Slides from 2012 in videos assigned for lectures on 8 and 10 - - PowerPoint PPT Presentation

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.

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SAME SUBSHELL COUPLING + TOTAL L,S”MONOPOLE” (N-1)e- SHAKE-UP/ SHAKE-OFF ”MONOPOLE” 1e- DIPOLEd/d "Basic Concepts of XPS" Chapter 3

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SAME SUBSHELL COUPLING + TOTAL L,S”MONOPOLE” (N-1)e- SHAKE-UP/ SHAKE-OFF ”MONOPOLE” 1e- DIPOLEd/d "Basic Concepts of XPS" Chapter 3

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SAME SUBSHELL COUPLING + TOTAL L,S”MONOPOLE” (N-1)e- SHAKE-UP/ SHAKE-OFF ”MONOPOLE” 1e- DIPOLEd/d "Basic Concepts of XPS" Chapter 3

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SAME SUBSHELL COUPLING + TOTAL L,S”MONOPOLE” (N-1)e- SHAKE-UP/ SHAKE-OFF ”MONOPOLE” 1e- DIPOLEd/d "Basic Concepts of XPS" Section 3.D.

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SAME SUBSHELL COUPLING + TOTAL L,S”MONOPOLE” (N-1)e- SHAKE-UP/ SHAKE-OFF ”MONOPOLE” 1e- DIPOLEd/d "Basic Concepts of XPS" Section 3.D. Section 6.D.

tot

v0

e inc

(c)

f

K

f

k 0 = reference wave j = object wave

(a) (b)

CO C1s 500 eV

• ref. intens.

I0  |0|2

Photo toele electr ctron n Dif iffrac fraction ion

0.65 5 Å Forward d Scat atter tering ng

X-ray ay Photoe

• elect

ectron ron Di Diffr fract action: n:1ML 1ML FeO on Pt(1 (111) 11) (a) (b)







9 PLUS SPIN: ()= )= msi

si = +½ = 

()= )= msi

si = -½ = 

() () () () ms = = msf

sf - msi si

= 0 !

10

- = antibonding

 1sa - 1sb

+ = bonding  1sa + 1sb The quantum mechanics of covalent bonding in molecules: H2

+ with one electron

=R Total Energy

antibonding

11 a.u.

• u. = -16.

6.16 16 eV (Com

• mpar

pare e – 13. 3.61 61 for r H atom

• m 1s)

a.u.

• u. = +7.21

1 eV

 negat ative (occupied) upied)  positive (unoc

• ccupi

upied) ed)

Bonding Anti-Bonding

anti

MO  1sa - 1sa

bonding

MO  1sa + 1sa  

Ha Hb

12 36

The LCAO or tight-binding picture for CO:

Chemist’s picture (no core): C O

x x X x      

NON/WEAKLY CORE:

13

THE ELECTRONS IN HF (OR HCl): ionic molecules

F H 1 E = -25.6 a.u.

F 1s core 12 HF: F1s222321x

2 1y 2

1 e- 9 e-

14

"Basic Concepts of XPS" Chapter 3 PLUS SPIN: ()= )= msi

si = +½ = 

()= )= msi

si = -½ = 

() () () () ms = = msf

sf - msi si

= 0 !

ˆ   ^  ^

PLUS SPIN: ()= )= msi

si = +½ = 

()= )= msi

si = -½ = 

() () () () ms = = msf

sf - msi si

= 0 !

ˆ  ˆ   ^  ^

ˆ   ^  ^

15

The free-electron solid at absolute zero

2 2 2 e

k E(k ) 3.81(k(in )) (in eV ) 2m  

Å-1 = the density of states

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.

17

L

18

Aluminum—fcc, a = 4.05 Å 1s22s2 2p63s2 3p1 Electronic bands and density of states for “free-electron” metals - Rydberg = 13.605 eV a 2/a =1.55Å-1 Lithium—bcc, a = 3.49 Å 1s22s1 a 2/a =1.8Å-1 kx

2 2 x x

(k ) E(k ) 2m 

2 2 x x

(k ) E(k ) 2m 

19

Electronic bands and density of states for a semiconductor-Germanium— 1s22s2 2p63s2 3p63d104s24p2 Bonding (filled at T = 0) Anti- Bonding (empty at T = 0) EF

Vacuum Level Work Function,  = 4.8 eV Inner Potential, V0  4.8+0.3+12.6 = 17.7 eV

