Inelastic XInelastic X--ray Scattering by ray Scattering ... · 1018 t ons/s/mrad 2 /mm 2 /0. ......

Inelastic XInelastic X--ray Scattering by ray Scattering by Electronic ExcitationsElectronic ExcitationsElectronic ExcitationsElectronic Excitations

Th T i B mli P p tiTh T i B mli P p tiThe Taiwan Beamline PerspectiveThe Taiwan Beamline Perspective(BL12XU@SPring(BL12XU@SPring--8)8)

Yong CaiYong CaiggSPring-8 GroupNational Synchrotron Radiation Research Center, Taiwan

NSLS-II Seminar, 11 April 2007

The Taiwan Beamlines at SPringThe Taiwan Beamlines at SPring--88The biggest scientific investment overseas for Taiwan in her history

US$10M initial construction cost for 5 years, subsequent annual operation and instrumentation upgrade budget US$500 ~ 800K (excl. salary)

1020

1%bw

)

m pg g $ K ( . y)Motivation: To extend Taiwan Light Source’s spectral range to hard x-rays

1014

1016

1018

tons

/s/m

rad2 /m

m2 /0

.1

0 10 20 30 40 50 60 70 80

1010

1012

SP-8 IVXU3.2 (8GeV, 100mA) SP-8 BM (8GeV, 100mA) SRRC Wiggler (1.5GeV, 200mA)

Bril

lianc

e (P

hot

Photon Energy (keV)Photon Energy (keV)

Two Beamlines:BL12B2: Biostructure & Materials ResearchMultiple Purposes (Scattering Powder Diffraction Protein Crystallography)Multiple Purposes (Scattering, Powder Diffraction, Protein Crystallography)BL12XU: Inelastic X-ray ScatteringFor a broad range of applications, focusing on the study of electronic excitations in correlated electron systems and high-pressure physics (sciences)

(Yong Cai, NSLS-II Seminar, 11 April 2007)

excitations in correlated electron systems and high-pressure physics (sciences)

Location and AccessLocation and AccessClose Proximity:

Flight time 2.5 hours between Taipei and Osaka (Kansai Airport)Fast train connection 2.5 hours from Kansai to SPring-8Almost the same time zone

Taiwan


SPringSPring--8 Site8 Site

Sport Center Sport Center Sport Center Sport Center

Taiwan BeamlinesTaiwan Beamlines

Café & Café & Guest House Guest House


OutlineOutline

Brief Review of IXS by Electronic ExcitationsTheory and Experiment (BL12XU Setup)

Performance and Selected ResultsEl t S ifi A li ti (XRS/XES/FPY XAS)Element-Specific Applications (XRS/XES/FPY-XAS)XRS: High pressure phases of H2O, liquid & solid He, SiO2, Ba8Si46 ...

XES/XAS: P/T-induced charge instability in TmTe Prussian Blue XES/XAS: P/T induced charge instability in TmTe, Prussian Blue ...

Low-Energy Charge Dynamics in (ω,q) Space (NIXS/RIXS)NIXS: Graphite, MgB2, Py-SO, CaMnO3, NiO ...p g 2 y 3

RIXS at the K-edge of TM: NiO, Sr2CuO3, La2CuO4/La2NiO4 ...

Possible Further Developments and OutlookPossible further developmentsOutlook with the Taiwan Photon Source


IXS by Electronic ExcitationsIXS by Electronic Excitations

),( 2,222 εω qh=E photon-out

2θ),,( 1111 εω qh=E

q

photon-in

ωh=−=Δ 21 EEE

)2/2sin(2 121 θqq =−= qq

A rather weak scattering probe:

( )22 2

0

250 10 cmf

i fi

d r e ed

ωσω

−⎛ ⎞⎛ ⎞ = ⋅ ≈⎜ ⎟⎜ ⎟Ω⎝ ⎠ ⎝ ⎠

r r Hard x-rays:Thomson scattering

1 22 4

0

5104 cmB

dd a q

σ −⎛ ⎞ = ≈⎜ ⎟Ω⎝ ⎠Fast electrons:Rutherford scattering

Therefore IXS measures properties of the scattering system by itself, but requires intense hard x-ray beam for practical applications


Possible only with 3rd generation photon sources !!

Advantages of IXSAdvantages of IXS… as compared to other scattering probes (light, neutrons, electrons)

Kinematics Photoabsorption

Accessible (∆E, q) covers the full range of dielectric response: ∆E : meV ~ keV q : typical BZ sizes∆E and q are effectively decoupled

BL12XUBL12XU

∆E : 100 meV ~ 1 keV

Photoabsorption

Coupling to matter

∆E and q are effectively decoupled q : 1 ~ 100 nm-1

X-rays

Electron

Coupled directly to the electronic charge, therefore sensitive to all kinds of electronic excitationsT l b lk iti i i ith

Neutron

Truly bulk-sensitive, in comparison with VUV and SX photoemission and absorptionApplicable to systems under external environments (high pressure, electric and magnetic fields high and low temperatures etc ) and systems that are not magnetic fields, high and low temperatures, etc.), and systems that are not compatible with vacuum (e.g., liquids)Energy tuneability provides element specific experiments (XRS/XES/PFY-XAS)Small beam size offers the possibility to study small samples (incl HP-DAC samples)


Small beam size offers the possibility to study small samples (incl., HP DAC samples)

Resonant and/or NonResonant and/or Non--resonant IXS?resonant IXS?Interaction Hamiltonian with Electrons(neglecting spin and orbital degrees of freedom)

