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2.3. Magnetic properties of EuO 11 Figure 2.6.: Calculated Eu 5d conduction bands. The calculated DOS of the first five conduction bands in the quasi- particle model (Q-DOS) for spin-up electrons, and the one-electron Bloch density of states (B-DOS). After Nolting et al. (1987). 44 comes possible through the EuO 5d majority conduction band, or (ii) the lowered conduction bands overlap with donor levels or trap states of oxygen vacancies near the Fermi level. In that case one observes an insulator-to-metal transition (IMT, also: Mott transition), when cooling down the sample below the ferromagnetic ordering temperature. This effect was first reported by Oliver et al. (1970). 15,23,46–52 2.3. Magnetic properties of EuO Figure 2.7.: Plot of ionic radii versus atomic number for lanthanide ions (La–Lu). For comparison, the ionic radius of divalent Eu is highlighted, and the inset shows a space-filled image of the EuO unit cell. Additionally, Sr 2+ ,Ca 2+ , and Y 3+ ions are included, which represent the cations in important oxide substrates for EuO growth. The regular decrease of ionic radii of the lanthanides is called the lanthanide contraction. Remarkably, the ionic radii of the lanthanides are much larger than for Fe 2+ or Mg 2+ . After Atwood (2013). 53 The magnetic order in ferromagnetic insulators is induced by indirect exchange interactions
12 2. Theoretical background such as superexchange, 37 and is thus of a different origin than the itinerant electron ferromagnetism of the elemental 3d ferromagnets. In EuO, the strong ferromagnetic coupling is directly related to unique crystal features, the large ionic radius (see Fig. 2.7), combined with a high density of magnetic Eu 2+ ions (inset) both ensure a strong long-range ferromagnetic order. In the following, we briefly discuss the microscopic origin of the magnetic coupling in EuO, including competing exchange interactions. Finally, we show up tuning possibilities for T C and the benefits of EuO for an application as a spin filter tunnel barrier. Weiss’ mean field model We begin with a simple model for the magnetic order of EuO, in which the molecular mean field is proportional to the macroscopic magnetization. This mean field model considers a local magnetic moment interacting with the mean magnetic field of the crystal. In EuO, the Eu 2+ ions carry a magnetic moment of 7μ B (see Ch. 2.2.1) which is interacting with the effective magnetic field of the EuO crystal. The reduced magnetization σ can be expressed in a simple form, σ ≡ m(T ) m(T =0) ∝ (T C − T ) β , where β = 1 2 . (2.4) The Weiss molecular field is responsible for the long-range interatomic magnetic order and its magnitude determines the Curie temperature. 54 However, experimentally β =0.37 instead of 1/2 was found. 55 For a better description of the magnetic coupling between the localized Eu 2+ ions, the Heisenberg model is applied. Heisenberg models for the magnetization of EuO The Heisenberg model suggests that a spontaneous magnetization arises from the exchange interactions between spins moments of neighboring atoms. In EuO, the 4f 7 spin magnetic moment of a Eu 2+ ion interacts with the 4f 7 spin moments of its nearest neighbors. Since the 4f 7 orbital has maximum spin multiplicity S = 8 and L = 0 (term symbol 8 S7/2) inthe ferromagnetic ground state, † it is of spherical s-like symmetry. Thereby, the exchange is considered isotropic, and one effective Hamiltonian is sufficient to describe the nearest neighbor interaction: ∑ H = −J ex S i ·S j (2.5) H denotes the Heisenberg Hamiltonian which sums up the spins over nearest neighbors, where J ex is the positive exchange energy describing a pure ferromagnetic interaction. Although there is no exact solution of eq. (2.5), the Bloch T 3/2 law was found, 54 σ ≡ m(T ) ( ) 3 1 sc structure, 0.0587 kB 2 T ⎧⎪ ⎨ =1− , Q = 2 bcc structure, m(T =0) S ·Q 2J ex S ⎪ ⎩ 4 fcc structure. (2.6) Remarkably, the density of Eu 2+ ions in fcc EuO is 44% larger than in bcc Eu metal, and comparable to the density of Gd ions in ferromagnetic Gd metal. 22 † The occupation of the 4f 7 orbital is described in Ch. 2.2.1.
Page 1 and 2: Member of the Helmholtz Association
Page 4 and 5: Forschungszentrum Jülich GmbH Pete
Page 6: Zusammenfassung In dieser Doktorarb
Page 10 and 11: Contents 1. Introduction 1 2. Theor
Page 12 and 13: List of Figures 2.1. Phase diagram
Page 14: List of Figures xi 5.12. Resulting
Page 18 and 19: 1. Introduction Smart and powerful
Page 20 and 21: 3 In the thesis at ha
Page 22 and 23: 2. Theoretical background . . . The
Page 24 and 25: 2.1. The challenge of stabilizing s
Page 26 and 27: 2.2. Electronic structure of EuO 9
Page 30 and 31: 2.3. Magnetic properties of EuO 13
Page 36 and 37: 2.4. Hard X-ray photoemission spect
Page 46 and 47: 2.5. Magnetic circular dichroism in
Page 52 and 53: 3. Experimental details Die Pläne
Page 54 and 55: 3.1. Molecular beam epitaxy for oxi
Page 56 and 57: 3.2. In situ characterization techn
Page 58 and 59: 3.2. In situ characterization techn
Page 60 and 61: 3.3. Experimental developments at t
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Page 74 and 75: 4. Results I: Single-crystalline ep
Page 76 and 77: 59 Table 4.1.: Parameters for stoic
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4.1. Coherent growth: EuO on YSZ (1
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4.2. Lateral tensile strain: EuO on
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4.2. Lateral tensile strain: EuO on
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4.3. Lateral compressive strain: Eu
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5. Results II: The integration of t
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5.1. Chemical stabilization of bulk
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5.2. Thermodynamic analysis of the
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5.3. Interface engineering I: Hydro
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5.4. Interface engineering II: Eu p
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5.5. Interface engineering III: SiO
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5.5. Interface engineering III: SiO
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5.6. Summary 121
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6. Conclusion and Outlook In the th
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125 Outlook and perspectives In the
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A.1. EuO-related phases and cubic o
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A.1. EuO-related phases and cubic o
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A.2. In situ analysis of the Si (00
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Bibliography 133 [13] S. S. P. Park
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Bibliography 135 [36] R. E. Dickers
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Bibliography 137 [65] R. Sutarto, S
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Bibliography 139 [91] P. Braun, M.
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Bibliography 141 [116] S. Hüfner.
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Bibliography 143 [144] R. Feder and
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Bibliography 145 [171] H. Miyazaki,
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Bibliography 147 [197] J. Qi, T. Ma
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Software and Internet Resources [21
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List of own publications 151 [10] R
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List of conference contributions 15
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Schriften des Forschungszentrums J
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Schlüsseltechnologien / Key Techno
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