20

V0,Cu =13.0eV

• 8.6 eV

Vacuum level

The electr tron

• nic

ic str tructure cture of a transiti nsition

• n meta

tal —fcc cc Cu

Cu = 4.4 eV = work function Experime rimenta ntal points ts from m angle-reso resolved ved photoelectron ctron spectro ctroscop scopy (more re later) r)

21

1x 3 4 1y 5 – + ++ – +

Atomic orbital makeup

,

( ) ( )

MO AO j Ai j Ai Atoms A Orbitals i

r c r    

1x 3 4 1y 5 – + ++ – +

Atomic orbital makeup

1x 3 4 1y 5 – + ++ – + 1x 3 4 1y 5 – + ++ – +

Atomic orbital makeup

,

( ) ( )

MO AO j Ai j Ai Atoms A Orbitals i

r c r    

Solid state tight-binding approach

j j

BF k ik R AO Ai j Ai,k 1/ 2 Ai= basis set of AOs j = 1.....N unit cells at R in unit cell

φ (r ) = a Bloch function 1 e c φ (r R ) N



 

 

Crystal potential-1D Tight-binding wave function Atomic orbitals

j-1 j j+1

j

R

Bonding Anti- Bonding

Ej

Molecular

• rbital

approach

22

And the same e thing g for the d or

• rbita

itals: s:

e

g

t

2g

3z

2

• r

2

x

2

• y

2

yz zx xy x y z

e

g

t

2g

3z

2

• r

2

x

2

• y

2

yz zx xy x y z

eg and t2g not equivalent in

• ctahedral (cubic)

environment

Transition Metal (e.g. Mn) Ligand (e.g. O)

eg and t2g not equivalent in

• ctahedral (cubic)

environment

Transition Metal (e.g. Mn) Ligand (e.g. O)

Face-centered cubic— 12 nearest neighbors

x y z

xy yz zx

23

Copper densities of states-total and by orbital type:

~Bonding ~Anti-Bonding

More localized 3d-like Delocalized free electron-like

24

The ele lectr tron

• nic

ic struc ructur tures es of the 3d 3d tran ansiti sition

• n meta

tals ls—  “rigid-band and model”

3s23p6 filled + 3d,4s CB 3d24s2 3d34s2 3d54s1 3d64s2 3d74s2 3d84s2 3d104s1 3d104s2 + Flat “core- like” Zn 3d bands at -0.8 Rydberg + Flat “core- like” Ar 3s, 3p bands at -1.0- 1.5 Rydbergs + + Ex Exchange! + + Excha hang nge! e! + + Ex Exchange! + + Ex Exchange!

25 k = 0 k = 0

Spin-down (Minority) Spin-up (Majority) The electronic bands and densities of states of ferromagnetic iron Exchange splitting S = 2.2 Bohr magnetons (Atomic iron: 2.0 Bohr magnetons)

4 x ½ = 2

26 Hathaway et al., Phys. Rev. B 31, 7603 (’85) Eexch

V0,Fe =12.4 eV Vacuum level Fe = 4.3 eV

• 8.1 eV

27

Fe: AN e: ANGLE AND GLE AND SPIN SPIN-RESOL RESOLVED VED SP SPECT ECTRA A RA AT T  PO POIN INT

28

And the same e thing g for the d or

• rbita

itals: s:

e

g

t

2g

3z

2

• r

2

x

2

• y

2

yz zx xy x y z

e

g

t

2g

3z

2

• r

2

x

2

• y

2

yz zx xy x y z

Face-centered cubic— 12 nearest neighbors

x y z

xy yz zx

• +
• +
• +
• +

+

• +
• +

+

• +
• +

eg and t2g not equivalent in

• ctahedral (cubic)

environment

Transition Metal (e.g. Mn) Ligand (e.g. O)

eg and t2g not equivalent in

• ctahedral (cubic)

environment

Transition Metal (e.g. Mn) Ligand (e.g. O)

yz plane

29

E.g.—Crystal field in Mn3+ & Mn2+ with negative octahedral ligands Mn3+ 3d4

Bonding- Delocalized Non/Weakly-Bonding- Localized

10 Dq Xstal fld. JH > 0 Exchange

Jahn- Teller x y z

Mn2+ 3d5

High-spin* High-spin*: 10Dq << JH /Low-spin* Low-spin*: 10Dq >> JH

+

• A1

B1 E B2 Group theoretical symmetry  bonding

+

• +

 bonding

+

• +
• +

+

• O2pz

O2pz

• yz plane

Chikamatsu et al., PRB 73, 195105 (2006); Plucinski, TBP Plucinski, TBP with expt’l. band offset Zheng, Binggeli, J. Phys.