2

- : 1st order expansion, photon in photon out process

term−2A

Double Differential Cross Section

2(1) (2) 2

int int int 22 j j jj j

e eH H Hmc mc

= + = + ⋅∑ ∑A A pphoton-in photon-out process

- : 2nd order expansion,involving intermediate states

term−⋅pA

2( 2 ) ( 2 )2int int(1)

int,2 1

...( )I F N N I N

F H N N H Id F H Id d E E i

σω ω

∝ + +Ω − + − Γ∑ ∑

h

Double Differential Cross Section

Non-resonant

Non-resonant IXS (NIXS):2

( , )d d Sd d d

σ σ ωω

⎛ ⎞= ⎜ ⎟Ω Ω⎝ ⎠q

Resonant

Resonant IXS (RIXS):

( )2

12 2

1( , ) Im , Im ( , )4

qSe n n

ω ε ω χ ωπ π

−= − ⋅ = − ⋅q q qh

02d d dωΩ Ω⎝ ⎠Secondary processes involving intermediate statesResonant enhancement

S(q,ω): charge density-density correlation functionFluctuation-dissipation theorem provides the macroscopic connectionFi t i i l l l ti ibl

Element, charge, and spin specific experiments (RXES/PFY-XAS)Non-dipole excitations


First-principles calculations possible Theo: Model dependent

IXS IXS SpectroscopicSpectroscopic InformationInformationNIXS (XRS/XES/PFY-XAS)

NiONiO4p 4p →→ 1s1s1E

Loss features by phonons magnons orbitons excitons gap

2E

RIXS (RXES/PFY-XAS)Loss features by phonons, magnons, orbitons, excitons, gap excitations, plasmons, and electron-hole pair excitations, etc

NiONiORIXSRXES NiONiORIXSRXES

E

1E


2E

Taiwan Taiwan IXSIXS Beamline Beamline (BL12XU@SPring(BL12XU@SPring--8)8)

Si/Pt collimatingmirror

Pt focussingmirror

Detector AnalyzersSPring-8 Si/Pt collimatingmirror

Pt focussingmirror

Detector AnalyzersSPring-8

Design principle 1: Maximize the flux within the required energy width !

mirror mirror

Sample

(E1, q1)

(E q )

2θdΩ

mirror mirror

Sample

(E1, q1)

(E q )

2θdΩ

Photon Source(undulator)IVXU3.2

Pre-monochromator(double-crystal mono.)Si(111): ΔE = 1~1.5eV

High-resolution mono.Si(333)/Si(400):ΔE = 50~150meV

IXSspectrometer

(E2, q2)Beam Focus:

120(H) x 80(V) μm2Photon Source

(undulator)IVXU3.2



IXSspectrometer

(E2, q2)Beam Focus:

120(H) x 80(V) μm2

Design principle 2: Maximize flexibility to accommodate changing needs !

DetectorTotal energy resolution : 60 ~ 350 meV or ~ 1 eV with DCM beamSample

X-rays

Total energy resolution : 60 ~ 350 meV, or ~ 1 eV with DCM beamFlux: 1 x 1013 photons/sec/eV, and basically scaled with band widthBeam size : 120 x 80 μm2 (16 x 20 μm2 optional with KB mirrors)Energy transfer range: 100 meV ~ 1 keV with a single setup

Analyzer

Rowlandcircle

Energy transfer range: 100 meV ~ 1 keV with a single setupq-range : 1 ~ 100 nm-1

Count-rate : 0.1 ~ 100 cps (system dependent)


(Cai et al, AIP Conf. Proc. 705, 340)

y

Taiwan Taiwan IXSIXS Beamline Beamline (BL12XU@SPring(BL12XU@SPring--8)8)

Si/Pt collimatingmirror

Pt focussingmirror

Detector AnalyzersSPring-8 Si/Pt collimatingmirror

Pt focussingmirror

Detector AnalyzersSPring-8

Micro focusing system (optional), compact and low cost

mirror mirror

Sample

(E1, q1)

(E q )

2θdΩ

mirror mirror

Sample

(E1, q1)

(E q )

2θdΩ

Photon Source(undulator)IVXU3.2



IXSspectrometer

(E2, q2)Beam Focus:

120(H) x 80(V) μm2Photon Source

(undulator)IVXU3.2



IXSspectrometer

(E2, q2)Beam Focus:

120(H) x 80(V) μm2

Routinely achieving 16(H) x 20(V) μm2

141000

B t H F

Detector AnalyzersKB mirror set Detector AnalyzersKB mirror set

Transmission up to 80%Flux density gain ~ 20 times

6

8

10

12

400

600

800

ed In

tens

ity

Best Hor. Focus

FWHM13 μmnt

ensi

ty (-

dI/d

x)

Sample

(E1, q1)

(E2, q2)2θ

dΩSample

(E1, q1)

(E2, q2)2θ

dΩ

-0.66 -0.64 -0.62 -0.60 -0.58 -0.56 -0.54

0

2

4

-0.66 -0.64 -0.62 -0.60 -0.58 -0.56 -0.54

0

200

Nor

mal

ize3 μ

Der

ivat

ive

In

With Pt focussingmirror detuned

IXSspectrometer

( 2, q2)0.2m 0.25m

Beam Focus:16(H) x 20(V) μm2

With Pt focussingmirror detuned

IXSspectrometer

( 2, q2)0.2m 0.25m

Beam Focus:16(H) x 20(V) μm2


(Huang et al, AIP Conf. Proc. 879, 971)

