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

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Chapter 5 Fe monolayers on hexagonal nonmagnetic substrates Describing the magnetic order of the square lattices (001) monolayers, using Heisenberg model equation (3.22) up to the second nearest neighbor interaction (J1, J2), is relatively simple. As long as the nearest neighbor interaction is the dominating one, there are only two phases to be considered: the ferromagnetic p(1×1) structure (J1 > 0) the antiferromagnetic c(2×2) superstructure (J1 < 0). If we describe the solution of the Heisenberg model as spin-spirals with a q�-vector from the first Brillouin zone, the c(2×2) structure corresponds to the M-point in the 2DBZ of the square lattice. If the next-nearest neighbor interaction is antiferromagnetic, J2 < 0, and sufficiently strong, |J1| < 2|J2|, then the ground state changes to be magnetic structure with a 2Dq� vector at the X-point in the 2DBZ. This means that an anti-ferromagnetic p(2×1) or p(1×2) structure (ferromagnetic rows of atoms along the [001] or [010] direction coupling antiferromagnetically from row to row) becomes the magnetic ground state. A recent theoretical study was preformed to predict the magnetic ground state of Fe monolayers on a TaxW1−x alloy if the substrate is tuned by changing the Ta concentration x[14]. Non-collinear magnetic structures at critical Ta concentration were predicted. This means that complex magnetic order can be obtained even in single monolayer (ML) magnetic films on non-magnetic (001) substrates. Furthermore, recently a spin-spiral state was discovered for a Mn ML on W(110) [132] and for a Mn ML on W(001) [12], although the driving force in this case is not a Heisenberg-type interaction but rather Dzyaloshinskii- Moriya type exchange. As a result, one can control the magnetic order of 3d monolayer by tuning the substrate. By that, the investigation of the magnetic order on square lattices started from late (Ag, Pd) and ended with early (W) transition metals substrates as illustrated in figure (5.1). For the hcp elements there is no square lattices which could help to have a complete understanding of the magnetic order trend of 3d monolayers on nonmagnetic substrates. Our case of study focuses on Fe because it has intensively been studied theoretically and experimentally. This leads us to continue investigating the Fe magnetic ground state on hexagonal sub- 73
74 5 Fe monolayers on hexagonal nonmagnetic substrates E [meV./3d-atom] Δ 300 200 100 0 −100 −200 bcc substrates hcp substrates fcc substrates −300 Ta W Rh Pd Ag Figure 5.1: Total-energy difference between the FM (ground state if ΔE >0) and c(2×2)- AFM (ΔE
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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
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 89 and 90: 76 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
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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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