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26 2. Theoretical background I. Photoemission cross-sections Due to the large energy difference between exciting X- rays and the binding energy of the initial state electrons in the solid, in particular for valence band photoemission, the photoionization cross-section σ for hard X-ray excitation is small. For an individual orbital (nlj), it is continuously reduced as ⎧ ⎪⎨ (E σ nlj (hν) ∝ kin ) −7 /2 , for s subshells, and ⎪⎩ (E kin ) −9 /2 , for p, d, and f subshells. 100 (2.25) The significant decrease of atomic cross-sections for hard X-ray photoelectron excitation is shown in Fig. 2.15 (inset). intensity (a.u.) → 15 Au valence band 10 5 0 soft x-rays (LDA) HAXPES (hν=5950 eV) E F 5938 5940 5942 5944 5946 5948 5950 kinetic energy (eV) Figure 2.15.: Photoemission cross-sections for hard X-ray excitation. Au valence levels in HAX- PES deviate significantly from soft X-ray photoemission. 85 The inset exemplifies the drop of photoemission crosssection with excitation energy for Al. 101 II. Forward scattering and Debye-Waller factors for photoemission Only unscattered or coherently elastically scattered photoelectrons contribute to an analyzable spectrum. Elastic scattering events can deflect the photoelectrons which are emitted in direction of the surface normal away from that direction. For high excitation energies (hν = 5–15 keV), Thompson and Fadley (1984) have shown 102 that the forward scattering (i. e. within 90 ◦ in direction of the original emission direction) becomes significantly narrower for photoemission from surface layers (Fig. 2.16). This reduces the directional anisotropy of the photoelectrons which is advantageous for angular-resolved PES. Moreover, the narrow emission plume of photoelectrons can be better approximated by a simple expression for the electron’s effective attenuation length, and thus allows one to predict information depths of a HAXPES experiment more accurately. 86 The photoemission process inside a solid can be thought of as a scattering process of the photoexcited ion inside the crystal. 80 Thus, the photoelectrons reflect the effect of the lattice vibrations of the crystal in a way similar to that in X-ray diffraction or neutron scattering, which is described by the Debye-Waller factor. The Debye-Waller factors for photoemission intensities are strongly dependent on temperature and on the excitation energy: an increase of temperature leads to a decreased intensity of coherently scattered photoelectrons. A calculated example is shown in Fig. 2.17, from which we clearly see that low sample temperatures are advantageous, and for larger X-ray excitation energies the Debye-Waller factor significantly drops. In practice, at a fixed excitation energy, the cooling of the sample will significantly increase the analyzable intensity (i. e. unscattered or coherently scattered photoelectrons). The effective attenuation length, λ ∗ , is introduced by eq. (2.26) on page 28.
2.4. Hard X-ray photoemission spectroscopy 27 hν = 1000 eV FWHM = 20° hν = 10 000 eV FWHM = 8° Figure 2.16.: Comparison of the intensity profiles of elastic photoelectron forward diffraction. The intensity plumes are drawn as expected for C 1s photoemission at hν = 1 keV or hν = 10 keV from a vertical CO molecule on the surface. Adapted from Thompson and Fadley (1984). 102 surface surface molecule Figure 2.17.: Calculated Debye-Waller factors for valence-level 250 300 Debye-Waller PES from factor W surface photoemission. The values are strongly dependent on the photoelectron kinetic energy. At 200 150 high kinetic energy, cooling well below room temperature 100 reveals significantly larger Debye-Waller 50 factors. Adapted from Plucinski et al. (2008). 103 0 1 2 3 4 5 6 7 8 9 10 photoelectron energy, E kin (keV) temperature T (K)
Page 1: Magnetic Oxide Heterostructures: Eu
Page 5: Abstract In the thesis at hand, we
Page 8 and 9: viii Contents 4. Results I: Single-
Page 10 and 11: x List of Figures 3.18. Photoelectr
Page 13: List of Tables 2.1. Photoemission f
Page 16 and 17: 2 1. Introduction Ferromagnetic oxi
Page 18 and 19: 4 1. Introduction EuO heterostructu
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Page 50 and 51: 36 3. Experimental details γ F fil
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76 4. Results I: Single-crystalline
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86 5. Results II: EuO integration d
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100 5. Results II: EuO integration
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m(T) / m(2 K) moment (µ B /f.u.) e
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124 6. Conclusion and Outlook we fo
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A. Appendix A.1. Properties of EuO-
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Table A.2.: Cubic oxides as substra
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130 A. Appendix The MgO and Si cubi
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Bibliography [1] G. Binasch, P. Gr
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134 Bibliography [25] A. Schmehl, V
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136 Bibliography [49] M. Arnold and
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138 Bibliography [77] H. Hertz. Üb
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140 Bibliography [103] L. Plucinski
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142 Bibliography [130] W. Braun. Ap
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144 Bibliography [158] K. Kobayashi
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146 Bibliography [184] B. Sinković
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148 Bibliography [211] D. Wandner,
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List of own publications [1] Casper
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List of conference contributions [1
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Acknowledgement . . . These days, i
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Erklärung Hiermit erkläre ich, da
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