Horizontal Translation (mm)

Spectrometer SetupsSpectrometer SetupsNIXS Setup RIXS Setup

DetectorE1

E2 SampleDetectorAnalyzerE1

Sample AnalyzerX-rays

E1 scannedE2 fixed

E1 2 p AnalyzerX-rays

E fixed but stepped thru edge E scanned

E2

E1


E2 fixed E1 fixed but stepped thru edge, E2 scannedCFS: E1 & E2 scanned together

XX--ray Crystal Analyzersray Crystal Analyzers

Spherically bent Si(111) analyzerBending radius: 2m

SEM image of a Si(111) test wafer diced with the DRIEg

Diameter: 100mmWafer thickness: 0.5mmdiced with the DRIE technique.

wafer diced with the DRIEtechnique under similar conditions as those for the analyzer shown on the left.


y(Shew et al, SPIE Proc. 4783, 131)

Analyzer PerformanceAnalyzer PerformanceDRIE Analyzer Diced AnalyzerBent Analyzer

0.25 I/I0Lorentzian Fit

units

)

0 16 I/I0Gni

ts)

0.12 I/I0G i Fitni

ts)

0.10

0.15

0.20 Lorentzian Fit

nten

sity

(arb

.u

230meV 0.08

0.12

0.16 Gaussian Fit

ensi

ty (a

rb.u

n

70meV0.06

0.08

0.10Gaussian Fit

ensi

ty (a

rb.u

n

160meV

0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8

0.00

0.05

Nor

mal

ized

In

0 2 0 1 0 0 0 1 0 2

0.00

0.04

orm

aliz

ed In

t

0 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 8

0.00

0.02

0.04

orm

aliz

ed In

te-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8

E - E0 (eV)-0.2 -0.1 0.0 0.1 0.2N

E - E0 (eV)-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8N

E - E0 (eV)

Test ConditionsI id B 50 V id h @ 9886 2 VIncident Beam: 50 meV width @ 9886.2 eVScatter: 2 mm thick PMMAAnalyzer: 2-m bending radius, Si(555) reflection at near backscattering

Controlled dicing tailors the strain left in the wafer, allowing tuning of the energy resolution to match the incident beam band width - The most efficient configuration for a given energy resolution !


ff f g f g gy

RIXS Analyzers (R=1,2m)RIXS Analyzers (R=1,2m)θ=89deg θ=60deg

Si (hkl) Back Scattering Emin Ti V Cr Mn Fe Co Ni Cu Zn Emax004 4.5661 4.5918 Ti 5.2725

3d Transitional Metal K-edge

133 4.9758 5.0038 V 5.7455224 5.5923 5.6237 Cr 6.4574115 5.9315 5.9649 Mn 6.8491333 5.9315 5.9649 6.8491044 6.4574 6.4937 Fe 7.4564135 6.7533 6.7913 Co 7.7981026 2196 2602 Ni 8 336026 7.2196 7.2602 Ni 8.3365335 7.4855 7.5276 8.6435444 7.9087 7.9532 Cu 9.1322117 8 1521 8 1979 9 4132117 8.1521 8.1979 9.4132155 8.1521 8.1979 9.4132246 8.5424 8.5904 Zn 9.8639137 8 7682 8 8175 10 1247137 8.7682 8.8175 10.1247355 8.7682 8.8175 10.1247008 9.1322 9.1835 10.5449337 9 3438 9 3963 10 7893


337 9.3438 9.3963 10.7893

Available analyzers

Configurations and PerformanceConfigurations and Performance

Beamline IXS Spectrometer@ 9884 7 eV

NIXS Setups

Beamline IXS SpectrometerHRM

ConfigurationFlux (×1011

photons/sec)Bandwidth

(meV)Multiple Analyzer(s) Resolution

(meV)Si(333) 1 5 50 Si(555) 2m diced (x9) 70

@ 9884.7 eV

Si(333) 1.5 50 Si(555) 2m diced (x9) 70

Si(400) 5.7 150Si(555) 2m diced (x9) 175Si(555) 2m bent (x3) 300

N (DCM) 120 1250 Si(555) 1 b t ( 1) 1300None (DCM) 120 1250 Si(555) 1m bent (x1) 1300

RIXS Setups

Beamline IXS SpectrometerResolution Mode Bandwidth (ΔE/E) Spherical Analyzer Energy Range (eV) Resolution (eV)

LR: Si(111) DCM 1.4×10-4 1m bent Various edges ~1

HR: Si(400) HRM 1.5×10-5 2m bent Various edges ~0.35


OutlineOutline








Why Study HWhy Study H22O?O?

H2O consists of the first and third most abundant elements in the solar system, and plays an exceedingly important role in a wide range of geophysical, planetary, physical, chemical, and biological systems.


g p y , p y, p y , , g y

Phase Diagram of HPhase Diagram of H22O (before 2004)O (before 2004)

??

