Scope & Outline

Inelastic X-Ray Scattering
NOTE
Preliminary Version of Slides – Some will be Changed/Updated.

Alfred Q.R. Baron
Materials Dynamics Laboratory (RIKEN)
Facilities and Utilization Division (JASRI)
SPring-8

Main Goal:
Introduce Capabilities & Put them in Context
What properties can be measured?
Why consider these techniques?
Outline:Introduction
Instrumentation
Non-Resonant Techniques
Resonant Techniques (Briefly)

Huge & Complex Topic - Appropriate for a semester, not an hour…

Comment: Notes…
AQRB @ AOFSRR Cheiron School 2009

Table Of IXS Techniques/Applications
TechniqueComment

Energy Scale

Information

X-Ray Raman(E)XAFS in Special Cases

Ein~10 keV!E~100-1000 eV

Edge Structure, Bonding

ComptonOldestNote: Resolution Limited

Ein ~ 150 keV!E ~ keVElectron Momentum Density
Fermi Surface Shape

Magnetic Compton

Weak But Possible

Ein ~ 150 keV!E ~ keV

Density of Unpaired Spins

High Rate
Somewhat ComplicatedEin ~ 4-15 keV!E ~ 1-50 eV

Electronic Structure

Non-Resonant IXS

Low Rate
SimplerEin~10 keV!E ~ <1-50 eV

Electronic Structure

IXS

Large Instrument

Ein~16-26 keV!E ~ 1-100 meV

Phonon Dispersion

Atom SpecificVia Mossbauer Nuclei

Ein ~ 14-25 keV!E ~ 1-100 meVElement SpecificPhonon Density of States
(DOS)

RIXS
Resonant IXS

NRIXS

High-Resolution IXSNIS
Nuclear IXSAQRB @ AOFSRR Cheiron School 2009

Some References
Shulke, W. (2007), Electron Dynamics by Inelastic X-Ray Scattering.!
New York: Oxford University Press.!
& References therein!
Squires, G. L. (1978). Introduction to the Theory of Thermal Neutron Scattering.!
New York: Dover Publications, Inc.!
van Hove, L. (1954). Phys. Rev. 95, 249-262.!
Born, M. & Huang, K. (1954). Dynamical Theory of Crystal Lattices.!
Oxford: Clarendon press.!
Bruesch, P. (1982). Phonons: Theory and Experiments, Springer-Verlag.!

Cooper, M.J. (1985). Rep. Prog. Phys. 48 415-481

Note: !E = Typical Energy Transfer (Not Resolution)
Note also: Limit to FAST dynamics (~10 ps or faster)
AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

X-Ray Scattering Diagram

Spectroscopy

Absorption vs. Scattering
Absorption
Spectroscopy
Optical, IR, NMR

k1

Measure absorption as you
scan the incident energy
E 1 = !"1 =When energy hits a resonance,or exceeds a gap, or… get a change!

E2 k2 e2E1 k1 e1

IXS, Raman, INS

k 1 = k1 =Optical Spect. NiONewman, PR 1959

Free Parameters: E1, e1, k1-> In principle, 3+ dimensions
but in practice mostly 1 (E1)

Scattering
Spectroscopy"#

E1 k1 e1E2 k2 e22"

Two Main Quantities:#1

hc = 12.398 keV• Å

Momentum Transfer

Energy Transfer!
!

Q " k 2 # k1

E or "E = E 1 # E 2 $ !%Free Parameters: E1, e1, k1, E2, e2, k2-> In principle, 6+ dimensionsin practice, mostly 4: E1-E2, Q = k2-k1

Scattering is much more complex, but gives more information.

Q = k２- k1

hc= !ck 1
#1

Q" Q $

4%

&1

sin '
2

( )

Periodicity Probed
Note: For Resonant Scattering
E1 and E2 and Poln.
Are also important

!

d=

!

AQRB @ AOFSRR Cheiron School 2009

2"
Q

AQRB @ AOFSRR Cheiron School 2009!

