Study on Momentum Density and Fermi Surface in Paramagnetic Cr and W by Positron Annihilation

Abstract

The three-dimensional electron-positron momentum densities in paramagnetic Cr and W are reconstructed from measurements of two-dimensional angular correlation of positron annihilation radiations (2D-ACAR) by the image reconstruction technique based on a direct Fourier transformation. The experimental momentum density for paramagnetic Cr and W shows the contribution of the Fermi surface sheets; the electron surface at r, the hole surface at H, the hole surface at N. The Fermi surface topology obtained from the present results agrees with the theory and other experiments.La trois demensionne electron-positron impulsion densite de paramagnetetique Cr et W a ete reconstruit de mesures de deux dimensionne angulaire correlation de position aneantissement radiations (2D-ACAR) par la image reconstruction technique base sur une directe Fourier transformation. L'experimentateur impulsion densite pour paramagkntique Cr et W montre la contribution de la Fermi surface feuille; la electron feuille a r, la trou feulle a H, la trou feuille a N. La Ferme surface topologie, qui a ete obteni des present resultats, consentissent a la theorie et autre experiences.

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

“…Compared with the experimental densities, for Cu, where there is a significant Kahana-like enhancement [31], only the LDA(E) (or WDA(E)) and BML theories satisfactorily describe the experimental densities (the same occurs for simple metals). In Cr, a typical transition metal, where there is no Kahana-like enhancement [32] (a similar situation takes place in Y [23]) the B-N, GGA and BML theories (even the IPM) are in good agreement with the experimental 3D densities. Such a similarity between the BML and the momentum (or the energy) independent B-N and GGA theories is connected with the fact that the higher the lattice effects, the weaker the Kahana-like momentum dependence of the BML enhancement [5].…”

“…To answer this question we would like to note figure 1 in [24] where e-p densities ρ( p) for Cu, Cr and Y, are calculated within four essentially different e-p interaction approaches, LDA(E)-state-dependent LDA [25], whose results are qualitatively similar to the WDA(E) approach [26], B-N-state-independent LDA [20], GGA [27][28][29] and Bloch modified ladder (BML) theory [30], were confronted with three-dimensional (3D) densities reconstructed from 2D ACAR experimental data [31][32][33]. For all these metals the B-N and GGA theories give similar results.…”

Probing the Fermi surface by positron annihilation and Compton scattering

“…The first positron annihilation experiment to show a difference between data measured in the PM and AFM phases was that of Singh, Manuel, and Walker. 54 The first three-dimensional reconstruction of the momentum density and Fermi surface in Cr was by Kubota et al, 55 followed a few years later by Fretwell et al who emphasized the advantages for deconvoluting the measured spectra prior to reconstruction. 56,57 One of the particularly perplexing issues was that the comparison of the experimental Cr spectra with theory, for both the positron annihilation measurements 58 and later Compton scattering, 59,60 was always substantially less favorable than the comparison between measurement and theory in Sec.…”

Fermiology via the electron momentum distribution (Review Article)

“…Such a procedure, called Fourier-Bessel (F-B) method, was applied to reconstruct 2D densities from 2D ACAR data [56] and 3D densities from 1D Compton profiles [57][58][59][60]. However, because calculations of Bessel functions of a higher order make some difficulties, lately the direct FT (instead of F-B) algorithm [61,62] has been used to both 2D ACAR [63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82] and 1D Compton profiles, reconstructing either fully 3D densities [83][84][85][86][87][88][89] or 2D ones [90][91][92][93][94][95][96]. Such techniques involving both fast FT algorithm and different ways of interpolations (instead of angular interpolation as used by us in MFBP) were elaborated by many authors, e.g.…”

“…Al FS on (100) and (110) planes [68] Al hole surface around Γ, electron surfaces along lines WUW and WKW. No gap between electron surfaces at W interpreted as effect of the experimental resolution [80] Mg quantitative information on distortion of FS from sphericity [23] Cd lack of the 3 rd & 4 th zone electrons around L; reduction of hole monster to 6 separate hole surfaces nearby K [23] Cu FS on (100) and ( 110) planes [49, 71, 82] Cr in 323 K & 30 K small differences at R & Γ points and along Λ & Σ lines in paramagnetic & antiferromagnetic states [75] Cr (323 K), Mo & W (30 K)Γ-centered electron surface and hole surfaces at H and Nthe later only in Mo and Cr[67,77] V, Nb & Ta Γ-centered hole octahedron, multiplay connected jungle-gym arms and N-centered hole ellipsoids[76]…”