After de Pater & Lissauer (2001)

Structure of Ice Ih

There exist at least 15 phases including stable, metastable, crystalline, and amorphous phases of H2O. All of these phases observed over modest P-T below 60 GPa conditions have structures closely dictated by the Pauling ice rules (Pauling, 1935). At higher pressures, symmetrization of the hydrogen-bonded network occurs, forming an ionic state, ice X.


y g , g ,

XX--ray Raman Scatteringray Raman Scattering (XRS)(XRS)First observed by Das Gupta in the 1950’s Clear connection to XAS was Clear connection to XAS was established theoretically by Mizuno and Ohmura and experimentally by Suzuki in

~ 535 eV p y y

1967, with different strengthsSynchrotron Radiation experiments by Tohji and Ud i 1987 Udagawa in 1987 Established as a routine technique in the 1990’s -- see work by Uwe Bergmann work by Uwe Bergmann (Bergmann et al. Microc. 71 (2002) 221).High-pressure DAC applications

Bowron et al, Phys. Rev. B 62, R9223

A powerful probe that provides detailed information on the local l t i b di t t f li ht l m t d hi h

g p ppin recent years


electronic bonding structure of light elements under high pressure

XAS versus XRSXAS versus XRSThe energy of the incident photon in XAS = The energy transfer in XRSThe momentum transfer q = photon polarization vector

XASEF

XRSEF

E1E1 E2

O K-shellE(O1s) = 543eV

ks eOEE += )( 11

O K-shellE(O1s) = 543eV

ks eOEEE +=− )( 121

Limitations due to the use of soft x-rays for light elements:Surf c s nsitivit

Advantages of using hard x-rays : Non-dipole regimes (qr ≥ 1)True bulk sensitivitySurface sensitivity

Restricted sample environmentse.g., incompatible with high pressure

True bulk sensitivityFlexible sample environmentse.g., compatible with high pressure


XRS: PossibleXRS: Possible ApplicationsApplicationsVarious Systems

Aqueous systems, organisms with high water content (vacuum non-compatible)First and second row elements T iti t l L d d M dTransition metal L edges and M-edges

High Pressure / TemperatureDifferent forms of ice, supercritical water and aqueous solutionsM th h d tMethane hydratesN2, O2, CO, CO2, NO, etc. Hydrogen storage in nanotubes under pressurePressure induced superconductivity (most light elements)Pressure-induced superconductivity (most light elements)

Notable High-Pressure Related Works:W.L. Mao et al., “Bonding Changes in Compressed Superhard Graphite”, SCIENCE 302, 425 (2003)30 , 4 5 ( 003)Y. Meng et al., “The Formation of sp3 Bonding in Compressed BN“, Nature Mat. 3, 111 (2004)Y.Q. Cai et al., “Ordering of Hydrogen Bonds in High-Pressure Low-Temperature H O” Ph R L tt 94 025502 (2005)H2O”, Phys. Rev. Lett. 94, 025502 (2005)S.K. Lee et al., “Probing of Bonding Changes in B2O3 Glasses at High Pressure with Inelastic Xray Scattering”, Nature Mat. 4, 851 (2005).W.L. Mao et al. “X-ray-induced Dissociation of H2O and Formation of an O2-H2


W.L. Mao et al., X ray induced Dissociation of H2O and Formation of an O2 H2Alloy at High Pressure”, SCIENCE 314, 636 (2006).

Proton Disordered to Ordered TransitionProton Disordered to Ordered Transition1000

H2OCritical Point

VaporCritical Point

Liquid III V VII

X ?atur

e (K

)

100

IhIX

II VI

VIII

X ?

Tem

pera

500.01 0.1 1 10 100

XI

0.25 Disordered Ordered Pressure (GPa)

Proton disordered to Ice polymorph Crystal structure Proton Network

(after S. Dutch, University of Wisconsin)

ordered phase transitions:ice III – ice IX (two O sites)ice VI – ice VIII (one O sites)

Ice III / ice VI Tetragonal Disordered

Ice II Rhombohedral Ordered

Ice IX / ice VIII Tetragonal Ordered


Ice IX / ice VIII Tetragonal Ordered

Effect of ProtonEffect of Proton--Ordering in HOrdering in H22O O

1 [1atm 300]

[P(GPa), T(K)](a)

High resolution (300meV) allows fine details of the edge structure to be resolved !

0

1 [1atm, 300]

[0.25, 300]Water

(arb

.uni

t)

(E ) (E )0

0

Liquid

0 2 20Ice III

Inte

nsity

(

[0.25, 245](E1, q1) (E2, q2)

0

0

[0.25, 150]Ice II

[0.25, 205]

rmal

ized

Ice polymorph Crystal structure Proton Network

Scattering thru Be: Less absorption, larger angular range!

0Ice IX

[0.25, 6]

Ice ?

No Ice III Tetragonal Disordered (~75%)

Ice II Rhombohedral Ordered (100%)Ice IX Tetragonal Ordered (~92%)

530 535 540 545 550

0

Energy (eV)The decrease of the pre-edge intensity is a key signature of proton ordering in the H2O fr me rk!

g ( )


Pre-, Main-, Post-edge(Cai et al, Phys. Rev. Lett. 94, 025502)

frame work!

A New LT Phase ?A New LT Phase ?2

[P(GPa), T(K)](b)

ΔE = 175 meV XRD at 0.26GPa and various temperatures

0

1

Ice IX

[0.25, 150]

arb.

unit)

[0 25 100]

H2O

0Ice IX

Inte

nsity

(a

[0.25, 50]

[0.25. 100]

0

Ice ?

Nor

mal

ized

[ , ]

[0.25, 4]

530 535 540 545 550

0

N

Ice ?

