Soft X-ray Absorption and Resonant...
Transcript of Soft X-ray Absorption and Resonant...
Soft X-ray Absorption and Resonant Scattering
Di-Jing HuangNat’l Synchrotron Radiation Research Center, TaiwanDept. of Physics, Nat’l Tsing Hua University, Taiwan
Chairon 2008, SPring8, JapanOct. 3
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Soft X-ray Absorption and Resonant Scattering
1. Soft X-ray AbsorptionBasicExperimental SetupApplications- Chemical analysis- Orbital polarization- Magnetic Circular Dichroism
2. Resonant Soft X-ray Scattering IntroductionBasic of resonant X-ray scatteringExamples:Magnetic Transition of a Quantum Multiferroic LiCu2O2
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Soft x-ray: 250 eV ~ a few keV3
Interaction of photons with matter:
• lattice structure: arrangement of atoms • electronic states• magnetic order• excitations (electronic states or phonons)
Photoelectric effectSynchrotronRadiation
Transmission(absorption)
Inelastic Scattering
photoemissionReflected Photons
Fluorescence
Crystal
Bragg Diffraction
Scattering/diffraction
Photoabsorption
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core level
Continuum
Photon energy
Abs
orpt
ion
Atom
core level
Continuum
Solid
EF
EV
Photon energy
Abs
orpt
ion
Band resonance + atomic multiplet
atomicbackground
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( )2
f if i
d E E hd
σ δ ν∝ ⋅ ⋅ − −Ω ∑ Ψ ΨPAPhoto-absorption
2 3p d→
1s np→ K-edge XAS can be accurately described with single-particle methods.
L-edge XAS: the single-particle approximation breaks down and the pre-edge structure is affected by the core hole wave function. The multiplet effect exists.
Dipole approximation: 1 1ie i⋅ ≈ + ⋅ ≈k r k r( )i t i te eω ω⋅ − −≈k rA ε ε=
( )2f i
d f i E E hd
σ δ ν∝ ⋅ ⋅ − −Ω ∑ Pε
polarization of x-ray
ε ε εˆ[ , ] ( )f iim imf i f H i E E f i im f iω⋅ ≈ ⋅ = − ⋅ = ⋅ε P r r rQh h
ˆ[ , ] , if [ ( ), ] 0H V ri m
= =Pr rh
If ⋅k r < < 1 ,
1s
2s
3s
K
L1
M2,3
L2
L32p1/2
2p3/2
3p1/2, 3/2M1
( )2f if i E E hδ ν∝ ⋅ − −⋅∑ ε r
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ˆijM f i∝ ⋅ε r)(2 2
ifij EEMW +−= ωδπh
h
2p
3d
Dipole transition
1Δ ≡ − = ±f il l lΔ ≡ −( )l f im m m
( )θφθφθ cos,sinsin,cossinr̂ =
),(cos 0,134 φθθ π Y= ),(sin 1,13
8 φθθ πφ±
± =⋅ Ye i m
41,1 1, 1 1,2 03 2
r̂ ( )xx y yiz
i Y Y Yεε επ ε ε− +−
+⋅ = + +ε
sin cos sin sin cr̂ osx y ze e e= +⋅ +ε θ φ θ φ θ
Absorption probability:
L. circularly polarized
Y1,1: Δ ml = +1R. circularly polarized
Y1,-1: Δ ml = - 1
Δ ml = 0
5 1 62 3 2 3n nijM p d p d+∝ ⋅ε rFor 2p 3d:
Selection rule:
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•Two absorption “peaks” from 2p 3d:
3 22 /p
L3
d
1 22 /p
L2
•Absorption cross section is proportional to numbers of d holes and density of states in the core level.