Dynamic Structure Factor

Different Views of S(Q,$)

It is convenient, especially for non-resonant scattering, to separate theproperties of the material and the properties of the interaction of thephoton with the material (electron)

2

S(Q," ) = $ p# # '
#,# '

!

(

" T hom son = re 2 e2* •e1)2Thomson Scattering
Cross Section

AQRB @ AOFSRR Cheiron School 2009!

1=
( dt d 3r d 3r' e&iQ•r )(r',t = 0)) + (r + r',t )2'!

=

S(Q," )
“The Science”“A Scale Factor”!

)

Dynamic Structure Factor# % ( E# '&E# & !" )electrons
j

2

2 "
d 2$
2
*
2
I scattered (Q," ) #= re e2 •e1
S(Q," )
d%d"
"1

(

$ e

iQ•r j!

1
1Im{& , (Q,")}' 1& e&!" /kBT

=

*

N$
q

$ $
Modes

d
Atoms
/Cell

fd (Q) &W d (Q)eQ •eqjd eiQ•x d %(Q&q),+ Fqj (")
2M d

1
1
1
Im{&- &1(Q,")}' 1& e&!" /kBT v(Q)See Squires, Lovesy, Shulke, Sinha (JPCM 13 (2001) 7511)

AQRB @ AOFSRR Cheiron School 2009

The IXS Spectrometer
An Optics Problem

Kinematics
M
k1

Monochromator:

E1 k1 e1

Q = k２- k1
E2 k2 e2

E recoil

Take: M=57 amu, Q/c = 7 Å-1 -> Er=2.3 meVCompton Form: " 2 # " 1h=(1 # cos $)
Mc

"c

!

Straightforward
Only Need Space!E small, E tunable!

!Q# d" !" S(Q," )=2M# d" S(Q," )2

Large Solid Angle
Difficult

The Goal: Put it all together and
Keep Good Resolution, Not Lose Fluxh== 0.0243Åm ec!

SampleMonochromator!

Analyzer:2

f-sum! rule:

Analyzer!
Fixed bandwidth at a !
selected Q transfer

Sample Stages

p2! 2Q 2==2M
k"2M
E" eˆ '!

Detector

Modestly Difficult
Only needs to accept 15x40 µrad2"#

Kinetic Energy Given to Sample:

k ! E ! eˆ'Main Components

AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009!

!

Analyzer Crystals

Basic Optical Concept
Bragg’s Law : % = 2d sin("&)! =>!

"# = tan%'&$ (*) "E
B E

Working closer to "B~90 deg. maximizes the angular
acceptance for a given energy resolution…
!

The more difficult optic…

Detector

Require:!
Correct Shape (Spherically Curved, R=9.8 m)!
Not Strained (!E/E~few 10-8-> !d/d<<few10-8)!

Sample!

!

!
!

Analyzer
Crystal

Method: Bond many small crystallites to a curved substrate.
Note: For resolution >300 meV, bending can be OK.

Better energy resolution-> Closer to 90 degrees-> Large Spectrometer

1. Cut!

2. Etch!

3. Bond to !
Substrate!

4. Remove Back!
X-Rays!

104 Independent!
Perfect Crystals!
AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

Analyzer Crystal

Spectrometer Photo
Spectrometer Photo

Collaborative R&D with NEC Fundamental Research Laboratory, H. Kimura, F. Yamamoto!

Slit System!

12 Chan. CZT Detector!

Sample!

Analyzer Array!

10m Arm & 12 Analyzers
Vacuum Flight Path!

Incident�Beam!
'(100 µm!
' < 20 µm Possible!

Present Parameters (9.8 m Radius, 10cm Diameter)!
50 or 60 µm blade, 2.9 mm depth, 0.74 mm pitch!
Channel width (after etch): ~ 0.15 mm!
60 to 65% Active Area!

Granite Base w/Airpads!

