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

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4.2 Results of 3d-Monolayers on Rh(001) Substrate 57 Magnetic moment [μ Β ] 4.0 3.0 2.0 1.0 0.0 0.4 0.2 0 FM AFM 1 ML 3d on Ag(001) Pd(001) Rh(001) V Cr Mn Fe Co Ni Rh(I) V Cr Mn Fe Co Ni Figure 4.5: Magnetic moments of 3d TM monolayers on Ag, Pd and Rh(001) surfaces (top) and the interface Rh moments (bottom). The TM moments are denoted by full (empty) symbols for the FM (AFM) solutions. For the FM case the magnetic moment of the interface Rh atoms is given by full green squares. The data for the 3d TMs on Ag(001) and Pd(001) are taken from Ref.[3] and [5]. 4.2.2 Magnetic order: The total energy difference ΔE = EAFM − EFM between the c(2 × 2) AFM and the FM configuration is plotted in Fig.4.6 for the 3d TM monolayers on different substrates. For the Rh(001) substrate, we found a FM ground state for V, Co and Ni, while it is c(2 × 2) AFM for Cr, Mn and Fe. The data for Ag(001) and Pd(001) are taken from Ref.[3] and [5]. For the V and Ni we see that the energy differences are small, 4 meV and 15 meV respectively. Experimentally, the case of 1 ML V on Ag(001) was discussed controversially, claiming ferromagnetic order [125, 126], or the absence of ferromagnetic order [127], as well as evidence for antiferromagnetic order [6]. Therefore, we checked ΔE carefully as function of several computational parameters, like k-point sampling of the temperature broadening at the Fermi level. No change in the magnetic order was found even in the presence of external electric fields. From Fig.4.6 we see for V and Cr a magnetic trend towards FM as we change the substrate from Ag through Pd to Rh, while an increasing tendency towards AFM is observed for Mn and the late TMs. We notice that the magnetic order of the 3d monolayers on Rh(001) changes when relaxations are included, which lead to change in magnetic order for Fe since it is close to the phase transition region. This highlights the importance of relaxations to predict the correct magnetic ground state, especially when the nearest neighbor interactions become weak and higher order interactions cannot be ignored as we will see later.
58 4 Collinear magnetism of 3d-monolayers on Rh substrates E [meV./3d-atom] Δ 500 400 300 200 100 0 −100 −200 −300 −400 −500 FM Rh(001) Rh(111) Ag(001) Pd(001) W(001) Rh(001) Rh(001)(ur) Rh(001) Rh(001) c(2x2)-AFM Rh(100) Rh(001)(r) V Cr Mn Fe Co Ni Figure 4.6: The magnetic order of 3d TMs on Ag (circles), Pd (diamonds) Rh (squares) and W(001) (up triangles): positive ΔE = EAFM −EFM indicates a FM ground state, while negative values denote AFM order. The open squares connected by dashed line represent the magnetic order of unrelaxed 3d TMs on Rh(001). For a weakly interacting substrate, like Ag(001), the trends of ΔE can be understood on the basis of the densities of states of the TM monolayers[3]. As we move on to more strongly interacting substrates like Pd or Rh, this sinus-like curve is shifted gradually to the right, i.e. hybridization with the substrate effectively lowers the d-band filling in the TM film. This trend is even more pronounced for strongly interacting early TM substrates, like W(001), causing a complete reversal of the magnetic trends[7]. To analyze the role of the hybridization between the Fe ML and the Ag, Pd or Rh substrate, the local density of states (LDOS) for the nonmagnetic (NM) and the FM configuration of one ML Fe on different substrates are shown in Fig.4.7. We see from the NM LDOS, that there is no overlap of the Ag 4d-band with the Fe DOS, that is pinned at the Fermi level due to its incomplete 3d-band filling. Therefore, the Fe bandwidth is small and the high DOS at the Fermi level favors ferromagnetism. In contrast there is a strong 3d-4d hybridization between the Fe ML and the Rh(001) substrate. The broadening of the Fe d-band reduces the DOS at the Fermi level leading finally to an antiferromagnetic ground state. The case of Fe/Pd(001) is in between these extremes, but still a FM order is obtained as a ground state. From the FM DOS it can be seen that a small FM moment can be induced in the Pd interface that is absent in the case of Fe/Ag(001). We now compare Fe on Rh(001) to Cr/Rh(001), since the latter has a strong tendency towards a c(2 × 2) AFM ground state. From the NM LDOS (top of Fig.4.8) we see, that the Fermi level falls in a minimum of the Cr LDOS, favoring the AFM ground state even more than in the case of Fe (see Fig. 4.6). A comparison of the magnetic DOS shows that in Fe/Rh(001) the minority DOS is pinned at the Fermi level, while in the Cr
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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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Page 21 and 22: 8 1 Density functional theory (DFT)
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Page 29 and 30: 16 2 The FLAPW method 1 0 0 1 Figur
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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
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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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108 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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