L3
L2
Fe
L-edge XAS provides information on the chemical state, orbital symmetry, and spin state of materials. 8
2 64 3s d
2 74 3s d2 84 3s d 1 104 3s d
Each element has specific absorption energies. “finger print” element specific spectroscopy
Fe
CoNi
Cu
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soft x-ray absorption & scattering
TM: 2p 3dO: 1s 2p
direct, element-specific probing of electronic structure of TMO
TM 2p
In transition-metal oxides
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Soft X-ray Absorption and Resonant Scattering
1. Soft X-ray AbsorptionBasicExperimental SetupApplications- Chemical analysis- Orbital polarization- Magnetic Circular Dichroism
2. Resonant Soft X-ray Scattering IntroductionBasic of resonant X-ray scatteringExamples:Magnetic Transition of a Quantum Multiferroic LiCu2O2
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Incident light
transmitted light
Measurement of Soft X-ray absorption
electrometer
mesh
detector
I0
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Photoelectric absorption
2p1/2
2p3/2
3p1/2
3p3/2
3d
1s
2s
3s
K
L1
M
L2
L3
3d
K
L1
M
L2
L3
Fluorescent x-ray emission
3d
K
L1
M
L2
L3
Auger electron emission
Photoexcitation and Relaxation
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Auger electronshν
M1
L2
L3
Photoabsorption
2p
d
3s
Auger electrons
secondary electrons
Kinetic energy
Inte
nsity
(log
)
secondary electrons
PhotoelectronsAuger electrons
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Auger electrons(20 Å)
Fluorescence(1000 Å)
Incident light
transmitted light
electrometer
total electrons(40 ~ 50 Å)
Measurement of Soft X-ray absorption
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Soft X-ray Absorption and Resonant Scattering
1. Soft X-ray AbsorptionBasicExperimental SetupApplications- Chemical analysis- Orbital polarization- Magnetic Circular Dichroism
2. Resonant Soft X-ray Scattering IntroductionBasic of resonant X-ray scatteringExamples:Magnetic Transition of a Quantum Multiferroic LiCu2O2
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L-edge XAS provides information on the chemical state, orbital symmetry, and spin state of materials.
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Polarization of Synchrotron Radiation
Linearly polarized Left-handed circularly polarized
Right-handed circularly polarized
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Soft X-Ray Magnetic Circular Dichroism in Absorption
MCD is defined as the difference in absorption intensity of magnetic systems excited by left and right circularly polarized light.
−+ −≡ σσMCD
Right-handedcircularly polarized light preferentially excites spin-downelectrons.
Left-handed circularly polarized light preferentially excites spin-upelectrons.
For 2p3/2 3d
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Soft X-Ray Magnetic Circular Dichroism in Absorption
Soft X-ray MCD in absorption providesa unique means to probe:
element-specific magnetic hysteresisorbital and spin momentsmagnetic coupling.
There are two ways to obtain a MCD spectrum:1) Fixing M, measure XAS with left and right
circular lights.1)
2) Fixing the helicity of light, measure XAS with two opposite directions of M.
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Chen et al., PRB 48, 642 (1993)
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Nature 416, 301 (2001)
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Soft X-ray Absorption and Resonant Scattering
1. Soft X-ray AbsorptionBasicExperimental SetupApplications- Chemical analysis- Orbital polarization- Magnetic Circular Dichroism
2. Resonant Soft X-ray Scattering IntroductionBasic of resonant X-ray scatteringExamples:Magnetic Transition of a Quantum Multiferroic LiCu2O2
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Spin, Charge, and orbital ordering in correlated electron systems
Sternlieb et al. (1996)
La0.5Sr1.5MnO4
La1.6-xNd0.4SrxCuO4
J. Tranquda et al. (1995)
Moritomo et al. (1995)
Murakami et al.(1998)
C. H. Chen et al. (1998)
La1/3Ca2/3MnO3
Small valencedisproportionation !
ΔQ/Qtotal << 1
modulation vector k = 2π/λ
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Elastic x-ray scattering
2
qfdd
∝Ωσ
scattering form factor
kv
'kv
q k' k= −v vv
h h h
momentum transferqv
2 sin4 sin
q k θπ θλ
=
=
θ2
A volume element at will contribute an amount to the scattering field with a phase factor .
r3vd rvre iq ⋅v v jr
j(r )eiqq
jf ρ ⋅≡ ∑
v vv
Fourier transform of charge distribution.
rv
rk vv⋅ r'k vv ⋅
' kkvv
=k
q 'k
θ2θ
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0( , ) ( ) '( ) ''( )q qω ω ω= + +h h hsf f f i f
Resonant scattering
As the photon energy approaches the binding energy of one of the core-level electrons,
ωh
dispersion corrections
2222
222
)()()('Γ+−
−=
ωωωωωω
s
ssf
2222
2
)()(''
Γ+−Γ
−=ωωω
ωω
s
sf
Absorptionωh
'f
''f
' ''f f i f≡ +
4 Im( )fkπσ = −
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• With ω =E3d − E2p, fres enhanced dramatically and ordering of Ψ3d focused.