AQRB @ AOFSRR Cheiron School 2009

Medium Resolution

AQRB @ AOFSRR Cheiron School 2009

Other Spectrometers @ SPring-8
NRS Optics BL09

Medium Resolution Spectrometer:
Arm Radius: 1 to 3 m
Resolution: ~0.1 to 1 eV
Used for RIXS and NRIXS
BL12XURIXS Spectrometer
2m Arm, BL11XU

BL11XU

3m Arm at BL12XU
BL12XU (Early)

Emission Spectrometer)(1.5m Chamber
10

NRIXS: Choose the energy to match the optics
RIXS: Resonance chooses energy -> usually worse resolution!E (meV)!E (meV)

Note difference between RIXS and NRIXS

1Compton Spectrometer BL08

0.1

10

15

20

25

30

35

40

(~eV Resolution)
Hayashi, et alE(keV)AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

Disordered Materials

Atomic Dynamics: Systems and Questions
Disordered Materials (Liquids & Glasses):
Still a new field -> Nearly all new data is interesting.
How do dynamical modes survive the cross-over from thelong-wavelength continuum/hydrodynamic regime toatomic length scales?

Liquids & Glasses

First Glance: Triplet response similar for most materials.
Dispersing Longitudinal Sound Mode
+ Quasi-Elastic peak

Crystalline Materials:
Basic phonon model does very well ->Specific questions needed.

Phonon softening & Phase transitions (e.g. CDW Transition)
Thermal Properties: Thermoelectricity & Clathrates
Sound Velocity in Geological Conditions
Pairing mechanism in superconductors
AQRB @ AOFSRR Cheiron School 2009l-Mg

(Kawakita et al)a-Se (Scopigno et al)l-Si (Hosokawa, et al)
AQRB @ AOFSRR Cheiron School 2009

Metal to Insulator Transition in Liquid Mercury“Fast Sound” at the Metal-Non-Metal Transitionin Liquid Hg

Universal Phenomenon in Liquids:
Expand a liquid metal enough and it becomes an insulator.

Universal Phenomenon in Liquids:
Expand a liquid metal enough and it becomes an insulator.

Ultrasonic
Velocity

For Hg~1500 C & ~ 1.5 kbar

Suggests a change in the microscopic
density fluctuations…
Probably general phenomenon…
but no confirmation yet.

15 mm Be, 200 m He (STP), 0.15 mm Sapphire~ 20 microns Hg
D. Ishikawa, M. Inui, K. Tamura, et al.

(Next M-I transition under discussion)

D. Ishikawa, et al, PRL 93 (2004) 97801
AQRB @ AOFSRR Cheiron School 2009

~2 months of beam time…
AQRB @ AOFSRR Cheiron School 2009

Elastic Inhomogeneity in a Glass
Ichitsubo, et al.

Pd42.5Ni7.5Cu30P20

Shear Mode in a Simple Liquid
Pressure Wave in a Liquid: Always

Electron Micrograph of a
Re-crystallized Sample
Note: ~1 Day/Spectrum @ Low Q
Subsidiary Structure in Spectra

Fast sound a signature of elastic inhomogeneity.
(Detailed analysis: possible failure of DHO Model)
AQRB @ AOFSRR Cheiron School 2009

Phonons in a Crystal

Shear Wave -> Harder..

Hosokawa, et al, PRL (2009)

AQRB @ AOFSRR Cheiron School 2009

MgB2 As An Example
Layered Material
Hexagonal Structure

Normal Modes of Atomic Motion
Must have enough modes so that each atom in a crystal can be moved ineither x,y or z directions by a suitable superposition of modes.
If a crystal has N unit cells and R atoms/Cell then it has
3NR Normal Modes
Generally: Consider the unit cell periodicity separately
by introducing a continuous momentum variable, q.