530 535 540 545 550Energy (eV)

XRS: is a sensitive probe to local bonding variations XRD: provides information on long-range structural variations


(Cai et al, unpublished)

XRD: provides information on long range structural variations

XX--rayray--induced Dissociation of induced Dissociation of HH22OO

Before and after X-radiationO2 features 8.8 GPa

15.3 GPa

zed

coun

ts

2 4 GPa

3.0 GPa

Ice VII

2.6GPa 2.6GPa

Nor

mal

iz

1 0 GPa

1.2 GPa

2.4 GPa

Ice VI At pressure above 2.5 GPa, H2O cleaves d l d d f 1.0 GPa

2.6 GPa, high-res

Liquid

Ice VII

under prolong x-radiation and forms a new alloy of H2 and O2 molecules that does not follow Pauling’s ice rules!

520 540 560 580Energy loss (eV)

g

New way to study H2 and O2 interaction

(W.L. Mao et al, Science 314, 636)


( , , )

Synergy for HP SciencesSynergy for HP SciencesAn excellent example of HP research that illustrates the necessity of using a multitude of experimental techniques for proper characterization f h (A i f El h d h Bli d M ) of the system (A scenario of Elephant and the Blind Men) .

d-spacing (Ǻ)4 3.5 3 2.5 2 1.8 1.6

×3×3

nsity ice VII

17.1 GPa nten

sity

×20

Rel

ativ

e in

te

irradiatedsample R

elat

ive

in

4200 4280 4360320028001560 1600400 8000

R sample17.6 GPa

5 6 7 8 9 10 11 12 13 14

R

ε-O2

ice VII

Raman shift (cm-1) Diffraction angle (2θ)

Laser Raman Spectroscopy X-ray Diffraction


(W.L. Mao et al, Science 314, 636)

OutlineOutline








NIXS of Charge Dynamics: Key AspectsNIXS of Charge Dynamics: Key Aspects

( )2

12 2

1( , ) Im , Im ( , )4

qSe n n

ω ε ω χ ωπ π

−= − ⋅ = − ⋅q q qh

Fluctuation-Dissipation Theorem links S(q,ω) to ε(q,ω), the latter defines all physical responses of the target system to external field:

4 e n nπ π

p y p g yInsight into the excitations of the N-particle many-body system and their interplay with the electronic structure:

G ll ( ) l f f d

1 2( )Internal external externaliε ε ε= = +D E E

Generally, ε(q,ω) is a complex function of momentum and energyThe real part represents features of collective excitations (e.g., plasmons)The imaginary part describes single-particle excitation (e.g., interband transitions).g y p g p gFor core excitations, the real part and the imaginary part are well decoupled (ε1 ~ 1, ε2 ~ μ), while they are strongly coupled for valence excitations


NIXS NIXS v’sv’s Optical & EELS StudiesOptical & EELS StudiesCompared to optical studies (q=0), the q-dependent information provides full knowledge of the charge dynamics and a stringent test of theoryIXS is almost free of multiple scattering (cf EELS) even at high q providing a IXS is almost free of multiple scattering (cf. EELS), even at high q, providing a clean way to study the charge dynamics at high q, where short-range correlation effects showing interesting and new physics can be expected Cross section is proportional to q2 in contrast to q-4 in the case of EELSCross section is proportional to q , in contrast to q in the case of EELSAt sufficiently high q, non-dipole transitions become possible, allowing additional excitation channels to be explored

R flO d i ( ) b i th f l

IXS

Refl.

0

One derivesε(q,ω) by using the f-sum rule:

1 2 2Im ( , ) 2 /d e n mε ω ω ω π− = −∫ qIXS

0 Interbandtransition

and the Kramer-Kronig transformation:

2' ( , ')2( ) 1 'P dω ε ωε ω ω∞

= + ∫qq

Plasmonfeature εreal

εimag

0

1 2 20( , ) 1

( ')P dε ω ω

π ω ω= +

−∫q

Practical application of NIXS to study ( ) h d !


realε(q,ω) has just started !

GraphiteGraphiteSimilar crystallographic and electronic structure to C based novel materials C or Similar crystallographic and electronic structure to C-based novel materials C60 or nanotubesVarious types of properties such as superconductivity, H storage, or super hard form, induced by intercalation, nano-structuring, or applying pressure

20eVDOSCrystal structure

10

Brillouin zone

0 •• • EF

-10

Gapless

An important fact is that graphite is semi metallic. However, there are few

-20

K Γ M K H


p g preports that have observed semi-metallic electronic structure.

q||ky

3 7 nm-1 ~1/8 G(x3)q||k

x 4.2 nm-1 ~1/12 G(x3)

1000q||k

z 3.5 nm-1 ~3/8 G(x3)

Plasmons： Collective excitationsGraphiteGraphite (100) (110) (001)

IXS spectra:

3.7 nm ~1/8 Gy

( )

7.4 nm-1 ~2/8 Gy

11.0 nm-1 ~3/8 Gy

14.7 nm-1 ~4/8 G

x( )

8.5 nm-1 ~2/12 Gx

12.7 nm-1 ~3/12 Gx

16.9 nm-1 ~4/12 Gxts

[cou

nts/

20se

c]

0

0

0 z( )

4.7 nm-1 ~4/8 Gz

5.9 nm-1 ~5/8 Gz

7.0 nm-1 ~6/8 G

(x3)

(x3)

(x3)

Collective mode and single-particle mode are mixed.

y

18.4 nm-1 ~5/8 Gy

22.1 nm-1 ~6/8 Gy

25.7 nm-1 ~7/8 Gy

21.2 nm-1 ~5/12 Gx

25.4 nm-1 ~6/12 Gx

29.6 nm-1 ~7/12 GxN

orm

aliz

ed C

ount 0

0

0

z

8.2 nm-1 ~7/8 Gz

10.5 nm-1 ~9/8 Gz

11.7 nm-1 ~10/8 Gz

(x3)

0 10 20 30 40 50 60 70 80

E-E0 [eV]

33.1 nm-1 ~9/8 Gy

0 10 20 30 40 50 60 70 80

E-E0 [eV]

33.8 nm-1 ~8/12 Gx

0

0

0 10 20 30 40 50 60 70 80

12.8 nm-1 ~11/8 Gz

14.0 nm-1 ~12/8 Gz

KK Transform.