0, k εv v
, 'k εv v
2 pΨ
3dΨ
'q k k≡ −v vv
momentum transfer
modulation vector
h
0
3 3 2
32 23'
~( )
dik r ik r
resd d
p pd
p
re ref
E E iε ε
ω
⋅ ⋅⋅ ⋅ΨΨ Ψ
−
Ψ
− − Γ∑v vv vv v v v
h
Advantage of Resonant Soft X-ray Scattering
TM
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1.5 GeVNSRRC, Taiwan
UHV two-circlediffractometer
EPU
Setup of Soft X-ray Scattering
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2 2
2 2 22
2 22 )int (( ) ( )e e
j jmc me e
j jmc mcj
cj j j
AA r A P AH At
s s+ ⋅ − ⋅∇ ×=∂
− ⋅ ×∂∑ ∑∑ ∑ hh
2
222
int
2
2 2
2
2 2 ' 'j jiq
j
rq r
j
ijf ec e
V mi f
f H i
mcce s ii ε ε
πσ
π π ε εωω
⎛ ⎞= ⎜ ⎟
⎝ ⎠− ⋅ ×⋅∑ ∑ h
h
h
h
kinetic energy m.B SO
Non-resonant
mag 32
charge
~ ~ 10f
f mcω −h 6
e
mag 10~ −
σσ
for ω ~ 600 eV
X-ray magnetic scattering
Resonant
int i2
nt2 ( )n i n
i f
f H n n HE
iE
E Eπσ δ
ω −−
+∑h
h
Blume, J. Appl. Phys. (1985)
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h
Resonant X-ray magnetic scattering
1±=Δ lm
electric dipole transitions
1=Δ lm
0ε ε
F1,1 F1,-1
'kv
kvq σ=0ε
π=ε
[ ]001
[ ]100
[ ]010
σπ ×
scattering amplitudes )(ˆ)εε(83
1,11,10*
−−⋅×−= FFzif resmag π
λHannon et al., PRL(1988)
As a result of spin-orbit and exchange interactions,magnetic ordering manifests itself in resonant scattering.
1−=Δ lm
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Resonant soft x-ray magnetic scattering:
•Cross section comparable to that of neutron scattering.
•Good k resolution (Δk < 0.0005 Å-1)
•Spectroscopic information.
•Limited to a small k space, less bulk sensitive.
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Soft X-ray Absorption and Resonant Scattering
1. Soft X-ray AbsorptionBasicExperimental SetupApplications- Chemical analysis- Orbital polarization- Magnetic Circular Dichroism
2. Resonant Soft X-ray Scattering IntroductionBasic of resonant X-ray scatteringExamples:Magnetic Transition of a Quantum Multiferroic LiCu2O2
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Magnetism: ordering of spins
Ferroelectricity: polar arrangement of chargesMagnetization can be induced by H field
Electric polarization can be induced by E field
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Induction of magnetization by an electric field; induction of polarization by a magnetic field.
- first presumed to exist by Pierre Curie in 1894 on the basis of symmetry considerations
However, the effects are typically too small to be useful in applications!
Magnetoelectric effect
Multiferroics: materials exhibiting ME couplingCr2O3BiMnO3BiFeO3…..
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Two contrasting order parameters
:
⇒ − ⇒ −
⇒
v
v
v
vt t M M
P P
Magnetization: time-reversal symmetry broken
Polarization: inversion symmetry broken
: , ⇒ − ⇒ − ⇒v vv v v v
r P MP Mr P qr=v r
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2 0
2 5
3 0
3 5
0 1 0 2 0 3 0 4 0
-4 0
-2 0
0
2 0
4 0
0
( b )
( a )
0 T 1 T 3 T 5 T 7 T 9 T
E //b , H / /a ( F C )1 k H z
w a r m in g
ε
P1
P2T
P
0
40
-80
40
P1
P2T
P
0
40
-80
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E p o le / /+ bH //a ( Z F C )
P (n
C/cm
2 )
T ( K )
• 3 transitions on cooling. • Magnetic field induces a sign reversal
of the electric polarization.
