Association

More documents

Recommendations

Info

2.3. Magnetic properties of EuO 13 which fits the experimental data very well. The three-dimensional Heisenberg model provides a power law for temperatures below the magnetic phase transition: 56 σ ∝ (T C − T ) β , where β =0.36. (2.7) For EuO an experimental value β =0.37 was found, 55,57 thus EuO is considered as a clear realization of a 3D Heisenberg ferromagnet. In the Weiss-Heisenberg mean field model, the most-used temperature dependence of the spontaneous magnetization σ follows a Brillouin function B J (x). 58 This behavior can be derived from the mean field theory for ideal paramagnets by substituting the external field B ext by the Weiss molecular field βH Weiss . Then, at constant H Weiss , the temperature dependence is ( σ ∝Bσ 3J J +1 ) T C . (2.8) T A more complex Heisenberg model has been proposed by Mauger and Godart (1986) including two exchange interactions J 1 and J 2 for the EuO magnetic order, which are the nearest neighbor and next-nearest neighbor Eu 2+ –Eu 2+ interactions, respectively. 18 The nearest neighbors interaction is ferromagnetic with an experimental value of J 1 = ∼5.3 × 10 −5 eV. 59 The next-nearest neighbor exchange J 2 is more complex and still under debate, one experimental value being J 2 ∼ 1.05 × 10 −5 eV. 59 The ordering temperature T C is expressed via the mean field approach T C =2S(S +1)·12J 1 +6J 2 3k B , (2.9) where S is the total spin of the EuO magnetic shell (4f 7 ). The dominant interaction J 1 acts between the 4f orbitals of the 12 nearest neighbors via a virtual exchange involving the unoccupied 5d conduction states for transfer. Between the six next-nearest neighbors, the J 2 interaction is of mainly super-exchange nature and involves different mechanisms. Until now, the nature of the J 2 interaction is not clear – is it antiferromagnetic or ferromagnetic in EuO? Several mechanisms are currently discussed in order to describe the J 1 and J 2 parts of the magnetic coupling in EuO, and we summarize the most established ones in the following. Competing exchange interactions in EuO The microscopic origin of the exchange interaction is still under discussion. Proposed by Kasuya (1993), 42 several competing exchange mechanisms exist in EuO: Nearest neighbor exchange A4f electron is excited to the 5d band where the electrons are itinerant, is then influenced by the exchange interaction of the 4f spins of the nearest neighbors, and falls back to the initial state. This indirect interaction leads to ferromagnetism. This idea is first proposed by Mauger and Godart (1986). 18 The Kramers-Anderson superexchange An f electron is transferred via oxygen to an f orbital of a neighboring atom. This exchange is antiferromagnetic and very small. Superexchange via the d–f interaction Oxygen electrons are transferred to the d orbitals of neighboring Eu atoms, where they influence the 4f spins via the d–f exchange. This leads to an antiferromagnetic exchange. 60–62
14 2. Theoretical background Hybridization of the 5d and 2p orbitals Via hybridization, bonding and antibonding molecular orbitals are formed between Eu 5d and O 2p ligands. An oxygen electron is excited from the bonding to the antibonding 5d–2p molecular orbital, which experiences exchange interaction with both Eu spins. Its place is filled by a Eu 4f electron, and a 5d electron falls into the 4f hole. This could lead to ferromagnetic exchange. From the Heisenberg theory (large J 1 coupling) and Kasuya (1993) it is evident, that the ferromagnetic nearest neighbor exchange between 4f 7 via 5d states is most dominant. This emphasizes the important role of the nearest neighbor distance and the 5d conduction band with its possible population with donor electrons – both of which can easily be tuned by suitable synthesis parameters. 