P||kz

Re (ε1)

P||kx

ε 1

2

4

6 P||ky

Dielectricfunction

0.35[1/A]~3/8G0.47[1/A]~4/8G0.59[1/A]~5/8G0.70[1/A]~6/8G0.82[1/A]~7/8G1 05[1/A] 9/8G

0.35[1/A]~3/8G0.47[1/A]~4/8G0.59[1/A]~5/8G0.70[1/A]~6/8G0.82[1/A]~7/8G1 05[1/A] 9/8GIm (ε )

0.42[1/A]~1/12G0.85[1/A]~2/12G1.27[1/A]~3/12G1.69[1/A]~4/12G2.12[1/A]~5/12G2 54[1/A]~6/12G

0.423[1/A]~1/12G0.846[1/A]~2/12G1.27[1/A]~3/12G1.69[1/A]~4/12G2.12[1/A]~5/12G6

0

80.37[1/A]~1/8G0.74[1/A]~2/8G1.10[1/A]~3/8G1.47[1/A]~4/8G1.84[1/A]~5/8G2.21[1/A]~6/8G

0.37[1/A]~1/8G0.74[1/A]~2/8G1.10[1/A]~3/8G1.47[1/A]~4/8G1.84[1/A]~5/8G2 21[1/A]~6/8G

0 10 20 30 40 50 60

1.05[1/A]~9/8G1.17[1/A]~10/8G1.287[1/A]~11/8G1.404[1/A]~12/8GOpt. 0G

1.05[1/A]~9/8G1.17[1/A]~10/8G1.28[1/A]~11/8G1.40[1/A]~12/8GOpt. 0G

Im (ε2)

0 10 20 30 40 50 60

2.54[1/A] 6/12G2.96[1/A]~7/12G3.38[1/A]~8/12GOpt. Og

2.54[1/A]~6/12G2.96[1/A]~7/12G3.38[1/A]~8/12GOpt. 0G

0

2

4

6

ε 2

0 10 20 30 40 50 60

[ ]2.57[1/A]~7/8G3.31[1/A]~9/8GOpt. 0G

2.21[1/A] 6/8G2.57[1/A]~7/8G3.31[1/A]~9/8GOpt. 0G


(Hiraoka et al. Phys. Rev. B 72, 075103)

0 10 20 30 40 50 60

E-E0 [eV]

0 10 20 30 40 50 60

E-E0 [eV]

0 10 20 30 40 50 60

E-E0 [eV]

20eV

πq||k

y q=0 ( *)

*Optical data: EXP. Klucker et al. Phys. Status Solidi B 65 703 (1974)THEO: Marinopolous et al. Phys. Rev. B 69 245419 (2004)

π π σ σGraphiteGraphite10

σ

π

π

σπ

~1/8Gy

~2/8Gy

opt. (opt.*)

2 ••• Μ

ΚΤ

Κ

q||[100]

-10

0 • •σ

π

ππ

σ

π~3/8G

y

~4/8Gy

~5/8Gy

~6/8Gy

log

ε 2•• ••

•Γ

Μ

ΜΚ

-20K KΓ TM M

20 V

~7/8Gy

~9/8Gy q=9/8Gσ → σ∗

π → π∗π → σ∗σ → π∗

forbiddenallowed

10

20eV

σ

πq||k

x

~1/12Gx

opt.q=0 (opt.*)q||[110]

0 • • •ππ

σ

σ

σπ

~2/12Gx

~3/12Gx

~4/12Gx

~5/12Gxog

ε 2

• •• •• •ΓΚ Μ

ΜGΜ

•Κ

•Κ

20

-10σ

σ

π~6/12G

x

~7/12Gx

~8/12Gx

loΓΚ ΜΚ


Γ MK-20

K K M MG0 4020 30 10

E-Eo [eV]

q=8/12G

IXS clearly observes semi-metallic features in graphite

SuperconductivitySuperconductivity of MgBof MgB22Superconductivity (Tc=39K) is dominated by strong e-p coupling between the B sub-lattice (the E2g optical phonons) and the 2D boron σ bands

Mg

B

Β π-bands Β σ-bandsKortus et al, Phys. Rew. Lett. 86, 4656Strong charge inhomogeneityThe Realization of a Demon?

Demon = distinct electron motion (D. Pines, 1956), formed in the presence of two distinct types of carriers in the system (the heavy B 2D σ holes and the light 3D

l t i M B ) Th li ht i ld th C l b l i f th π electrons in MgB2). The light carriers could screen the Coulomb repulsion of the heavy carriers effectively, thereby reducing the plasmon frequency of the heavy carriers, leading to the so-called acoustic plasmon that follows generally: ωa = vaq, where v ~ the Fermi velocity of the heavy carriers


where va ~ the Fermi velocity of the heavy carriers.