B Layer

B-B Bond is Short& Stronger

Mg Layer

Mg-Mg Bond isLonger & Weaker-> 3R modes for any given q

AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

Acoustic and Optical Modes

Dispersion of an Optical Mode

Acoustic Modes are Continuum (Smooth) Modes(0.25 0 0)

(0 0 0)LA ModeCompression ModeTA ModeShear Mode

(0.5 0 0)

Optical Mode
Atoms in one unit cellmove against each-other

AQRB @ AOFSRR Cheiron School 2009

Phonons in a Superconductor
Conventional superconductivity is driven by lattice motion.
“Phonon Mediated” - lattice “breathing” allows electron pairs to move without resistance.

Original Picture: Limited interest in specific phonons…
Now: Lots of interest as this makes a huge difference.
Particular phonons can couple very strongly to theelectronic system.

How does this coupling appear in the phonon spectra?
Softening:

Screening lowers the energy of the mode
(abrupt change <=> Kohn Anomaly)

Broadening:

Additional decay channel (phonon->e-h pair)reduces the phonon lifetime
AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

Electron Phonon Coupling& Kohn Anomalies

On the scale of electron energies, a phonon has nearly no energy.
A phonon only has momentum.
So a phonon can move electrons from one part of the Fermi
surface to another, but NOT off the Fermi surface.

PhononMomentaQ<2kF

Large Momentum
Q>2kF
Can Not Couple to theElectronic system
Fermi Surface
Diameter = 2kf
AQRB @ AOFSRR Cheiron School 2009

MgB2

Superconductors @ BL35XU

Phonon StructureHigh Tc (39K)

Systems Investigated at BL35XU include
MgB2, Doped MgB2, CaAlSi, B-Doped Diamond
Hg1201, LSCO, YBCO, LESCO, Tl2212, BKBO, NCCO,
Bi2201, Bi2212, Nickelates, Oxychlorides
Fe-As Systems: LaFeAsO, PrFeAsO, BaKFeAs

Nagamatsu, et al, Nature 410, (2001) 63.

Simple Structure…
straightforward calculation.

Electronic Structure

Kortus, et al, PRL 86 (2001)4656

From T. Fukuda

Bohnen, et al. PRL. 86, (2001) 5771.

BCS (Eliashberg) superconductor with mode-specific electron-phonon coupling.

Dark Blue Line: Conventional, Phonon-Mediated Superconductors
AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

Carbon Doped Mg(CxB1-x)2Electron-Phonon Coupling in MgB2
SpectraDispersion
100(2.31, 0, 0.01)

E2g(2.27, 0, - 0.01)(meV)

Energy (meV)

60

300K
44K
16K

(2.23, 0, - 0.03)

A2u

40

!
Points: Measurements at BL35

A

12.5% C, Tc=2.5K(2.37,0,0.01)

AlB2 (Not SC)(2.37,0,-0.01)(2.37,0,0.01)

0

50

100
(2.29,0,-0.03)

0

50

0

50

0

50

50(2.13,0,0.01)
100

0

50

50

0

50

0

50 (2.29,0,0.03)
100

100(2.22,0,0.03)

0

50

0

50(2.13,0,-0.01)
100

0

0

50

0

100
(2.30,0,0.03)

10*#(2.19, 0, 0.03)

0

M

20

0

E1u
20

2%C, Tc=35.5K

30

FWHM

B1g
80

M

Linewidth!-M (Å-1)100(2.22,0,-0.03)

100(2.24,0,-0.03)

M!

(2.15, 0, 0.01)

100(2.16,0,0.01)(2.11, 0, -0.01)

Lines: Calculations by Bohnen et al.

Clear correlation between
0
50
100!
linewidth & softening.
Excellent agreement with LDA Pseudopotential calculation.

