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

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4.2 Results of 3d-Monolayers on Rh(001) Substrate 55 In our study, we determined the structural, electronic and magnetic properties of 3d TM monolayers on Rh(001) by performing the first principles calculations using the full potential linearized augmented plane wave (FLAPW) method in film geometry as implemented in the (FLEUR) code (see chapter 2). The generalized-gradient approximation of Perdew, Burke and Ernzerhof was applied (see section 1.5) leading to a Rh bulk lattice constant of 3.819 ˚A which is only 0.4% larger than the experimental lattice constant of 3.804 ˚A[120]. The film was modeled by a symmetric seven layer Rh(001) slab covered by a single 3d monolayer (see figure 2.2), using the calculated in-plane Rh lattice constant. Relaxations were considered for the topmost two layers, i.e., the 3d ML and the interface ML Rh(I). Both, the FM and the c(2×2) AFM configuration were relaxed. We used about 120 LAPW basis functions per atom with a muffin-tin radius of 1.22 ˚A for the 3d monolayer atoms and 1.28 ˚A for the Rh atoms. The irreducible part of the two-dimensional Brillouin zone (I2DBZ) was sampled with 78 k� points for the FM (AFM) configuration. 4.2.1 Relaxations and magnetic moments: Here we present relaxations results of 1 ML 3d/Rh(001). The formula we used to calculate the relaxation, Δdxy, between the layer i and j is: Δdij = dij − do do (4.1) where, dij is the interlayer distance and do is the ideal bulk interlayer distance of the substrate. First we relaxed the top most monolayers of the clean Rh(001) surface. The nonmagnetic relaxations of the interlayer spacing between the topmost monolayer and the second layer, Δd12, and the second Rh interlayer spacing, Δd23, were −0.3% and +0.2% respectively. Our prediction of top most two monolayers’ Rh(001) relaxations are in a very good agreement compared to the experimental relaxations:Δd12 = +0.5±1.0 (−1.6±1.6)% and Δd23 =0±1.5% (0±1.6)%[121]([122]). The relaxations of the interlayer spacing between the 3d monolayer and the topmost substrate layer, Δd12, and the first Rh interlayer spacing, Δd23, are presented in Figure 4.4 for both FM and AFM configurations. For the FM configuration, we notice that the smallest inward relaxation of the 3d monolayer occurs for Mn and Fe on Rh(001), where the magneto-volume effect (the atomic volume dependence of the magnetic susceptibility) is strongest, i.e. the large magnetic moments (see Fig. 4.5) of these TM compensate the strong inward relaxation – caused by the larger Rh lattice constant – most efficiently. Of course there are also other factors controlling the Δd12 that is, e.g., for V smaller than for Cr although the magnetic moment of the latter is much larger that of vanadium. Here, also the fact that the bulk lattice constant of V is 5% larger than that of Cr has to be considered. With the exception of Ni, in all cases the equilibrium distance between the interface Rh layer and the bulk Rh underneath increases with respect to the substrates bulk interlayer spacing. Moving from left to right through the periodic table, we find that Δd23 decreases, supporting the interpretation that the d-band filling controls these relaxations[123, 124]. This highlights
56 4 Collinear magnetism of 3d-monolayers on Rh substrates Δd 12 [%] Δd 23 [%] −2 −4 −6 −8 −10 −12 8 6 4 2 0 −2 (a) (b) FM AFM FM AFM V Cr Mn Fe Co Ni Figure 4.4: Relaxations of the first and second interlayer spacing, Δd12 (circles) and Δd23 (squares), respectively, for 3d TM monolayers on Rh(001) for the FM (solid symbols connected by solid lines) and the c(2 × 2) AFM (open symbols connected by dashed line) configuration. The corresponding changes are given with respect to the substrates bulk interlayer spacing, which is 1.91 ˚A. the importance of multilayer relaxations for the early transition monolayers. The same trend can be seen for the monolayers with c(2 × 2) AFM configuration: while Δd12 is also influenced by the magnetic moment of the 3d monolayer, Δd23 depends almost solely on the d-band filling. In Fig. 4.5 the magnetic moments of the 3d TM monolayers on Rh(001) are compared with the Ag(001) and Pd(001) substrates for the FM and AFM structures at the relaxed interlayer distances. The magnetic moments for on Rh(001) are smaller than those on Ag(001) or Pd(001) for the early TMs, while they are quite similar for the late TMs. This can be understood on the basis of the observation, that the overlap of the d-wavefunctions with the substrate is larger for the early than for the late TMs. Therefore, the dependence of the TMs magnetic moments on the chosen substrate is largest at the beginning of the TM series. The largest moment, in all cases, is found for Mn. The V and Ni magnetic moments vanish for the c(2 × 2) AFM structure. The induced magnetic moment of the Rh interface layer couples antiferromagnetically with Cr and ferromagnetically with Mn, Fe, Co and Ni, while almost no moment is induced by V. The largest induced magnetic moment is caused by the Co monolayer. The induced moments are much larger for Rh than for substrates like Ag(001), highlighting the importance of the substrate for magnetic properties like the magnetocrystalline anisotropy (MCA), which will be discussed later. Of course the AFM ordered TM films induce no magnetic moment in the interface Rh layer, and the induced moments in the deeper layers are considerably smaller (and of opposite orientation).
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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
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
Page 65 and 66: 52 4 Collinear magnetism of 3d-mono
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Page 87 and 88: 74 5 Fe monolayers on hexagonal non
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106 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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