• Cond. Matt. 21, 115602 (2009)

Plucinski, TBP

La0.67Sr0.33MnO3- Half-Metallic Ferromagnet

SrTiO3 and La0.67Sr0.33MnO3 band structures and DOS

Projected DOSs Spin-down

Spin-up Spin-down Mn eg Mn t2g

Expt’l. band

• ffset 3.0 eV

Expt’l. bandgap 3.3 eV

dxz+dyz dxy dz2 dx2-y2 O 2p Spin-up dxz+dyz dxy

SrTiO3-band insulator No spin down!

Experiment- spin-resolved PS La0.70Sr0.30MnO3 as thin film

Park et al., Nature, PRB 392, 794 (1998)

T << TC T > TC

Half-Metallic Ferromagnetism

O 2p  O 2p 

Egap JH

Mn 3d    EF O 2p  O 2p      FM : T << TC PM : T > TC Mn 3d t2g eg



Energy (eV)

Pickett and Singh, PRB 53, 1146 (1996)

O 2p La 4f 

Egap 

 

JH

LDA theory- FM La0.75Ca0.25MnO3

t2g t2g t2g

33

SURF SURFACE E CE ELE LECTR CTRON ONIC ST IC STATE TES

(d character, localized) (s,p character, delocalized)

34

Shockley surface State: s,p makeup Tamm surface state: 3d makeup

Su Surface face states ates

• n Cu

Cu(111) 1)

35

“The UPS Limit”

Vary  to scan 

,|| ,|| f f

K k 

36

The Nobel Prize in Physics 2010 Andre Geim, Konstantin Novoselov …"for groundbreaking experiments regarding the two-dimensional material graphene"

Bostwick et al., Nature Physics 3, 36 - 40 (2007)

Photoelectron spectroscopy

38

The Soft X-Ray Spectroscopies

Core VB EF CB e- e- Valence PE PE = photoemission = photoelectron spectroscopy XAS = x-ray absorption spectroscopy AES = Auger electron spectroscopy XES = x-ray emission spectroscopy REXS/RIXS = resonant elastic/inelastic x-ray scattering h h

Electron-out: surface sensitive

Core PE

39

hv i(bound) f(free) Vacuum MATRIX ELEMENTS IN THE SOFT X-RAY SPECTROSCOPIES: DIPOLE LIMIT  Photoelectron spectroscopy/photoemission:

2

ˆ (1) (1)

f i

I e r    



40

41

"Basic Concepts of XPS" Figure 1

42

43

 NO. ATOMS  QUANTITAT NTITATIV IVE SURFACE FACE ANALYSIS IS

44 36

The LCAO or tight-binding picture for CO:

Chemist’s picture (no core): C O

x x X x      

NON/WEAKLY CORE:

45

Valence-level Photoelectron spectra of CO adsorbed on various transition metal surfaces

46

– + Ni Ni 3d 3dxy

xy

 “back bond” + + – –

Zangwi will, l,

• p. 307,

, plus PRL 55, 2618 (’85)

Theoretical Calculations

• f charge

density for CO bound to Ni(001)- “on- top”: O | C | Ni CO CO 5 Ni Ni 3d 3dz  bond bond + – – – – + CO CO 2 = = * De Density ty gain

Ni Ni

2

+ –

47

Vibrational fine structure

Kimura et al., “Handbook of HeI Photoelectron Spectra”

48

SAME SUBSHELL COUPLING + TOTAL L,S”MONOPOLE” (N-1)e- SHAKE-UP/ SHAKE-OFF ”MONOPOLE” 1e- DIPOLEd/d "Basic Concepts of XPS" Chapter 3

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VIBR VIBRATI TION ONAL AL ST STRUCTURE UCTURE IN IN VALE ALENCE NCE-LE LEVEL VEL (MO) (MO) SP SPECTRA ECTRA Dia Diatomic A tomic A-B B example xample (Also a (Also applie pplies t s to

• cor

core- le level emiss el emission ion if if equilibrium dis equilibrium distance tance changes on f hanges on for

• rming

ming cor core hole) e hole)

50

VIBR VIBRATI TION ONAL AL ST STRUCTURE IN UCTURE IN VALENCE ALENCE-LEVEL ( LEVEL (MO MO) S ) SPE PECTRA CTRA

51

SAME SUBSHELL COUPLING + TOTAL L,S”MONOPOLE” (N-1)e- SHAKE-UP/ SHAKE-OFF ”MONOPOLE” 1e- DIPOLEd/d "Basic Concepts of XPS" Chapter 3.D.

spin-orbit +