*

100

100

100

Phonon structure correlates nicely with Tc for charge doping.
(Electron doping fills the sigma Fermi surface)

PRL 92(2004) 197004: Baron, Uchiyama, Tanaka, ... Tajima
AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

Phonons in the Cuprates…

More Superconductors
Similar types of results for
Mn Doped MgB2
CaAlSi
Boron Doped Diamond

Everyone has their favorite mode, or modes, usually focus on Cu-O planes(0 0)In-Plane Mode:(0.5 0)Stretching mode
Extrapolation to the High Tc Copper Oxide Materials….
1. Much More Complex
2. Calculations Fail so interpretation in difficult

Out of Plane Modes:
Buckling Mode
Apical ModeAt the level of phonon spectra, the anomaly of theBond Stetching Mode is very large

AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

Copper Oxide Superconductors
Remain Challenging…
C-axis modes

De-Twinned YBCO:YBa2Cu3O7-+
Tc = 91 K

La1.48Nd0.4Sr0.12CuO4

In-Plane Modes

Phonon anomaly (blurring) is highly localized in
momentum space…

Lines = Calculation
Points = IXSExpt done by a neutron scatterer because
he could not get good enoughresolution using neutrons
Forces a reinterpretation of some Neutron
data (Reznik, Nature, 2006)

Beautiful Agreement
Shows Bond Stretching Anomaly
Is Huge (>> Buckling Anomaly)

Problems

Compare IXS to Calculation
At low T (~30K)

Bohnen, et al.

AQRB @ AOFSRR Cheiron School 2009

Note:
D. Reznik, et al, Accepted

IXS Q Resolution
Analyzer array
Count rate limited.

2.5 days
AQRB @ AOFSRR Cheiron School 2009

Fe-As Superconductors

Superconductors @ BL35XU

From February 2008

“1111” System
LaFeAsO1-xFx
Kamihara, et al.

Tc up to 56K“122” System
Ba1-xKxFe2As2
Rotter et al

Common Features:

Systems Investigated at BL35XU include
MgB2, Doped MgB2, CaAlSi, B-Doped Diamond
Hg1201, LSCO, YBCO, LESCO, Tl2212, BKBO, NCCO,
Bi2201, Bi2212, Nickelates, Oxychlorides
Fe-As Systems: LaFeAsO, PrFeAsO, BaKFeAs

Fe Planes with Tetrahedral As
Parent (non SC) Shows Magnetic OrderAnd
Tetragonal-> Orthorhombic
Transition at ~140 K
Superconductors Remain
Tetragonal

Tc to 38 K
From T. Fukuda

Dark Blue Line: Conventional, Phonon-Mediated Superconductors
AQRB @ AOFSRR Cheiron School 2009

Phonon Calculations (LaFeAsO)

AQRB @ AOFSRR Cheiron School 2009

Phonon Density of States
The First Indication of Disagreement with Simple Models

Using the Tetragonal Non-Magnetic Structure

Reasonable Agreement Except
Highest Energy PeakAppropriate for Super-conducting materials

Conclusion from Calculation: Not a phonon mediated superconductor
Various Calculations Consistent.

Similar data published simultaneously

Singh & Du, PRL 100, 237003 (2008).
Boeri, Dolgov, & Golubov, PRL 101, 026403 (2008).

INS @ SNS (Christianson, et al)
IXS @ ESRF (LeTacon et al)

All show significant (~5 meV) softening
Present calculations(Nakamura & Machida)
VASP (PAW method)
GGA & PHONON
Direct method

Softened peak is primarily Fe-As modes.
This discrepancy is large by the standards of modern
ab-initio, pseudo-potential calculations

But… these calculations do NOT agree with experiment
AQRB @ AOFSRR Cheiron School 2009

RIKEN, JAEA, JASRI, AIST, JST
Fukuda, et al, JPSJ L 77 (2008)
AQRB @ AOFSRR Cheiron School 2009

Single Crystal Dispersion

Modifying the Model…

Fe1

PrFeAsO1-y
150 x 100 x 20 um3

Fe2

Fe1

Ishikado, Kito,& Eisaki (at AIST)

Fe2
b

Fe2

Fe1

a
Fe2

Fe1

“Clipped”

Original LSDA

(H 0 0)AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

Strong Asymmetry of
Magnetic Interaction

A Short-Lived Magnetic Structure?
Magnetic calculations agree more nearly with experimental results.

