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

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5.2 Results of Fe monolayer on different hexagonal substrates from non-collinear cal. 93 Figure 5.11: Vortex-like structure, with sixteen atoms per unit cell, each four atoms have the same spin rotating by π with respect to each other(left). The two spin spiral Q-points 2 used to construct such a coplanar vortex-like structure (right). atom. 5.2.3 Results for the Fe monolayer on Tc(0001) substrate: Employing the same procedure as for Fe/Rh(111), we performed also non-collinear calculations to calculate total energies in terms of spiral vectors for Fe monolayer on technetium (0001) surface, Tc(0001). The aim of that is to have a complete picture about Fe magnetism on different hexagonal substrates, especially after the theoretical study performed to study Fe ground state on Ru(0001) and Re(0001) from non-collinear DFT calculations [57]. Also, the ground state of Fe monolayer on Ir(111) was experimentally investigated and modeled by theoretical non-collinear DFT calculations [27, 28]. We used the experimental Tc lattice constants to calculate the spin spirals using the collinear ground state, RW-AFM, relaxations (Tab. 5.1). All numerical parameters were the same as for Fe/Rh(111). Results of total energies relative to the FM solution, using GGA are shown in figure 5.12(a). The moments of Fe, Tc(I) and Tc(I-1) are also presented in figure 5.12 (b). In addition we performed collinear calculations at the two double-Q, uudd � MΓ/2 � and uudd � 3ΓK/4 � states, to test the validity of equations (5.8 and 5.14), since the equality of the difference between the single- and double-Q total energies was broken for Rh(111) case. We see, from figure 5.12(a), that also here, we have different energy differences between the two double-Qs and their single-Q, even though these differences are rather small. These results indicate that the higher order interactions are very weak and cannot change the magnetic ground state from what is enforce by the nearest next nearest neighbor interactions. The global minimum energy is at K, which means that Fe has a Néel ground state on Tc(0001) with angles of 120 ◦ between adjacent spins, with −180 (−60) meV/Fe atom below the FM (RW-AFM) solution. The change of Fe ground state from a RW-AFM to a Néel structure, due to topological frustrations, highlights the importance of taking non-collinear magnetic structures into account. This can be seen from the RW-AFM
94 5 Fe monolayers on hexagonal nonmagnetic substrates E Q −E FM [meV/Fe] Magnetic moments [μ B ] 100 50 0 −50 −100 −150 2Q Fe/Tc(0001) 2Q 0 0.5 1 1.5 2.5 2.4 (a) (b) 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Tc(I-1) −0.2 Tc(I) ⎯Γ ⎯Κ ⎯Μ ⎯Γ Spin spiral vector Q (2π/a) Figure 5.12: (a) Total energy of spin spirals for 1 ML Fe/Tc(0001) are presented by solid squares. (b) Fe magnetic moments and the Rh(I), Rh(I-1) induced moments. The double-Q state results are presented by solid triangles. ground state predicted from collinear calculations including only next nearest neighbor interactions by the choice of two atoms per unit cell. We also can see that Tc surface layers were not strongly polarized, from the Tc(I) and Tc(I-1) induced magnetic moments shown in figure 5.12 (b). On the other hand, if we look to the magnetic moments from the double-Q calculation, presented in table 5.4, the polarization between Tc(I) and Tc(I-1) is small as it is for the single-Q state. Interestingly, the Fe moments are strongly polarized for the uudd � MΓ/2 � double-Q state. We will discuss this result when we compare all Fe/4d results at the end of chapter Table 5.4: GGA Fe and Tc(0001) induced moments at the interface and the subsurface Tc layers, Tc(I) and Tc(I-1), for the double- and single-Q states in units of μB using. Fe Tc(I) Tc(I-1) uudd � 3ΓK/4 � : 2.42,2.43 0.02,0.01 0.0 Q 3ΓK/4 : 2.51 0.01 0.0 uudd � MΓ/2 � : 2.42,2.35 0.05,0.02 0.01 Q MΓ/2 : 2.44 −0.04 0.01 Using equations (5.14 and 5.8), from the uudd � 3ΓK/4 � double-Q and the multi-Q states results, we can now calculate the higher order interaction terms B1 and K1. Then we use equation (A-20) to fit the spin spiral results along Γ-K-M. The GGA results are 3Q Fe
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Mitglied der Helmholtz-Gemeinschaft
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Forschungszentrum Jülich GmbH Inst
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Abstract In this thesis, we investi
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”A human being is part of the who
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II Contents 4.2.1 Relaxations and m
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2 INTRODUCTION (ao =3.80 ˚A) is in
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4 INTRODUCTION understanding of our
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6 INTRODUCTION
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8 1 Density functional theory (DFT)
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10 1 Density functional theory (DFT
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16 2 The FLAPW method 1 0 0 1 Figur
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18 2 The FLAPW method nonlinear pro
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20 2 The FLAPW method metal systems
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22 2 The FLAPW method Then one can
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24 2 The FLAPW method Evac is the v
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26 2 The FLAPW method of the operat
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28 2 The FLAPW method a matrix expr
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30 3 Magnetism of low dimensional s
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Page 55 and 56: 42 3 Magnetism of low dimensional s
Page 65 and 66: 52 4 Collinear magnetism of 3d-mono
Page 87 and 88: 74 5 Fe monolayers on hexagonal non
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Page 117 and 118: 104 6 Co MCA from monolayers to ato
Page 129 and 130: 116 rather subtle. To shed more lig
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Page 133 and 134: 120 where, the relation � i H =
Page 135 and 136: 122 Figure 6.8: The real (left) and
Page 137 and 138: 124 E(q) = −M 2 ( 2J2 +2J6 +cos(
Page 139 and 140: 126 For a 2D hexagonal lattice, the
Page 141 and 142: 128 Bibliography [12] P. Ferriani,
Page 143 and 144: 130 Bibliography [39] A. Dallmeyer,
Page 145 and 146: 132 Bibliography [68] J. Perdew and
Page 147 and 148: 134 Bibliography [101] L. Nordströ
Page 149 and 150: 136 Bibliography [130] O. Le Bacq,
Page 151 and 152: 138 Bibliography [160] P. M. Marcus
Page 153 and 154: 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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