Diploma - Max Planck Institute for Solid State Research

More documents

Recommendations

Info

$diffraction from single powder grains - Max Planck Institute for Solid ...$

38 4 EuRh 2 Si 2 – semi-localized electrons Figure 4.11: a superposition of bulk and surface states as expected for different surface terminations; the k z -projected bulk band structure is depicted in shades of maroon (small k z -dispersion: dark maroon; large k z − dispersion: light maroon) overlayed by the bulk (grey lines) and surface states (coloured points) of the respective slab calculation; in (a) the Si terminated and in (b) the Eu terminated surface is depicted; for comparison some SS and SB are labelled, whereat in the case of the latter the dashed lines point to bulk and the continous lines to corresponding surface features; 1a/b in (a) mark the star-like surface state (cf. fig.4.10), 2 marks the conical SB around the Γ [in (a) as well as in (b)]
4.1 Overview – properties and classification 39 (a) FS: 33 (b) FS: 34 (c) FS: 35 Figure 4.12: Fermi sheets (FS) of EuRh 2 Si 2 ; outer face is depicted in red, the inner face in blue. They are probably not comparable to the “true” bulk Fermi sheets, if the 4f are in the range of the Fermi level. The numbering of the eigenvalues (sorted) is arbitrary originated in the distinction between valence and core orbitals (fplo 9.07.41, LDA, 4f 7 unpolarized open core). the calculated 4 projected bulk band structure (red). The border of the BZ is marked by white-dashed lines. Regarding the bulk Fermi surface (cf. fig. 4.12), one recognizes that the isosurface projected along the [001] direction consists mainly of Fermi sheet 34 and 35 representing the connected square-like structure around Γ with a gap at the M-point. Apparently, the intensities of the experimental bulk emuissions seem to be inverse to the calculated ones for the first BZ, but similar to the calculation in the second BZ. This points to selection rules (best seen at the BZ border in the measurement), which probably can be simulated by means of a sophisticated PE model. As already mentioned before, inside the bulk band gap around the M-point resides an electron-like SS at the Si terminated surface. In the measurement, there seem to be two nested states, whereas the calculation reproduces only one. But regarding the structures labelled 1a and 1b in fig. 4.11 one recognices that the second surface state (1b) is above the Fermi level in the calculation, hence it does not (severely) contribute to the shown isoenergy surface. The deviation can probably be explained by a surface relaxation, because the distances of the topmost layers are usually smaller than the corresponding bulk intervals (cf. fig. 4.6). Moreover, there is a lobe-like SB oriented from the Γ-point towards the M-point at Si terminated surfaces which motivates the observed intensityvariation around Γ in the first BZ. The nodal point of the surface state 2 in fig. 4.11 is above the Fermi level for Si termination (a), but below for Eu termination (b), which is in good agreement with the measurement depicted in fig. 4.8 despite of that the calculated SS seems to be weaker at Eu terminated surfaces. This has a more technical than physical reason since fixing the 4f occupation and treating these orbitals as open core, one reduces the freedom to generate an asymmetry in charge density at the surface. For 4 The projection onto the surface BZ has been obtained by a superposition of isosurfaces perpendicular to the z-axis of the BZ. A Gaussian was used for energy broadening, which has been chosen around 15 meV being in the order of magnitude of the integration interval chosen for the measured spectrum. The two major Fermi sheets which contribute to the projected bulk band structure, are depicted in fig. 4.12, FS 34 and FS 35.
Page 1 and 2: - Photoemission on EuRh 2 Si 2 - di
Page 3: Abstract A thorough knowledge of co
Page 7: vii Nomenclature AF APW ARPES BO BZ
Page 10 and 11: 2 1 Introduction conflicting limits
Page 12 and 13: 4 2 Theoretical foundation fore the
Page 14 and 15: 6 2 Theoretical foundation system a
Page 16 and 17: 8 2 Theoretical foundation such a s
Page 18 and 19: 10 2 Theoretical foundation Figure
Page 20 and 21: 12 2 Theoretical foundation Figure
Page 22 and 23: 14 2 Theoretical foundation Fi
Page 25 and 26: 17 3 Experimental foundations 3.1 P
Page 27 and 28: 3.2 General setup 19 Figure 3.2: ch
Page 29 and 30: 3.4 SLS: SIS-HRPES 21 1 3 ARPES the
Page 31 and 32: 23 4 EuRh 2 Si 2 - semi-localized e
Page 33 and 34: 4.1 Overview - properties and class
Page 45: 4.1 Overview - properties and class
Page 49 and 50: 4.2 Hybridization: localized versus
Page 61 and 62: 4.3 Perspective: quasi-linear dispe
Page 63: 4.3 Perspective: quasi-linear dispe
Page 66 and 67: 58 5 Summary to the f-d interaction
Page 68 and 69: 60 Bibliography [13] B. Kramer. A P
Page 70 and 71: 62 Bibliography [44] T. M. Rice and
Page 72 and 73: 64 Bibliography [75] Hari C. Manoha
Page 75: List of Tables 67 List of Tables 2.
Page 79: Erklärung Hiermit versichere ich,

Diploma - Max Planck Institute for Solid State Research

Create successful ePaper yourself

Delete template?

Save as template?