Fits to Dispersion in Ca122

Increasing evidence for (and speculation about) fluctuating magnetism
Upper limit for lifetime: ~ ns from Mossbauer (Kitao, et al, JPSJ)

SJ1a = 49.9+-9.9

Related work on 122 materials: (Zbiri, et al., PRB, Hahn, et al PRB)
Larger effects, but not superconducting samples (& esp. c-axis modes)

SJ1b = -5.9+-4.5
Theory:Zhao, et al , Nat. Phys. 5 (2009) 555
AQRB @ AOFSRR Cheiron School 2009

Model of anti-phase domains
Mazin&Johannes, Nat. Phys. (Feb)

Bonding & Lattice constants & Magnetism
Yildirim, PRL (Jan), arXiv
AQRB @ AOFSRR Cheiron School 2009

Phonons in a Quasicrystal

SmRu4P12

Mostly like a solid but some glassy character.

S. Tsutsui, et al.
JPSJ 77 (2008) 033601

Building a Quasicrystal (Zn-Mg-Sc)

Periodic (BCC) -> Crystalline Approximant
Aperiodic -> Quasicrystal

Compare to crystalline approximant &Simulation (2000 atoms/cell)
General Trend: Blurring out
past a cutoff energy“Pseudo-Brillouin” zone size
De Boissieu, et al.
Nature Materials, Dec 2007

Localized Nature Confirmed by IXS(No Frequency Dispersion, Weak Intensity Dispersion,
BUT Note Anticrossing!)

Sm Mode confirmed by (Sm specific)
Nuclear Inelastic Scattering
Red: Fits, AQRB
Blue:@Simulation
AOFSRR Cheiron School 2009

Intensity (Arb. Units)“Localized” Rattling Mode
SmRu4P12-7

2.0x10

25 K

1.0

0.0

-10

0

10

20

AQRB @ AOFSRR Cheiron School 2009

Elastic Constants in Geological Conditions

Liquid Surfaces

Required for Modeling Earths Interior & Interpreting Seismic Data (v->T)

Surface Dynamics are different than bulk…
Surface Sensitivity (~5nm) is possible at Extreme Grazing Incidence… but this is difficult to measure for samples in a DAC

30

Energy (meV)

Anti-Crossing Subsequently Confirmed
Christensen et al, Nature Materials

100e.g. Surface Layering… (fig. Spyrko, et al)q (nm-1)
10.3-1

S(q,! )/S(q) (1/meV)

10

10-2
10-3
3.6

10-1

MgO
5% Uncertainty in v-> 750K in T

10-2
-3

10

-15 -10Liquid Indium (ESRF)
Precision/Accuracy 0.2/0.8% using
Christoffel’s Eqn & 12 Analyzer Array

-5

0

5

! (meV)

10

15

Favorable Tests in Air…
UHV Chamber now being commissioned.
(D. Ishikawa)

Gate Valve
Residual Gas
Analyzer
Sputter Ion Gun

H. Fukui, et al., JSR

TMP Linear Transfer
Mechanism
Ionization
Gauge~1 Order Improvement Over Previous IXS

X-ray Window
Electrode Feedthrogh

One Scan with 12-Analyzers

AQRB @ AOFSRR Cheiron School 2009

Reichert, et al, PRL 2007

Ion Pump

Vibration Isolation Table

AQRB @ AOFSRR Cheiron School 2009

Atomic -> Electronic Dynamics
AtomicDynamics

d-d Excitations in NiOFirst something simple…

There exist well-defined excitations in the chargetransfer gap of NiO
Antiferromagnet (TN 523K), (111) Spin order

Correlated atomic motions (phonons) play a role in many phenomena(e.g. superconductivity, CDWs, phase transitions, thermoelectricity, magneto-elastic phenomena etc)

Electronic Excitations…. A New Field

High (~10 meV) Resolution
at Large Momentum Transfers

Long and Distinguished History

First (resonant) IXS experiments (Kao, et al)

Non-Resonant IXS, !E~300 meV

Orbiton Movie
S. Maekawa

1 electron-> Very Weak

Calculated Orbiton Dispersion
Ishihara

Key is to see momentum dependence (dispersion) -> Not Yet.
First Attempt via IXS: NJP 2004

