hcp crystals

Abstract Some anisotropic quantities in crystalline solids can be determined from their knowledge along a limited number of sampling directions. The importance of the choice of such directions is illustrated on the example of estimating, from angular correlation of annihilation radiation data, the isotropic electron momentum density in Gd.

Electronic Structure via 1D Electron Momentum Densities

We demonstrate what kind of information about the electronic structure one can get from plane projections of electron densities. As an example we use one dimensional (1D) angular correlation of annihilation radiation (ACAR) and Compton scattering spectra for Cd “measured” only for two crystal orientations. Spectra are interpreted in terms of reconstructed 2D densities both in the reduced and extended zone schemes.