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Chapter 3Substitutional Metallic Impurities inGraphene: Structural, Electronic andMagnetic PropertiesThis chapter is devoted to the study of the basic structural, electronic and magnetic propertiesof 3d metal, noble metal and Zn atoms interacting with carbon monovacancies in graphene.We pay special attention to the electronic and magnetic properties of these substitutional impuritiesand found that they can be fully understood using a simple model based on the hybridizationbetween the states of the metal atom, particularly the d shell, and the defect levelsassociated with an unreconstructed D 3h carbon vacancy.The chapter is divided as follows: we present a summary of the structure, energetics andmagnetic properties of all the studied elements in Sec. 3.1. In this section we also indicatethe general ideas behind our model of the metal-carbon hybridization in these systems. Theelectronic structure of the unreconstructed D 3h carbon vacancy in graphene is presented inSec. 3.2. This is one of the key ingredients to understand the binding and electronic structureof substitutional impurities in graphene. The electronic structure of the different groups of impuritiesis described in Sec. 3.3. In Sec. 3.4 the Zn substitutional impurity with its Jahn-Tellerdistortion is described. A full section (Sec. 3.5) is devoted to describe the special role of Fe atthe border between two different regimes. Finally, we close with some general conclusions.3.1 The main properties of substitutional transition metalsin grapheneWe review in this section our results for the structure, binding, and spin moments of substitutional3d transition metals, noble metals and Zn in graphene.3.1.1 Geometry and structural parametersThe typical geometry of the systems studied in this chapter is presented in Fig. 3.1. The metalatom appears always displaced from the carbon layer. The height over the plane defined byits three nearest carbon neighbors is in the range 1.7-0.9 Å. These three carbon atoms are alsodisplaced over the average position of the graphene layer by 0.3-0.5 Å. The total height (h z )59
60Chapter 3. Substitutional Metallic Impurities in Graphene: Structural, Electronic andMagnetic Propertiesh zzxyFigure 3.1: Typical geometry of transition and noble substitutional metal atoms in graphene. The metal atommoves upwards from the layer and occupies, in most cases, an almost perfectly symmetric three-fold positionwith C 3v symmetry.of the metal atom over the graphene plane is the sum of these two contributions and rangesbetween 1.2-1.8 Å, as shown in panel (c) of Fig. 3.2. In most cases the metal atom occupies analmost perfect symmetric configuration with C 3v symmetry. Exceptions are the noble metals,that are slightly displaced from the central position, and Zn that suffers a Jahn-Teller distortionin its most stable configuration. However, we have found that it is also possible to stabilize asymmetric configuration for Zn with a binding energy only ∼150 meV smaller. This configurationwas overlooked in a recently published study on these systems [112] and we will referto it as Zn C3v throughout the chapter.Figures 3.2 presents a summary of the structural parameters of substitutional 3d transitionmetals, noble metals and Zn in graphene. Solid circles correspond to calculations using theSIESTA code with pseudopotentials and a basis set of atomic orbitals, while open squares standfor VASP calculations using plane-waves and PAW potentials. The agreement between bothsets of calculations is quite remarkable. Data in these figures correspond to calculations usinga 4×4 supercell of graphene. For several metals we have also performed calculations usinga larger 8×8 supercell and find almost identical results. This is particularly true for the totalspin moments, which are less dependent on the size of the supercell, but require a sufficientlydense k-point sampling to converge. In the following we will mainly discuss the results obtainedwith the smaller cell since the plots of the band structures are easier to interpret in that
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126 Chapter 6. Summary and outlookd
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128 Chapter 6. Summary and outlook
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130 Chapter 6. Summary and outlook
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132 Appendix A. PublicationsAlso se
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134 Appendix B. Conference and Work
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140 Bibliography[14] H. W. Lee and
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142 Bibliography[44] A. J. Stone an
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144 Bibliography[73] W. Kim, A. Jav
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146 Bibliography[102] G. Kresse and
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148 Bibliography[128] R. K. Saini,
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