Larson, et al., PRL 99 (2007) 026401
AQRB @ AOFSRR Cheiron School 2009

High Resolution Experiment
7 meV resolution at 1800 meV energy transfer

Cleaner “Optical Spectroscopy” due to
1. Non-resonant interaction S(Q,$)
2. Large Q & Q dependence-> selects multipole order.
-> atomic correlations.
Linewidth -> information about environment
Spin fluctuations
Lattice interactions (Franck-Condon)
d-d Excitation in NiO

Baron et al, Fall 07, 3 Days/Spectrum

Collective interaction <-> dispersion(d-d excitations -> “orbiton”)

Relevance to correlated materials…
Gaps (Mott, Charge Transfer) and
Mid-IR band in high Tcs
f-electron transitions, etc

Cai, Hiraoka, et al, BL12XU
UnpublishedAQRB @ AOFSRR Cheiron School 2009

“Momentum Resolved Optical
Spectroscopy”
Conventional Optical
Spectroscopy:(Absorption, Reflectivity)

Information on electronic energy levels but without
information on inter-atomic correlations or
atomic structureWith x-rays, the short wavelength allows direct probe at atomic scale:

Is an excitation collective or local (does it disperse)?
What is the atomic symmetry of an excitation?
How does it interact with the surrounding environment?
Resonant experiment vs non-resonant IXS experiment.

Non-resonant experiment is simpler and can have higher resolution… but badly flux limited
AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

NRIXS

Larger Energy Range

MgB2 Collective Excitation

Hiraoka et al

Excitation repeats from one zone to the next…
AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

RIXS -> 2 Orbiton

RIXS & NRIXSThis is different…

30 to 300 meV resolution

Both are Methods of Probing Electronic Structure
RIXS = Resonant IXS = Near an absorption edge
NRIXS = Non-Resonant IXSRIXS: Higher Rate
Poorer Resolution (Optics must match resonance)
Element Specific (Somewhat)
More Complicated Data
NRIXS: Lower Rate
Higher Resolution (Choose energy to match optics)
Simpler & Cleaner Data

Ti L-Edge RIXS at the SLS
Signal from “2-orbiton”, someevidence of changes with Q
Nice,…but not real orbiton dispersion.

Slightly Different Experimental Setup
AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

2-Magnon Peak?

Copper K-Edge RIXS
120 meV resolution, APS, Sector 9
Q Dependence (over zone)
and polarization dependence
d-d Excitation or 2-Magnon?

AQRB @ AOFSRR Cheiron School 2009

IXS Beamline Evolution
Effective Flux [1014/s/0.1%BW]

For meV Resolution at 20 keV

NewBeamline

AQRB @ AOFSRR Cheiron School 2009

A Next Generation Beamline
Dramatic Improvement to Source and Spectrometerallows new science…
New Field: Electronic excitations

NSLS-II(Not Proven)

Also many expts now flux limited:

Phonons in complex materials
Extreme environments (HT, HP liquids)
High pressure DAC work (Geology)
Excitations in metal glasses
Super-cooled liquids
etc?
Present
Status
Source & BL
Improvements

ESRF

ERL
(~$1B,
Not Funded)
Machine Barrier

Expected
UpgradesImprovements

Flux On Sample: x10
Parallelization: x3
Small Spot Size: x5

AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

RIKEN Quantum NanoDynamics Beamline

Si Refection Order
Energy (keV)
Resolution (meV)
Flux (1014/s/0.1%)
BL35 (1014/s/0.1%)
Q Max (Å-1)c(888) EEa
15.816
40
68
4.9
16

(888)
15.816
6
68
4.9
16

(999)
17.7943
64
7.1
18(11 11 11)21.747
1.5
50
5.9
22

(13 13 13)25.7021 (0.7)b30 (40)b
4.7
26
AQRB @ AOFSRR Cheiron School 2009

X-Ray Raman Scattering

AQRB @ AOFSRR Cheiron School 2009

X-Ray Raman Scattering(Example of Ice Under Pressure)

Suppose you would like to measure the structure of the oxygen kedge (at 532 eV) of a sample inside of a high pressure cell with 1mm
thick diamond windows?
Diamond:labs < 0.5 um 500 eVlabs ~ 2 mm 10 keV
Easier at 10 keV than 0.5 keV
Note: need dipole approx. (Q.r<1) to be good tocompare with usual XAFS.