Dynamical Response of MgBDynamical Response of MgB22(W. Ku et al, Phys. Rev. Lett. 88, 057001)

Intraband transitionsNew Collective Mode

Interband transitions

Conventional Plasmon

At low q, crystal-local field effects (CLFE) are negligible, the new collective mode disappears into particle-hole continuum by Landau damping as q increases


mode disappears into particle-hole continuum by Landau damping as q increases

Charge Dynamics in (Charge Dynamics in (ωω,q,q) Space: MgB) Space: MgB22

MgB2 at 300K q // c-axis ΔE = 250 meVq//c-axis [001]

Δq = 0.06 Å-1

(Å-1)

0

400

800

n) 2 67

2.93

3.26

MgB2 at 300K q // a-axis

ΔE = 65 meVq//a-axis [100]a

(Å-1)

0

0

0

0

Cou

nts

(/mi

1 78

2.08

2.36

2.67

20

40

s (/m

in)

1.88

Mg

B

(Å-1)

0

0

0

0

1.20

orm

aliz

ed C 1.78

1.480

0

zed

Cou

nts

1.02

1.48

[001]A

M

0

0

0

0 15

0.30

0.58

0.89N

0

0

0 30

0.58

Nor

mal

iz

A L

A

0 10 20 30 40 50 600

Energy Transfer (eV)

0.150 10 20 30 40

0


0.30

Bulk plasmon of conduction electrons [100]K

MH


Bulk plasmon of conduction electrons

LowLow--EnergyEnergy Charge ExcitationsCharge Excitations: q//c: q//c**--axisaxis

MgB2 at 300K q // c-axis

ΔE = 250 meVMgB at 300K q // c axis

ΔE = 250 meVMgB2 at 300K q // c-axis

ΔE = 65 meV

0

400

800

MgB2 at 300K q // c axis

) 2.93

3.26

0

120

240MgB2 at 300K q // c-axis

3.26

3.38

3.50

0

10MgB2 at 300K q // c axis

1.68

1.48

0

0

0

ount

s (/m

in)

2.08

2.36

2.67

0

0

0 2.80

2.93

3.10

0

0

0

1.20

1.36

0

0

0

1.20rmal

ized

Co

1.78

1.480

0

0

2.36

2.46

2.67

0

0

0

0 70

0.89 1.10

0

0

0

0

0.30

0.58

0.89Nor

0

0

0

2.08

2.20

1.880

0

0

0.42

0.58

0.70

0 10 20 30 40 50 600

0


0.150

1 2 3 4 5 6 70

Energy Transfer (eV)1 2 3 4 5 6

0

00.30



(Cai et al, Phys. Rev. Lett. 97, 176402)

Periodic Dispersion: q//cPeriodic Dispersion: q//c**--axisaxisFirst ever periodic collective charge excitation observed in a metallic system !

Empirical energy dispersion follows entirely a cosine follows entirely a cosine function :

)cos(20 qcγωω −=

ω0 = 3.55 eVγ = 0.49 eVc = 3.52 Å


PeriodiPeriodicity of Dielectric Functioncity of Dielectric Function

( ) ( ); ;qG G G Gq G kε ω ε ω′ ′− =r r r rrrr( ) ( ), ,; ;qG G G Gq


PeriodiPeriodicity of the Dielectric Responsecity of the Dielectric Response??The density-response matrix can be expressed in terms of the

inverse of the dielectric matrix asinverse of the dielectric matrix as

( ) ( ) ( )1 1; ;q qG q GG Gq Gq G v q G G ε ωχ ω δ

−−′ ′

⎡ ⎤−⎛ ⎞− = − + −⎜ ⎟⎣ ⎦r r r r

rr rr rr r( ) ( ) ( ) ,, ,; ;q qG q G GGG Gq Gq G v q G G ε ωχ ω δ

′′ ′+ ⎜ ⎟⎝ ⎣ ⎦ ⎠

r r

For the latter we have derived the exact resultFor the latter, we have derived the exact result,

( ) ( )1

;qq G ωε−

=⎡ ⎤−⎣ ⎦ rrr 1( ) ( )

( ) ( ) 1

,;

;

q qq G G

q GF q G

q G

q ω ω

ω

ε

ε

−+

⎣ ⎦

⎤⎦

⎡⎣

rr

rr

rr r

rr

rr

q q qG Gε q -G ;ω

( ) ( )0, 0

,, ; q G Gq q GF q Gq ω ωε= =

+ ⎤− ⎦− ⎡⎣ r r r r

for q’s in BZ’s higher than the first one.


MgBMgB22: Strong : Strong CLFECLFE at Large q ! at Large q !

1

,

1( , )( , )

ε ωε ω

−⎡ ⎤− = +⎣ ⎦ −q q

q G GG G

q Gq G

Matrix Response to Include CLFEReF ~ 60 times larger in MgB2 than Al, Si !

,

1

,

( , )

( , ; ) ( , )F

ε ω

ω ε ω−

⎡ ⎤− −⎣ ⎦

q qq qG G q

q q 0 0

q G

q q G q G

Momentum Transfer (nm-1) CalculationE 65 V

Momentum Transfer (nm-1) CalculationS(q,ω) Imε(q,ω)

F Function is Material-Dependent

0 5 10 150

2

( )20 25 30 35

log(S(q,ω))

ΔEexp=65meV ΔEexp=250meV(S) ΔEexp=250meV(L)

0 5 10 150

2

( )20 25 30 35

log(Imε(q,ω))

ΔEexp=65meV ΔEexp=250me ΔEexp=250me

4

6 E

nerg

y (e

V)

-3.238

-2.297

-1.4004

6 E

nerg

y (e

V)

-0.4609

0.7988

2.000

8

10

E

-6.059

-5.119

-4.178 8

10

E

-4.240

-2.980

-1.721


12 -7.000 Γ A Γ A Γ

12 -5.500 Γ A Γ A Γ

(Cai et al, Phys. Rev. Lett. 97, 176402)

OutlineOutline








Future Future Plan 1Plan 1IXS under high pressure at low temperature (already started)

Dynamic variation of temperature and pressureLaser Raman spectroscopy to ensure phases of samples.Laser Raman spectroscopy to ensure phases of samples.

