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

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4.2 Results of 3d-Monolayers on Rh(001) Substrate 63 E MCA [meV/atom] 3 2.5 2 1.5 1 0.5 0 −0.5 −1 −1.5 −2 −2.5 −3 3d UML FM AFM OMA MCA V1 2 Cr Mn 3 Fe 4 5 6 Co Ni 0.3 0.25 0.2 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25 Figure 4.10: Magneto-crystalline anisotropy (MCA) for 3d UML is presented as (×) connected by solid (dashed) black line for FM (AFM) configuration. The orbital moments anisotropy (OMA) Δml for FM (AFM) case is presented as filled (empty) squares connected by solid (dashed) red line. Note that the scale on the normal (MCA) is different from the opposite (OMA) y-axis. Fe (−0.015 μB) and Co (−0.056 μB) do fully agree withe the calculated MCA values. For more understanding of the substrate effect on MCA, we need to check the influence of the crystal field and the hybridization. For the crystal field effect, we calculated the 3d contribution in the MCA, by excluding the spin orbit coupling of the substrate atoms. We can see that the crystal field prefers the in-plane MCA. To see the effect of the induced moments in the substrate, we calculated the MCA for the c(2×2) AFM, where there are no induced moments for the substrate interface layer Rh(I). By that we understand that the induced moments, i.e. the hybridization strength, pushes the magnetization to be out of plane. This means that the out of plane tendency is coming from the hybridization between the 3d ML and the Rh(001) substrate. One should mention that Cr has an opposite trend to what we concluded because it has negative induced moments. Knowing the MCA value enables us to estimate Néel temperature for ferromagnets with uniaxial anisotropy as explained in subsection 3.4.1. If we want to use equation (3.59), then we need an estimated value of the nearest neighbor exchange interaction constant J1 obtained from classical Heisenberg model (sec. 3.2). The FM has −2J1M 2 on square lattice and +2J1M 2 for AFM configuration, then the energy difference between FM and AFM is equal to 4J1. From the obtained results of the magnetic order from total energy calculations (subsec. 4.2.2), we can estimate Néel temperature for 3d monolayers which have uniaxial anisotropy on Rh(001). This implies only on vanadium and Cr since it has FM with outof-plane MCA. Using equation (3.59) and the bulk experimental Néel temperatures, we Δm l = m l ( )-m l (||) [μ Β ] T
64 4 Collinear magnetism of 3d-monolayers on Rh substrates LDOS [states/eV] 10 5 0 −5 Spin up Spin down With SOC −10-5 0 5 10 5 0 −5 V −10 −5 0 5 10 5 0 -5 -10 -10 -5 0 5 -5 0 5 10 5 0 -5 -10 Cr Mn −5 0 5 E-E F [eV] 10 5 0 -5 10 5 0 -5 -10 −5 0 5 FM AFM Figure 4.11: Local spin density of states for UMLs of V, Cr and Mn for both FM and AFM configurations. Red (blue) solid line represents majority (minority) spin states without including the spin-orbit coupling interaction. The black solid represents the local density of state for both spin channels with spin-orbit coupling up to the Fermi level. LDOS [states/eV] 10 5 0 −5 Spin up Spin down With SOC −10-5 0 5 10 5 0 −5 Fe −10 −5 0 5 10 5 0 -5 -10 -10 -5 0 5 -5 0 5 10 5 0 -5 -10 Co Ni −5 0 5 E-E F [eV] 10 5 0 -5 10 5 0 -5 -10 −5 0 5 FM AFM Figure 4.12: Local spin density of states for UMLs of Fe, Co and Ni for both FM and AFM configurations. Red (blue) solid line represents majority (minority) spin states without including the spin-orbit coupling interaction. The black solid represents the local density of state for both spin channels with spin-orbit coupling up to the Fermi level.
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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
Page 25 and 26: 12 1 Density functional theory (DFT
Page 27 and 28: 14 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
Page 75: 62 4 Collinear magnetism of 3d-mono
Page 87 and 88: 74 5 Fe monolayers on hexagonal non
Page 113 and 114: 100 5 Fe monolayers on hexagonal no
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Page 117 and 118: 104 6 Co MCA from monolayers to ato
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114 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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