TbMn2O5 Nature, 429, 392 (2004)
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Recently discovery in the coexistence and gigantic coupling of antiferromagnetism and ferroelectricity in frustrated spin systems such RMnO3 and RMn2O5(R=Tb, Ho , …)
revived interest in “multiferroicity”
•TC < TN• Frustrated magnetic systems.
TbMnO3: Kimura et al., Nature 426, 55, (2003)TbMn2O5: Hur et al., Nature 429, 392 (2004)
Magnetism and ferroelectricity coexist in materials called “multiferroics.”
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LiCu2O2O2-
Cu2+
Cu1+
Li1+
orthorhombic, Pnmaa=5.734 Å, b=2.856 Å, c=12.415 Å
Qausi-1D spin ½ chain: •Characterization of the ground state?•Multiferroicity
(Park et al. PRL98, 057601; Seki et al., cond-mat 0810.2533)
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Seki et al., PRL (2008)
Two transitions ?
C (J
/mol
K)
Masuda et al., PRL (2004)
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Masuda et al., PRL (2004)
(1/ 2, ,0)q ζ=r
a
b
J1
J2
94°
1( )n ne S SP +∝ × ×rrr r
along the a axis(1/ 2, ,0)q ζ=
r
in units of 2 2 2( , , )a b cπ π π
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2p3/2
930 eV
3d
Cu2+
LiCu2O2 (100) single crystal
Resonant soft x-ray magnetic scattering
5 mm
Correlation length ξ = 1/HWHM
T = 10K: ξa = 690 Å ξb = 2100 Å42
Masuda et al., PRL (2004)
(1/ 2, ,0)q ζ=r
qa (2p/a)
qb (2p/b)
non-zero scatteringintensity above TN
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cleaved LiCu2O2(001) 5 mm
23.5 K transition temperature of the precursor phase
onset of the long-rangespin ordering and induced P
21.5 K
ξab: in-planecorrelation length
intensity( ,1)abq q=
r
ξc: correlation length along the c-axis
SW Huang et al., PRL (2008)44
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,( ,1)a bq q=rq1
q2
•There is an in-plane short-range AFM ordering above TN
•extension of the zero-temperature AFM ordering
• spin coupling along the c axis is essential for inducing P.
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2 /( ) e πρξ ∝ S Bk TT
•The ground state of LiCu2O2 exhibits a long range AFM ordering.
Above TN, in-plane correlation
averageJ ~ 4.25 meV
• The spin coupling along the c axis is essential for inducing P.
renormalized classical behavior
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END
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Appendix: Basic of Magnetic Circular Dichroism in X-ray Absorption
Considering L-edge 2p3/2 3d absorption, and ignoring the spin-orbit interaction in the 3d bands,
2p3/2
3d
1/3 1/3 1/6
m j = 3/2 1/2 -1/2 -3/2L3
m l = 2 1 0 -1 -2
σ+=5/6
22
1,1( )2
,lm jx yi
R r Y Y j mε ε
σ +
−∝ ⋅
2ˆ, r ,l jl m j mσ ∝ ⋅ε
1 1/3 1/18
m j = 3/2 1/2 -1/2 -3/2L3
m l = 2 1 0 -1 -2
Left-handed circularly polarized light preferentially excites spin-up electrons.
For left-handed circular light
radial part1/6 1/3 1/3
1/18 1/3 1
σ−=25/18
22
1, 1( )2
,x ylm jR r Y Y j m
iε εσ −−
+∝ ⋅
For light-handed circular light
Right-handed circularly polarized light preferentially excites spin-down electrons.
