So#	  X-­‐ray	  Absorp.on	  Spectroscopy	  	  Di-­‐Jing	  Huang	  	  djhuang@nsrrc.org.tw	  Nat’l	  Synchrotron	  Radia.on	  Research	  Center,	  Taiwan	  Dept.	  of	  Physics,	  Nat’l	  Tsing	  Hua	  University,	  Taiwan	  Cheiron	  2013,	  Oct.	  3	  	  1	  So#	  X-­‐ray	  Absorp.on	  Spectroscopy	  Basic	  Experimental	  Setup	  Unique	  Features	  of	  So#	  X-­‐ray	  absporp.on	  	  -­‐ Chemical	  analysis	  -­‐ Orbital	  polariza.on	  -­‐ Magne.c	  Circular	  Dichroism	  	  Applica.ons	  - 	   Magne.c	  materials	  - Energy	  materials	  2	  1

So#	  x-­‐ray:	  250	  eV	  ∼	  a	  few	  keV	  3Interac.on	  of	  photons	  with	  maZer:	  Photoelectric	  eﬀect	  Photoabsorp.on	  ScaZering/diﬀrac.on	  	  	  	  	  Ioniza)on	  photoemission	  Reﬂec)on	  Synchrotron	  Fluorescence	  Radia.on	  Crystal	  Inelas.c	  	  ScaZering	  ScaZering/Bragg	  Diﬀrac.on	  •	  la_ce	  structure:	  arrangement	  of	  atoms	  	  	  •	  electronic	  states	  •	  magne.c	  order	  •	  excita.ons	  (electronic	  states	  or	  phonons)	  Transmission	  	  (absorp.on)	  42Basics	  of	  X-­‐ray	  absorp.on	  I 0 I (z )Intensity	  decrease	  due	  to	  absorp)on	  by	  dz	  	  dz

−dI(z) = I(z) ρ dzA = I(z)µ dz#	  of	  atoms/area	  	  zarea	  absorp)on	  coeﬃcient:	  	  µ = ρσ a−dI ( z ) = µ I ( z ) dz

I ( z ) − dI ( z )σa:	  absorp)on	  cross	  sec)on	  dI(z)= - µ I(z)dz

I ( z ) = I 0e − µ zThe	  wave	  propaga)ng	  in	  the	  medium	  is	  	  index	  of	  refrac)on	  E 0 ei ( nkz ) = E 0 ei (1−δ ) kz e − βkzn ≡ 1 − δ + iβ(δ	  and	  β	  are	  real	  numbers)	  µ = 2β k I∝ E42

δ , β << 15Fe
δβ3x10-32
10-1-2

400

500

600
700
800
Photon Energy (eV)

900

1000

63

X-ray Absorption spectroscopy
An x-ray absorption (XAS) process excites one core electron to
the unoccupied state and a core hole is created.
eA ⋅ p
The interaction Hamiltonian H I =m
A=ε̂ ei(k⋅r−ωt )ε polarization of x-ray

Absorption probability

W=22π
M ij δ (ω − E f + Ei )
M ij = f me A ⋅ i ∇ i
Dipole approximationk ⋅ r << 1,eik⋅r ≈ 1

A ≈ ε̂ e −iωt

For 2p à 3d:

M ij ∝ 2 p5 3d n+1 ε ⋅ r 2 p6 3d n

M ij ∝ f ε ⋅ r i
7Atom	  Con.nuum	  Absorp.on	  EV	  core	  level	  Photon	  energy	  Solid	  EF	  core	  level	  Absorp.on	  Con.nuum	  Band	  resonance	  +	  atomic	  mul.plet	  atomic	  background	  Photon	  energy	  8	  4

Dipole	  allowed	  transi.ons	  :	   Δl = ±1, Δml = ±1, 0;

Δs = 01s → np	  	  	  	  	  K-­‐edge	  XAS	  can	  be	  accurately	  described	  with	  single-­‐par.cle	  methods.	  

2 p → 3d	  	  	  	  	  	  L-­‐edge	  XAS:	  the	  single-­‐par.cle	  approxima.on	  breaks	  down	  and	  the	  pre-­‐edge	  structure	  is	  aﬀected	  by	  the	  core	  hole	  wave	  func.on.	  The	  mul.plet	  eﬀect	  exists.	  

M2,3
M1

3p1/2, 3/2
3sL3L22p3/2

L12sK1s

2p1/2

9Measurement	  of	  So#	  X-­‐ray	  Absorp.on	  I0incident	  light	  electrometer	  mesh	  transmiZed	  light	  detector	  105

Photoexcita.on	  and	  Relaxa.on	  	  Photoelectric	  absorp.on	  	  M	  Auger	  electron	  emission	  	  	  Fluorescent	  x-­‐ray	  emission	  	  	  3d	  3d	  3d	  3p3/2	  3p1/2	  M	  M	  L3	  L2	  L3	  L2	  2s	  L1	  L1	  1s	  K	  K	  3s	  L3	  L2	  L1	  K	  2p3/2	  2p1/2	  11	  Auger	  electrons	  Auger	  electrons	  hn	  secondary	  electrons	  Photoabsorp)on	  Intensity	  (log)	  d	  secondary	  electrons	  M1	  3s	  L3	  L2	  2p	  Auger	  electrons	  Kine)c	  energy	  Photoelectrons	  12	  6

Measurement of Soft X-ray Absorption
total electrons(40 ~ 50 Å)

