Slides from 2012 in videos assigned for lectures on 8 and 10 November 2012-Lecture 10 starting from 0:33 until the end, all of lecture 11 and lecture 12 from start to 1:02.
tot SAME SUBSHELL COUPLING + TOTAL L,S ”MONOPOLE” (N-1)e - SHAKE-UP/ SHAKE-OFF "Basic Concepts of XPS" 1e- DIPOLE d /d ”MONOPOLE” 2 Chapter 3
tot SAME SUBSHELL COUPLING + TOTAL L,S ”MONOPOLE” (N-1)e - SHAKE-UP/ SHAKE-OFF "Basic Concepts of XPS" 1e- DIPOLE d /d ”MONOPOLE” 3 Chapter 3
tot SAME SUBSHELL COUPLING + TOTAL L,S ”MONOPOLE” (N-1)e - SHAKE-UP/ SHAKE-OFF "Basic Concepts of XPS" 1e- DIPOLE d /d ”MONOPOLE” 4 Chapter 3
tot SAME SUBSHELL COUPLING + TOTAL L,S ”MONOPOLE” (N-1)e - SHAKE-UP/ SHAKE-OFF "Basic Concepts of XPS" 1e- DIPOLE d /d ”MONOPOLE” 5 Section 3.D.
tot SAME SUBSHELL COUPLING + TOTAL L,S ”MONOPOLE” (N-1)e - SHAKE-UP/ "Basic Concepts of XPS" SHAKE-OFF 1e- DIPOLE d /d Section 3.D. ”MONOPOLE” 6 Section 6.D.
(a) (b) CO ref. intens. C1s I 0 | 0 | 2 500 eV j = object wave 0 = reference wave K f inc e v 0 (c) k f Photo toele electr ctron n Dif iffrac fraction ion
X-ray ay Photoe oelect ectron ron Di Diffr fract action: n:1ML 1ML FeO on Pt(1 (111) 11) (a) (b) Forward d Scat atter tering ng 0.65 5 Å
PLUS SPIN: ( )= )= m si si = +½ = ( )= )= m si si = -½ = ( ) ( ) ( ) ( ) m s = = m sf sf - m si si = 0 ! 9
The quantum mechanics of covalent bonding in molecules: H 2 + with one electron - = antibonding 1sa - 1sb + = bonding 1sa + 1sb antibonding Total Energy =R 10
H b H a Anti-Bonding anti MO 1sa - 1sa positive (unoc occupi upied) ed) a.u. u. = +7.21 1 eV negat ative (occupied) upied) Bonding bonding MO 1sa + 1sa a.u. u. = -16. 6.16 16 eV (Com ompar pare e – 13. 3.61 61 for r H atom om 1s) 11
The LCAO or tight-binding picture for CO: NON/WEAKLY CORE: Chemist’s picture ( no core): x X 36 C O x x 12
THE ELECTRONS IN HF (OR HCl): ionic molecules 1 2 HF: F1s 2 2 2 3 2 1 x 2 1 y 2 1 e - 9 e - F F 1s core H 13 1 E = -25.6 a.u.
PLUS SPIN: PLUS SPIN: ( )= ( )= )= m si )= m si si = +½ = si = +½ = ( )= ( )= )= m si )= m si si = -½ = si = -½ = ˆ ˆ ˆ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ^ ^ ^ ^ m s = m s = = = m sf m sf sf - m si sf - m si si si = 0 ! = 0 ! ˆ ^ ^ "Basic Concepts of XPS" 14 Chapter 3
The free-electron solid at absolute zero 2 k 2 Å -1 2 E(k ) 3.81(k(in )) (in eV ) 2m e = the density of states 15
NEARL NEARLY-FREE E FREE ELECTR LECTRONS ONS IN IN A A WEAK PE WEAK PERIODIC RIODIC PO POTE TENTI NTIAL AL — 1 1 DIM. DIM.
L 17
Electronic bands and density of states for “free - electron” metals - Rydberg = 13.605 eV Aluminum — fcc, a a = 4.05 Å 1s 2 2s 2 2p 6 3s 2 3p 1 Lithium — bcc, a = 3.49 Å 1s 2 2s 1 a 2 (k ) 2 0 E(k ) x 0 x 2m =1.55Å -1 2 (k ) 2 2 /a k x E(k ) x x 2m =1.8Å -1 2 /a 18
Electronic bands and density of states for a semiconductor-Germanium — 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 2 Anti- Bonding Vacuum (empty at Level Work T = 0) Function, = 4.8 eV E F Inner Potential, V 0 4.8+0.3+12.6 Bonding = 17.7 eV (filled at T = 0) 19
Vacuum level The electr tron onic ic str tructure cture of a transiti nsition on meta tal — fcc cc Cu Cu = 4.4 eV = work function V 0,Cu =13.0eV Experime rimenta ntal points ts from m - 8.6 eV angle-reso resolved ved photoelectron ctron spectro ctroscop scopy (more re later) r) 20
Atomic orbital makeup Atomic orbital makeup Atomic orbital makeup Solid state tight-binding approach MO MO ( ) ( ) r r c c AO AO ( ) ( ) r r j j Ai j Ai j , , Ai Ai Atoms A Atoms A Crystal potential-1D Orbitals i Orbitals i Molecular R j orbital 5 5 5 5 approach Atomic orbitals j+1 j j-1 1 y 1 y 1 y 1 y 1 x 1 x 1 x 1 x Tight-binding wave function + + + + – – – – Anti- Bonding 4 4 4 4 + + + + E j ++ ++ ++ ++ – – – – 3 3 3 3 BF φ (r ) = a Bloch function k Bonding 1 ik R AO e c φ (r R ) j Ai j Ai,k 1/ 2 N 21 Ai= basis set of AOs j = 1.....N unit cells at R j in unit cell