Si

He Gas

SiZ stage

X,Y stage

Pressureglass window

cryostat

Fluorescence

X-ray

Pressurecell

Laser

Fluorescenceor Raman


LaserChang et al. Phys. Rev. Lett. 54 2375 (1985)

Future Future Plan 2Plan 2IXS using 20 keV photons

High penetration power for XRS of compounds of heavy elementsI d fl ibilit f hi h i t ( B k t )Increased flexibility for high pressure experiments (e.g., no-Be gaskets)RIXS on 4d, 5f compounds (EB ~ 20 keV)

Large area-SSD

Pt mirror

Pt mirror sample

SSD

KB mirrors

Si(111) DCMDE~3eV

Bent-Laue Si(660)Analyzer

sourceSi220 Channel cuts0.7 eV

KB mirrors

DE 3eV

Total energy resolution : ~ 1 eV Flux: 5 x 1012 photons/sec/eVBeam size : 20 x 20 μm2 Beam size : 20 x 20 μm2

Energy transfer range: ~ 1 keVq-range : 10 ~ 200 nm-1

C nt t : ???


Count-rate : ???

New 3New 3--GeV Taiwan Photon Source (TPS)GeV Taiwan Photon Source (TPS)


TPSTPS Parameters Parameters –– Not the FinalNot the FinalTPS Non-achromatic

24p18K1Achromatic

24p18L1

E (G V) 3 0Energy (GeV) 3.0

Beam current (mA) 400

Circumference (m) 518 4Circumference (m) 518.4

Nat. emittance εx(nm-rad) 1.7 (εxeff = 2.17 LS center)

5.8

Cell / symmetry / structure 24 / 6 / DBACell / symmetry / structure 24 / 6 / DBAβx / βy / ηx (m) LS middle 10.59 / 9.39 / 0.11 12.9 / 9.79 / 0.0RF frequency (MHz) 499.654q y ( )

RF voltage (MV) 3.5Harmonic number 864SR loss/turn, dipole (MeV) 0.98733Straights 11.72m*6+7m*18Betatron tune ν /ν 26 22 / 12 28 26 24 / 12 28


Betatron tune νx /νy 26.22 / 12.28 26.24 / 12.28

Brilliance Comparison with Other SourcesBrilliance Comparison with Other SourcesSU15

Photon energy 2 5-25(keV) 2.5 25

Current (mA) 400

λ(mm) 15λ(mm) 15

Nperiod 133

By (Bx) (T) 1 5By (Bx) (T) 1.5

Kmax 2.1

L (m) 2L (m) 2

Gap (mm) 5.6

Peak Power 170density (kW/mr2) 170

Total power (kW) 23.5

Type SC


Type SC

SummarySummary

Versatile, state-of-the-art IXS facilities at 3rd generation synchrotrons provides a powerful probe of the charge dynamics of a wide variety of provides a powerful probe of the charge dynamics of a wide variety of systems, including those under extreme pressure and temperature.

The improved energy and momentum resolution and wide scan range have ll d i t l di l t i f ti t b t di d ith allowed experimental dielectric functions to be studied with

unprecedented details.

IXS experiments are flux limited. An ideal instrument should therefore p f fprovide the flexibility that allows maximum available flux within the appropriate energy band width for the problem to be attacked.

New 3rd generation medium energy rings such as the NSLS II and the New 3rd generation medium energy rings such as the NSLS-II and the TPS provide new opportunities and challenges.


AcknowledgementsAcknowledgements

NSRRCNozomu HIRAOKA Cheng Chi CHEN: Mechanical EngineeringNozomu HIRAOKAHirofumi ISHIIIgnace JARRIGE (now with JAEA)

Cheng-Chi CHEN: Mechanical Engineering

Shen-Yaw PERNG: Analyzer DevelopmentDuan-Jen WANG: Analyzer Development

Paul CHOW (now at HP-CAT, APS)

Key CollaboratorsChien-Te CHEN: Project Director

Chi-Chang KAO, BNL, USA Eric SHIRLEY, NIST, USAJohn S TSE NRC Canada

Donglai FENG, U. Fudan, ChinaChangyoung Kim, Yonsei U., KoreaAlfred BARON RIKEN/JASRI Japan John S. TSE, NRC, Canada

Wei KU, Phys., BNL, USAAdolfo G. EGUILUZ, UT, USA

Alfred BARON, RIKEN/JASRI, Japan Shik SHIN, RIKEN, JapanAhbay SHUKLA, U. P&M. Curie, France

Dave MAO, GL-CIW, USA

FundingNSC d NSRRC

Jean-Pascal RUEFF, Soleil, France

Thank You!Thank You!(Yong Cai, NSLS-II Seminar, 11 April 2007)

NSC and NSRRC Thank You!Thank You!

Inelastic XInelastic X--ray Scattering by ray Scattering ... · 1018 t ons/s/mrad 2 /mm 2 /0. ......

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