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3.1. The main properties of substitutional transition metals in graphene 63Figure 3.3: Spin moment of substitutional transition and noble metals in graphene as a function of the number ofvalence electrons (Slater-Pauling-type plot). Black symbols correspond to the most stable configurations usingGGA. Results are almost identical using SIESTA and VASP codes. Three main regimes are found as explainedin detail in the text: (i) filling of the metal-carbon bonding states gives rise to the non-magnetic behavior of Tiand Sc; (ii) non-bonding d states are filled for V, Cr and Mn giving rise to high spin moments; (iii) for Fe allnon-bonding levels are occupied and metal-carbon antibonding states start to be filled giving rise to the observedoscillatory behavior for Co, Ni, Cu and Zn. Open and gray (red online) symbols correspond, respectively, tocalculations of Fe using GGA+U and artificially increasing the height of the metal atom over the graphene layer(see the text). Symbol marked as Zn C3v corresponds to a Zn impurity in a high-spin symmetric C 3v configuration.simple model to understand the observed behavior which was not presented in that reference.One of the fundamental results of our study is a detailed model of the bonding and electronicstructure of substitutional transition metals in graphene. As we will see below, the evolutionof the spin moment can be completely understood using such model. In brief, we can distinguishdifferent regimes according to the filling of electronic levels of different (bonding,non-bonding and antibonding) character:(i) all the carbon-metal bonding levels are filled for Sc and Ti and, correspondingly, thespin-moment is zero;(ii) non-bonding 3d levels become populated for V and Cr giving rise to a spin moment of,respectively, 1 and 2 µ B with a strong localized d character;(iii) for Mn one additional electron is added to the antibonding d z 2 level and the spinmoment increases to 3 µ B ;(iv) finally, for Fe and heavier atoms all the non-bonding 3d levels are occupied and the
64Chapter 3. Substitutional Metallic Impurities in Graphene: Structural, Electronic andMagnetic PropertiesUnrelaxed D 3hC vacancy32(a)(b)1E spE p zEnergy (eV)0-1-2-3-4A p z-5Γ Κ Μ ΓA spE F00 1100 1100 1100 1100 1100 1100 1100 11E spA pzA spFigure 3.4: (a) Spin-compensated calculation of the band structure of an unrelaxed carbon vacancy (D 3h symmetry)in a 4×4 supercell of graphene. Symbols indicated those bands with larger weight on the carbon atomsaround the vacancy (solid symbols for bands with sp character and open symbols for a band with p z character).The electronic structure near E F is dominated by a fully symmetric p z level (A p z ) and two defect levels withE symmetry and sp character (E sp). Notice that, due to the strong hybridization with the rest of the graphenelayer, it is not possible to identify well defined defect levels with E symmetry and p z character. (b) Approximatescheme of the electronic structure of the spin-compensated D 3h C vacancy indicating the character and symmetryof the different levels and their occupations. Signal associated with the E p z level extends over the whole valenceand conduction band.spin moment oscillates between 0 and 1 µ B as the antibonding metal-carbon levels becomeoccupied.The sudden decrease of the spin moment from 3 µ B for Mn to 0 µ B for Fe is characterizedby a transition from a complete spin-polarization of the non-bonding 3d levels to afull occupation of those bands. However, this effect depends on the ratio between the effectiveelectron-electron interaction within the 3d shell and the metal-carbon interaction (seeSec. 3.5). As we will see below, if the hybridization with the neighboring atoms is artificiallyreduced, for example by increasing the Fe-C distance, Fe impurities develop a spin momentof 2 µ B . Our results also show that it is also possible to switch on the spin moment of Feby changing the effective electron-electron interaction within the 3d shell. This can be doneusing the so-called GGA+U method. For a large enough value of U (in the range 2-3 eV), Fe
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Ph.D ThesisFirst-Principles Study o
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8did together and for the friendshi
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10 Contents3 Substitutional Metalli
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Page 15 and 16: 14 Chapter 1. Introductionthat the
Page 17 and 18: 16 Chapter 1. IntroductionFigure 1.
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Page 31 and 32: 30 Chapter 1. IntroductionE = E F ,
Page 37 and 38: 36 Chapter 1. IntroductionA H atom
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Page 45 and 46: 44 Chapter 2. Electronic Structure
Page 61 and 62: 60Chapter 3. Substitutional Metalli
Page 63: 62Chapter 3. Substitutional Metalli
Page 89 and 90: 88Chapter 4. Real Systems that Beha
Page 101 and 102: 100Chapter 4. Real Systems that Beh
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Chapter 5. Effect of Strain on the
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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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