σ+=25/18σ−=5/6
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↑= 1,123
23 , Y
↓+↑= 1,131
0,132
21
23 , YY
↓+↑= −−
0,132
1,131
21
23 , YY
↓= −−
1,123
23 , Y
22
1, 1( ) ,2
x ylm j
iR r Y Y j m
ε εσ ± ±∝ ⋅
m
2
3 1 12,2 1,1 2 2 3,
2x y
j
iY Y j m
ε εσ +
−∝ = = =
2ˆ, r ,l jl m j m∝ ⋅εσ
( )θφθφθ cos,sinsin,cossinr̂ =
),(cos 0,134 φθθ π Y= ),(sin 1,13
8 φθθ πφ±
± =⋅ Ye i m
41,1 1, 1 1,03 2 2
r̂ ( )x y x yi izY Y Yε ε ε επ ε− + +
−⋅ = + +ε
r̂ sin cos sin sin cosx y ze e e⋅ = + +ε θ φ θ φ θ
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1,11,12,231
21
23
1,12,2 , ==== YYYmjYY jQ
∑+
−=
=21
21
2211)|( 2211
ll
llllmmlml YlmmlmlYY
2211
21
),|( 2211 mlmlmm
lm YYmlmlmlY ∑=
Clesbsch-Gordan coefficients
1/3 1/3 1/6
1/18 1/3 1
m j = 3/2 1/2 -1/2 -3/2
j=3/2
L3
m l = 2 1 0 -1 -2
2
3 1 12,0 1, 1 2 2 18,
2x y
j
iY Y j m
ε εσ − −
+∝ = = =
.....0,261
1,11,1 +=− YYY181
1,11,10,231
21
23
1,10,2 , ==== −− YYYmjYY jQ 2,21,11,1 YYY = 50
↑= 1,123
23 , Y
↓+↑= 1,131
0,132
21
23 , YY
↓+↑= −−
0,132
1,131
21
23 , YY
↓= −−
1,123
23 , Y
22
1, 1( ) ,2
x ylm j
iR r Y Y j m
ε εσ ± ±∝ ⋅
m
2
3 1 12,1 1,1 2 2 3,
2x y
j
iY Y j m −
+
−∝ = = =
ε εσ
2ˆ, r ,l jl m j mσ ∝ ⋅ε
41,1 1, 1 1,03 2 2
r̂ ( )x y x yi izY Y Yε ε ε επ ε− + +
−⋅ = + +ε
3 1 2 12,1 1,1 2,1 1,1 1,02 2 3 3, −= = = =Q jY Y j m Y Y Y
∑+
−=
=21
21
2211)|( 2211
ll
llllmmlml YlmmlmlYY
2211
21
),|( 2211 mlmlmm
lm YYmlmlmlY ∑=
Clesbsch-Gordan coefficients
1/3 1/3 1/6
1/18 1/3 1
m j = 3/2 1/2 -1/2 -3/2
j=3/2
L3
m l = 2 1 0 -1 -2
2
3 1 12, 1 1, 1 2 2 3,
2x y
j
iY Y j m
ε εσ −
− − −
+∝ = = =
.....1,221
0,11,1 += YYY
3 1 2 12, 1 1, 1 2, 1 1, 1 1,02 2 3 3, −
− − − −= = = =Q jY Y j m Y Y Y
.....1,221
0,11,1 += −− YYY51
↑= 1,123
23 , Y
↓+↑= 1,131
0,132
21
23 , YY
↓+↑= −−
0,132
1,131
21
23 , YY
↓= −−
1,123
23 , Y
22
1,1( ) ,2
x ylm j
iR r Y Y j m
ε εσ +
−∝ ⋅
2
3 1 12,1 1,1 2 2 3,
2x y
j
iY Y j m
ε εσ +
−∝ = = =
3 1 2 12,1 1,1 2,1 1,1 1,02 2 3 3, jY Y j m Y Y Y= = = =Q
∑+
−=
=21
21
2211)|( 2211
ll
llllmmlml YlmmlmlYY
2211
21
),|( 2211 mlmlmm
lm YYmlmlmlY ∑=
Clesbsch-Gordan coefficients
1 1/3 1/18
m j = 3/2 1/2 -1/2 -3/2
j=3/2
L3
m l = 2 1 0 -1 -2
.....0,261
1,11,1 +=− YYY3 1 1 1
2,0 1,1 2,0 1,1 1, 12 2 3 18, jY Y j m Y Y Y −= = = =Q
2,21,11,1 YYY =
1/3 1/3 1/6
m j = 3/2 1/2 -1/2 -3/2
j=3/2
L3
m l = 2 1 0 -1 -2
.....1,221
0,11,1 += YYY2
3 1 12,0 1,1 2 2 18,
2x y
j
iY Y j m
ε εσ −
+
−∝ = = =
11,1 1, 1 2,06 .....Y Y Y− = +
2
3 32,2 1,1 2 2, 1
2x y
j
iY Y j m
ε εσ +
−∝ = = =
3 32,2 1,1 2,1 1,1 1,12 2, 1jY Y j m Y Y Y= = = =Q
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