Ligand Ligand (e.g. O) (e.g. O) And the same e thing g for the d or orbita itals: s: e e g g Transition Transition Metal (e.g. Mn) Metal (e.g. Mn) e g and t 2g not e g and t 2g not equivalent in equivalent in z z octahedral (cubic) octahedral (cubic) environment environment y y z 2 2 2 2 x x - - y y 2 2 2 2 3z 3z - - r r t t x x 2g 2g zx y xy x yz Face-centered cubic — yz yz zx zx xy xy 12 nearest neighbors 22
Copper densities of states-total and by orbital type: ~Bonding ~Anti-Bonding More localized 3d-like Delocalized free electron-like 23
3s 2 3p 6 filled + 3d,4s CB 3d 2 4s 2 3d 3 4s 2 3d 5 4s 1 3d 6 4s 2 The ele lectr tron onic ic struc ructur tures es of the 3d 3d tran ansiti sition on meta tals ls — + Ex + Exchange! + Excha + hang nge! e! “rigid -band and model” + Flat “core - like” Ar 3s, 3p bands at -1.0- 1.5 Rydbergs 3d 7 4s 2 3d 8 4s 2 3d 10 4s 1 3d 10 4s 2 + + Ex Exchange! + + Ex Exchange! + Flat “core - like” Zn 3d bands at -0.8 Rydberg 24
The electronic bands and densities of states of ferromagnetic iron Exchange S = 2.2 Bohr splitting magnetons (Atomic iron: Spin-down (Minority) 2.0 Bohr Spin-up (Majority) magnetons) 4 x ½ = 2 25 k = 0 k = 0
Vacuum level Fe = 4.3 eV V 0,Fe =12.4 eV E exch -8.1 eV 26 Hathaway et al., Phys. Rev. B 31, 7603 (’85)
Fe: AN e: ANGLE AND GLE AND SPIN SPIN-RESOL RESOLVED VED SP SPECT ECTRA A RA AT T PO POIN INT 27
Ligand Ligand (e.g. O) (e.g. O) And the same e thing g for the d or orbita itals: s: yz plane e e g g + Transition Transition - Metal (e.g. Mn) Metal (e.g. Mn) + e g and t 2g not e g and t 2g not + - - equivalent in equivalent in z z octahedral (cubic) octahedral (cubic) + environment environment y y z 2 2 2 2 x x - - y y 2 2 2 2 3z 3z - - r r t t x x 2g 2g zx + - - y + - + xy + - + x - - + yz Face-centered cubic — xy yz yz zx zx xy 12 nearest neighbors 28
E.g. — Crystal field in Mn 3+ & Mn 2+ with negative octahedral ligands Group theoretical High-spin* /Low-spin* symmetry Mn 2+ 3d 5 Mn 3+ 3d 4 B 1 bonding - Bonding- O2p z Delocalized + A 1 + - J H > 0 10 Dq Exchange Xstal fld. + B 2 - Non/Weakly-Bonding- Localized bonding O2p z E - - + z + + + - - y x Jahn- yz plane Teller High-spin*: 10Dq << J H Low-spin*: 10Dq >> J H 29
SrTiO 3 and La 0.67 Sr 0.33 MnO 3 band structures and DOS La 0.67 Sr 0.33 MnO 3 - Half-Metallic SrTiO 3 -band insulator Ferromagnet Projected DOSs Spin-up Spin-down d xz +d yz d xy d z2 No spin Mn e g d x2-y2 Expt’l . bandgap down! d xz +d yz Expt’l . band 3.3 eV offset 3.0 eV Mn t 2g d xy O 2p Spin-up Plucinski, TBP Zheng, Binggeli, J. Phys. Spin-down with expt’l . band offset Cond. Matt. 21, 115602 (2009) Chikamatsu et al., Plucinski, TBP PRB 73, 195105 (2006); Plucinski, TBP
Mn 3d FM : T << T C Half-Metallic Ferromagnetism O 2p t 2g e g LDA theory - FM La 0.75 Ca 0.25 MnO 3 O 2p E gap t 2g t 2g J H t 2g PM : T > T C E F O 2p O 2p J H O 2p Mn 3d T > T C T << T C La 4f E gap Energy (eV) Pickett and Singh, PRB 53, 1146 (1996) Experiment- spin-resolved PS La 0.70 Sr 0.30 MnO 3 as thin film Park et al., Nature, PRB 392, 794 (1998)
SURF SURFACE E CE ELE LECTR CTRON ONIC ST IC STATE TES ( d character, localized) ( s,p character, delocalized) 33
Su Surface face states ates on Cu Cu(111) 1) Shockley surface State: s,p makeup Tamm surface state: 3d makeup 34
K k Vary to scan f ,|| f ,|| “The UPS Limit” 35
36
The Nobel Prize in Physics 2010 Andre Geim, Konstantin Novoselov …"for groundbreaking experiments regarding the two-dimensional material graphene" Photoelectron spectroscopy Bostwick et al., Nature Physics 3, 36 - 40 (2007)
The Soft X-Ray Spectroscopies Electron-out: surface sensitive Core PE e - Valence PE e - h CB E F VB h Core PE = photoemission = photoelectron spectroscopy XAS = x-ray absorption spectroscopy AES = Auger electron spectroscopy XES = x-ray emission spectroscopy 38 REXS/RIXS = resonant elastic/inelastic x-ray scattering
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