Incident light
I0electrometer	  Fluorescence(1000 Å)transmitted lightAuger electrons(20 Å)
13•Two	  absorp)on	  “peaks”	  from	  2p	  à	  3d:	  L3Fed	  L3	  2 p3 / 2L2L2	  2 p1/ 2•Absorp.on	  cross	  sec.on	  is	  propor.onal	  	  	  	  to	  numbers	  of	  d 	  holes	  and	  density	  of	  	  	  	  states	  in	  the	  core	  level.	  
• L-­‐edge	  XAS	  provides	  informa.on	  on	  the	  chemical	  state,	  orbital	  symmetry,	  and	  spin	  state	  of	  materials.	  	  	  
1474 s 2 3d 6Fe

4 s 2 3d 7
Co

4 s 2 3d 8Ni

4 s1 3d 10Cu

Each	  element	  has	  speciﬁc	  absorp.on	  energies.	  
“ﬁnger	  print”	  à	  element	  speciﬁc	  spectroscopy	  15L-edge XAS provides information on
the chemical state, orbital symmetry,and spin state of materials.

168Mn → Mn
hole doping:
LaMnO3 à La1-xSrxMnO33+4+La3+Sr2+

La0.7Ce0.3MnO3 electron doping?
Mn 3+ → Mn 2+
Mitra et al.,4+ PRB 67, 92404 (2003)
Mn
4+Mn

2 p 5 3d 6

15Udd

6U cd

Mn 2+
3dU ddMnO2
MnO2

2 p 5 3d 52+
3+2+3+Mn
Mn
Mn
Mn

5U cd

hν	3+
3d 4
10Udd Mn

510UddLaMnO3
LaMnO33+Mn
3+Mn

hν'6Udd• Coulomb interactions of 3d +core-hole valence interaction

2+2+MnMn

MnOMnOhν '− hν = U cd −U dd

High-Temperature Superconducting Cu oxides
La2CuO4(Cu2+ : 3d9)
3dCuOLa/Srx2-y2eg
crystalfieldt2g

3z2-r2
dxydyz, dzx

Sr doping: La2CuO4 à La2-xSrxCuO4
La3+Sr2+
hole doping:
Cu2+àCu2+ +O 2p holes

9Orbital Characters of Doped Holes in La2-xSrxCuO4

σ E⊥ĉ >> σ E//ĉeg
3dx2-y2

3z2-r2t2g

L3L2

dxydyz, dzxChen et al. PRL 68, 2543 (1992)	  L-­‐edge	  XAS	  provides	  informa.on	  on	  the	  chemical	  state,	  orbital	  symmetry,	  and	  spin	  state	  of	  materials.	  	  	  20	  10

Polariza.on	  of	  Synchrotron	  Radia.on	  Linearly	  polarized	  Right-­‐handed	  	  circularly	  polarized	  LeX-­‐handed	  	  circularly	  polarized	  21	  So#	  X-­‐Ray	  Magne.c	  Circular	  Dichroism	  in	  Absorp.on	  For	  2p3/2à3d	  Right-­‐handed	  circularly	  polarized	  light	  preferen.ally	  excites	  spin-­‐down	  electrons.	  

Le#-­‐handed	  circularly	  polarized	  light	  preferen.ally	  excites	  spin-­‐up	  electrons.	  

3dL3	  à3d	  For	  spin	  up,	  	  	  le#-­‐handed	  =	  5/3	  right-­‐handed	  For	  spin	  down	  	  le#-­‐handed	  =	  3/5	  right-­‐handed	  2211

So#	  X-­‐Ray	  Magne.c	  Circular	  Dichroism	  in	  Absorp.on	  For	  2p3/2à3d	  Right-­‐handed	  circularly	  polarized	  light	  preferen.ally	  excites	  spin-­‐down	  electrons.	  

3dLe#-­‐handed	  circularly	  polarized	  light	  preferen.ally	  excites	  spin-­‐up	  electrons.	  

MCD ≡ σ + − σ −MCD	  is	  deﬁned	  as	  the	  diﬀerence	  in	  absorp)on	  intensity	  of	  magne)c	  systems	  excited	  by	  leX-­‐	  and	  right-­‐handed	  circularly	  polarized	  light.	  

orbital	  moment	  ∝	  (A-­‐B)	  Spin	  moment	  ∝	  (A+2B)	  23So#	  X-­‐Ray	  Magne.c	  Circular	  Dichroism	  in	  Absorp.on	  So#	  X-­‐ray	  MCD	  in	  absorp.on	  provides	  a	  unique	  means	  to	  probe:	  element-­‐speciﬁc	  magne.c	  hysteresis	  	  orbital	  and	  spin	  moments	  magne.c	  coupling.	  
There	  are	  two	  ways	  to	  obtain	  a	  MCD	  spectrum:	  M,	  measure	  XAS	  with	  le#	  and	  right	  1) 	  Fixing	  	  	  circular	  lights.	  
2) Fixing	  the	  helicity	  of	  light,	  measure	  XAS	  with	  two	  opposite	  direc.ons	  of	  M.	  	  
24

12Chen et al.,
PRB 48, 642 (1993)

25

Nature 416, 301 (2001)

2613

27

14

References:F. de Groot & A. Kotani, “Core Level Spectroscopy ofSolids” (CRC Press 2008)
Phillip Willmott, “An Introduction to Synchrotron Radiation Techniques and Applications” (Wiley 2011)
Jens Als-Nielsen and Des McMorrow, “Elements of Modern X-rayPhysics” (Wiley & Sons)

29

Thank	  you!	  

30

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