Ab initio investigations of magnetic properties of ultrathin transition ...

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Contents Introduction II 1 Density functional theory (DFT) 7 1.1 Overview ..................................... 7 1.2 Origin of DFT .................................. 8 1.3 The Kohn-Sham equations ........................... 10 1.4 Spin Density Functional Theory ........................ 11 1.5 Approximations made to the exchange-correlation term EXC ........ 12 2 The FLAPW method 15 2.1 The generalized eigenvalue problem ...................... 15 2.2 From augmented planewaves (APW) to Linearized (L)APW ........ 17 2.3 The Full-Potential LAPW ........................... 19 2.3.1 Film Calculations within FLAPW ................... 22 2.4 The Kohn-Sham-Dirac Equation ........................ 24 2.4.1 The Scalar Relativistic Approximation ................ 25 3 Magnetism of low dimensional systems 29 3.1 Stoner Model .................................. 30 3.1.1 Role of coordination number: ..................... 33 3.2 Heisenberg Model and Beyond ......................... 34 3.3 Non-Collinear Magnetism ........................... 36 3.3.1 The Spin Space Groups ........................ 37 3.3.2 Spin Spirals ............................... 38 3.3.3 Generalized Bloch Theorem ...................... 39 3.3.4 Non-Collinear Magnetism in FLAPW ................. 41 3.4 Magnetic Anisotropy .............................. 43 3.4.1 Magnetic anisotropy and critical temperature: ............ 49 4 Collinear magnetism of 3d-monolayers on Rh substrates 51 4.1 3d-Monolayers on (001) oriented substrates ................. 51 4.1.1 3d monolayers on Pd, Ag and W (001) substrates: .......... 51 4.2 Results of 3d-Monolayers on Rh(001) Substrate ............... 54 I
II Contents 4.2.1 Relaxations and magnetic moments: . . . ............... 55 4.2.2 Magnetic order: ............................. 57 4.2.3 Magnetocrystalline anisotropy: ..................... 61 4.3 3d-Monolayers on Rh(111) Substrate: ..................... 66 4.3.1 Relaxations and magnetic moments: . . . ............... 66 4.3.2 Magnetic order: ............................. 69 5 Fe monolayers on hexagonal nonmagnetic substrates 73 5.1 Results of Fe monolayer on different hexagonal substrates from collinear calculations: ................................... 74 5.1.1 Structural optimization & relaxations: ................ 75 5.1.2 Magnetic order: ............................. 77 5.2 Results of Fe monolayer on different hexagonal substrates from non-collinear calculations: ................................... 79 5.2.1 Model Hamiltonian & Heisenberg model for 2D hexagonal lattices: . 79 5.2.2 Results of Fe monolayer on Rh(111): . . . .............. 86 5.2.3 Results for the Fe monolayer on Tc(0001) substrate: ......... 93 5.2.4 Comparison of Fe magnetic order on 4d hexagonal substrates: . . . 95 6 Co MCA from monolayers to atomic chains 103 6.1 Relaxations and magnetic order: ........................ 103 6.2 MCA of Co monolayer on 4d substrates: ................... 105 6.3 Co atomic chain on Rh(664): .......................... 108 6.3.1 Theoretical model and relaxation results: ............... 108 6.3.2 Magnetocrystalline anisotropy: ..................... 110 Summary and Conclusions 114 Appendix 118 Bibliography 127 Acknowledgement 141
Page 1 and 2: Mitglied der Helmholtz-Gemeinschaft
Page 4 and 5: Forschungszentrum Jülich GmbH Inst
Page 6 and 7: Abstract In this thesis, we investi
Page 10: ”A human being is part of the who
Page 15 and 16: 2 INTRODUCTION (ao =3.80 ˚A) is in
Page 17 and 18: 4 INTRODUCTION understanding of our
Page 19 and 20: 6 INTRODUCTION
Page 21 and 22: 8 1 Density functional theory (DFT)
Page 23 and 24: 10 1 Density functional theory (DFT
Page 29 and 30: 16 2 The FLAPW method 1 0 0 1 Figur
Page 31 and 32: 18 2 The FLAPW method nonlinear pro
Page 33 and 34: 20 2 The FLAPW method metal systems
Page 35 and 36: 22 2 The FLAPW method Then one can
Page 37 and 38: 24 2 The FLAPW method Evac is the v
Page 39 and 40: 26 2 The FLAPW method of the operat
Page 41 and 42: 28 2 The FLAPW method a matrix expr
Page 43 and 44: 30 3 Magnetism of low dimensional s
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48 3 Magnetism of low dimensional s
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50 3 Magnetism of low dimensional s
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52 4 Collinear magnetism of 3d-mono
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74 5 Fe monolayers on hexagonal non
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100 5 Fe monolayers on hexagonal no
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102 5 Fe monolayers on hexagonal no
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104 6 Co MCA from monolayers to ato
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116 rather subtle. To shed more lig
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118
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120 where, the relation � i H =
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122 Figure 6.8: The real (left) and
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124 E(q) = −M 2 ( 2J2 +2J6 +cos(
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126 For a 2D hexagonal lattice, the
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128 Bibliography [12] P. Ferriani,
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130 Bibliography [39] A. Dallmeyer,
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132 Bibliography [68] J. Perdew and
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134 Bibliography [101] L. Nordströ
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136 Bibliography [130] O. Le Bacq,
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138 Bibliography [160] P. M. Marcus
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140 Bibliography [190] R. Germar, W
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Acknowledgement I don’t know how
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Schriften des Forschungszentrums J
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