Three-dimensional electron momentum density (EMD) distribution (ρ^3D) for valence electrons in hexagonal Mg was reconstructed by the maximum entropy method (MEM) using four one-dimensional experimental projections of the ρ^3D, the so-called Compton profiles (CP’s). The high-resolution (0.12 a.u.) CP’s were measured with the use of synchrotron radiation at SPring-8 (station BL08W) [1]. Before being used in reconstructions, the experimental profiles were deconvoluted with experimental resolution function by the MEM method.

The two-step MEM reconstruction procedure was applied. First, deconvoluted one-dimensional EMD distribution (ρ^1D) was reconstructed in the isotropic approximation using averaged experimental Compton profile and the Schülke model of the EMD in the correlated electron gas [2] as a prior (initial information). The result of this reconstruction was then interpolated into 3D momentum space and was used as a prior in ρ^3D reconstruction together with four deconvoluted experimental CP’s.

The two-dimensional EMD distributions in the hexagonal plane (ρ^2D) were also calculated as a line integral of the ρ^3D along the Z (ΓA) axis. In order to observe the electron occupancy (in k space), Lock-Crisp-West (LCW) folding procedure [3] into the first Brillouin zone was then applied. The results (ρ^2D-LCW) were compared with the MEM reconstruction based on the five theoretical CP’s (Korringa-Kohn-Rostoker method [4, 5]) and adequate reconstruction results using Cormack’s method [6, 7] (Fig. 1). The both methods were compared with the calculations based on the free electron model.

The advantage of MEM in the EMD reconstruction with insufficient experimental information was affirmed despite of the low quality of the reconstructed ρ^3D. The reconstruction results, based on the experimental Mg profiles, showed that we are able to observe even small distortions of the Fermi surface in the regions of Brillouin zone boundaries. There are subtle but clear differences between the results obtained by the maximum entropy and the Cormack’s methods in the observed electron occupancy.

Figure 1 The ρ^2D-LCW densities reconstructed by the Cormack method (a, d) and MEM (b, c). (a, b) panels show the reconstruction results based on the experimental CP’s and (c, d) panels show the results based on the theoretical (KKR) CP’s. The locations of the special high-symmetry points projected to a MГK plane are marked on (b).

References

[1] Y. Sakurai, M. Itou, J. Phys. Chem. Solids 65 (2004) 2061.
[2] W. Schülke, G. Stutz, F. Wohlert, A. Kaprolat, Phys. Rev. B 54 (1996) 14381.
[3] D.G. Lock, V.H.C. Crisp, N.R. West, J. Phys. F: Met. Phys. 3 (1972) 561.
[4] J. Korringa, Physica 13 (1947) 392.
[5] W. Kohn, N. Rostoker, Phys. Rev. 94 (1954) 1111.
[6] A.M. Cormack, J. Appl. Phys. 34 (1963) 2722, 35 (1964) 2908.
[7] G. Kontrym-Sznajd, M. Samsel-Czekała, M. Pylak, L. Dobrzyński, M. Brancewicz, A. Andrejczuk, E. Żukowski, S. Kaprzyk, Phys. Stat. Sol. B 248, 3 (2011) 719.

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/24582 must be provided.

1. The influence of the substitution material on the ferrite nanoparticles prepared by chemical method - Mössbauer studies
2. Structure modifications in materials irradiated by ultra-short pulses of VUV free electron laser