2.3.1. The Curie temperature of EuO Stoichiometric EuO is ferromagnetic below the Curie temperature of T C = 69.3 K. 63 Many studies have been devoted to increase this transition temperature. One approach is the introduction of biaxial strain to heteroepitaxial EuO thin films by underlying substrates. In this way, decreasing the lateral lattice parameters of EuO is an ideal method to increase the Curie temperature T C due to enhanced nearest neighbor coupling. Ingle and Elfimov (2008) find by their first principles calculation, 64 that the semiconducting gap closes at a 6% in-plane lattice compression for epitaxial EuO. This value thus constitutes an upper limit of compressive strain on EuO, if EuO shall remain insulating. However, the biaxial lateral forces are likely compensated by expansion or reduction in the perpendicular z dimension for most oxides, thus conserving the volume of a unit cell. For EuO, this perpendicular compensation is extremely small, 64 thus biaxial forces should have a large effect on the total expansion or compression of the EuO unit cell, giving rise to a tuned magnetic coupling. Therefore, we investigate biaxial strain and the elasticity of heteroepitaxial EuO thin films in Ch. 4. Another approach of tuning T C of EuO involves electron doping. This is indeed the most common method and does not require epitaxial integration of the EuO thin films. A model system for electron doping in EuO is the substitution of Eu 2+ by Gd 2+ , thereby one 5d electron is provided. Initially, an RKKY model 18 suggested the support of the d–f exchange between Eu ions. A more recent model by Kasuya (1993) proposes that the donor electron is trapped at the Gd ion building up a bound magnetic polaron together with the surrounding Eu 2+ ions. 42 The increase of T C is then proportional to the Gd doping concentration for low doping ( 3%). An optimum Gd concentration (∼4%) for highest T C (∼125 K) has been experimentally determined. 65 In a similar way, the Curie temperature could be increased by La and Lu doping up to 200 K due to comparable effects, 66,67 thus rendering EuO as the rare earth magnetic insulator with the highest Curie temperature. Extra electrons are also provided by oxygen vacancy sites in EuO 1−x . For an oxygen vacancy, one Eu 2+ ion provides two conduction electrons to the crystal. This yields a weak magnetization tail up to 150 K, whose origin is subject to discussions. The magnetization above 69 K may be induced by antiferromagnetic Eu metal clusters. 15,23,68 A recent study, however, proposes magnetic polarons to increase T C of EuO 1−x . 60 Moreover, oxygen vacancies in EuO 1−x induce metallic conductivity, as discussed in Ch. 2.2.2, and are undesired in this thesis in
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 28 and 29: 2.3. Magnetic properties of EuO 11
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
Page 62 and 63: 3.4. Ex situ characterization techn
Page 74 and 75: 4. Results I: Single-crystalline ep
Page 76 and 77: 59 Table 4.1.: Parameters for stoic
Page 78 and 79: 4.1. Coherent growth: EuO on YSZ (1
Page 80 and 81:
4.1. Coherent growth: EuO on YSZ (1
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
4.2. Lateral tensile strain: EuO on
Page 94 and 95:
4.2. Lateral tensile strain: EuO on
Page 96 and 97:
4.3. Lateral compressive strain: Eu
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
5. Results II: The integration of t
Page 104 and 105:
5.1. Chemical stabilization of bulk
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
5.2. Thermodynamic analysis of the
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
5.3. Interface engineering I: Hydro
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
5.4. Interface engineering II: Eu p
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
5.5. Interface engineering III: SiO
Page 136 and 137:
5.5. Interface engineering III: SiO
Page 138 and 139:
5.6. Summary 121
Page 140 and 141:
6. Conclusion and Outlook In the th
Page 142 and 143:
125 Outlook and perspectives In the
Page 144 and 145:
A.1. EuO-related phases and cubic o
Page 146 and 147:
A.1. EuO-related phases and cubic o
Page 148 and 149:
A.2. In situ analysis of the Si (00
Page 150 and 151:
Bibliography 133 [13] S. S. P. Park
Page 152 and 153:
Bibliography 135 [36] R. E. Dickers
Page 154 and 155:
Bibliography 137 [65] R. Sutarto, S
Page 156 and 157:
Bibliography 139 [91] P. Braun, M.
Page 158 and 159:
Bibliography 141 [116] S. Hüfner.
Page 160 and 161:
Bibliography 143 [144] R. Feder and
Page 162 and 163:
Bibliography 145 [171] H. Miyazaki,
Page 164 and 165:
Bibliography 147 [197] J. Qi, T. Ma
Page 166 and 167:
Software and Internet Resources [21
Page 168 and 169:
List of own publications 151 [10] R
Page 170 and 171:
List of conference contributions 15
Page 172 and 173:
Schriften des Forschungszentrums J
Page 175:
Schlüsseltechnologien / Key Techno
show all

Association

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?