Nagasawa, et al, J. Phys. Soc. Jpn. 58 (1989) pp. 710-717
AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

Three-Dimensional Momentum Density
Reconstruction

Compton Scattering
For very large Q and !E<<E one can takem## dp x dp y $ (p z = pQ )!Q
m%J(pQ )!Q

S(Q," ) =!

Three-dimensional momentum density, n(p), can bereconstructed from ~10 Compton profiles.

From ShülkeJ(p z ) = !! n(p)dp x dp y

Typical: Q~100Å-1
E>100 keV

Reconstruction:
・Direct Fourier Method
・Fourier-Bessel Method
・Cormack Method
・Maximum Entropy Method

Ie: Compton scattering projects
out the electron momentum
density.

Momentum density, n(p)Typical of incoherent scattering…
AQRB @ AOFSRR Cheiron School 2009

Fermi surfaces of Cu and Cu alloys

AQRB @ AOFSRR Cheiron School 2009

Spin Polarization by Magnetic Compton
Scatetring
Magnetic Compton scattering combined with ab initio electronic structure
calculation is used to evaluate the degrees of spin polarization, Pn.Spin Polarization of Co2-xFexS2

Cu-15.8at%Al

Cu

Cu-27.5at%Pd

Determined by Compton scattering at KEK-AR
J. Kwiatkowska et al., Phys. Rev. B 70, 075106 (2005) 

AQRB @ AOFSRR Cheiron School 2009

C. Utfeld et al., PRL Accepted
AQRB @ AOFSRR Cheiron School 2009

Nuclear Inelastic Scattering

NIS SetupFirst Demonstrated (Clearly) by Seto et al 1995

Use a narrow bandwidth monochormator
The nucelar resonance becomes the analyzer.

Mössbauer Resonances Exist in Different Nuclei…

!E ~ eVHigh Heat Load
Monochromator

Resonances have relatively long lifetimes so that if one has apulsed source, one can separate the nuclear scattering by using afast time resolving detector.

!E ~ meVHigh Resolution
Monochromator

1. Ein = Eres
2. Ein + Ephonon = Eres
3. Ein - Ephonon = Eres

SampleForward Detector(NFS)
Incoherent Detector(NIS)

Single Photon
Creation

Element- Specific!
Projected!
Phonon DOS!

Nuclear Scattering

PhononCreation +Annihilation

Two Photon
Annihilation

-40

-30

Y

Single Photon
Annihilation

-20

-10

0

10

Two Photon
Creation

20

30

5

40

Energy (meV)AQRB @ AOFSRR Cheiron School 2009

NIS Gives the Partial Projected DOS
Projected= Weakly Directional

I ~ " •k1!

Calculation: Boeri et al

35

Time Domain!
Mossbauer Spectroscopy!
AQRB @ AOFSRR Cheiron School 2009

NIS: Good and Bad

Example of the Fe-As Superconductors

Partial= Element Specific

10
15
20
25
30
Time After Excitation [ns]Important things to note:
1. Element and isotope selective.
2. Gives Projected Density of states NOT Dispersion(But it does this nearly perfectly)

Measurement: Higashitaniguchi et al

AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009

NIS Example: Surface DOSNIS Example: Biological Macro-Molecules

Slezak et al PRL 99 (2007) 066103

57Fe monolayers near the surface of 56Fe

e.g.

Where element specificity
can help a lot.

Note projection!
AQRB @ AOFSRR Cheiron School 2009

AQRB @ AOFSRR Cheiron School 2009