Inelastic X-Ray Scattering
PRELIMINARY VERSION
Alfred Q.R. Baron
Materials Dynamics Laboratory (RIKEN)
Research and Utilization Division (JASRI)
SPring-8
AQRB @ AOFSRR Cheiron School 2011

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

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)

Comment: Mostly no history
AQRB @ AOFSRR Cheiron School 2011

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 IXS

Note: !E = Typical Energy Transfer (Not Resolution)
Note also: Limit to FAST dynamics (~10 ps or faster)
AQRB @ AOFSRR Cheiron School 2011

Excitations

0!

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Some References
Shulke, W. (2007), Electron Dynamics by Inelastic X-Ray Scattering.!
New York: Oxford University Press.!
& References therein (RIXS, X-Ray Raman, NRIXS…)!
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

AQRB @ AOFSRR Cheiron School 2011

Spectroscopy

Absorption vs. Scattering
Absorption
Spectroscopy
Optical, IR, NMR

Measure absorption as you
scan the incident energy
When energy hits a resonance,or exceeds a gap, or… get a changeFree Parameters: E1, e1, k1-> In principle, 3+ dimensions
but in practice mostly 1 (E1)

Scattering
Spectroscopy
IXS, Raman, INSE1 k1 e1

Optical Spect. NiONewman, PR 1959

E2 k2 e2

Free Parameters: E1, e1, k1, E2, e2, k2-> In principle, 6+ dimensionsin practice, mostly 4: E1-E2, Q = k2-k1

Scattering is more complex, but gives more information.
Note: Fluctuation Dissipation Theorem

AQRB @ AOFSRR Cheiron School 2011

X-Ray Scattering Diagramk1
Q!

E1 k1 e1E 1 = !!1 =hc= !ck 1"1

k 1 = k1 =Q = k２- k1

2!

"1

E2 k2 e2

hc = 12.398 keV• Å

Two Main Quantities:
Momentum Transfer

Energy Transfer

Q ! k 2 " k1

E or !E = E 1 " E 2 # !$Q! Q #

4$

%1

( )

sin &
2

Periodicity Probed

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

d=

2!
Q

AQRB @ AOFSRR Cheiron School 2011

Excitations“Low” Q (d ~ Å)Collective Response“High” Q ( d<<1Å)
Single Particle Response
AQRB @ AOFSRR Cheiron School 2011

Dynamic Structure Factor
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 !
d 2#
2
*
2
I scattered (Q,! ) "= re e2 • e1
S(Q,! )
d$d!
!1

(

(

! T hom son = re e2 •e1
2

*

)

)

S(Q,! )

2

Thomson Scattering
Cross Section

Dynamic Structure Factor“The Science”“A Scale Factor”

AQRB @ AOFSRR Cheiron School 2011

Different Views of S(Q,w)
2

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

# e

iQ•r j" $ ( E" '%E" % !! )electrons
j

2

=

=

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

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 2011

Kinematics
Mk1
Q!

E1 k1 e1

Q = k２- k1
E2 k2 e2Kinetic Energy Given to Sample:

E recoil =Take: M=57 amu, Q/c = 7 Å-1 -> Er=2.3 meV

p2! 2Q 2=2M
k!2M
E! eˆ '
!Q
" d! !! S(Q,! )=2M" d! S(Q,! )2

f-sum rule:
Compton Form: ! 2 " ! 1 =h(1 " cos #)
Mc

!c =

2

h
= 0.0243Å
m ec

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The IXS Spectrometer
An Optics Problem
Main Components

k ! E ! eˆ'Monochromator:
Modestly Difficult
Only accepts 15x40 !rad2

Sample Stages
Straightforward
Only Need Space

Analyzer:
Large Solid Angle
Difficult

The Goal: Put it all together and
Keep Good Resolution, Not Lose Flux
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Basic Optical Concept
Bragg’s Law : " = 2d sin(#B)! =>!

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

Working closer to #B~90 deg. maximizes the angular
acceptance for a given energy resolution…
Better energy resolution-> Closer to 90 degrees-> Large Spectrometer

AQRB @ AOFSRR Cheiron School 2011

High Resolution Analyzer Crystals
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.
1. Cut!

2. Etch!

3. Bond to !
Substrate!

4. Remove Back!
X-Rays!

104 Independent!
Perfect Crystals!

Note: For resolution >300 meV, bending can be OK.
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Analyzer Crystal
Collaborative R&D with NEC Fundamental Research Laboratory, H. Kimura, F. Yamamoto!

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!

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A High (meV) Resolution Spectrometer

Spectrometer Photo
Spectrometer Photo
Slit System!

12 Chan. CZT Detector!

Sample!

Analyzer Array!

10m Arm & 12 Analyzers
Vacuum Flight Path!

Incident�Beam!
%~100 µm!
% 20 µm Possible!

Granite Base w/Airpads!
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A Medium Resolution Spectrometer
Medium Resolution Spectrometer:
Arm Radius: 1 to 3 m
Resolution: ~0.1 to 1 eV
Used for RIXS and NRIXS
BL12XU
3m Arm at BL12XU
BL12XU (Early)

BL11XU

Shorter Possible(later, if time)

Note difference between RIXS and NRIXS

NRIXS: Choose the energy to match the optics
RIXS: Resonance chooses energy -> usually worse resolution

AQRB @ AOFSRR Cheiron School 2011

Other Spectrometers @ SPring-8
NRS Optics BL09

RIXS Spectrometer
2m Arm, BL11XU
Emission SpectrometerF~1.5m Chamber

Compton Spectrometer BL08(~eV Resolution)
Hayashi, et al
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Other High Resolution Spectometers
ESRF

APS

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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?

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 2011

Disordered Materials
Liquids & Glasses

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

(Kawakita et al)l-Si (Hosokawa, et al)a-Se (Scopigno et al)

AQRB @ AOFSRR Cheiron School 2011

The IXS Advantage
INS
Diagram

IXS has no kinematic limitations (DE<<<Eg)
Large energy transfer at small momentum transfer-> excellent access to mesoscopic length scales

Glassy-Se

Water
Teixeira, et al
INS (1985)

Data of Foret et al

INS (1998)

Scopigno et al
IXS (2004)

Sette et al
IXS (1996)+15 meV!

Also:-15 meV!

No Incoherent Background
Small Beam Size (f<0.1mm)

But:<1 meV resolution is hard
Low Rates for Heavy Materials

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Metal to Insulator Transition in Liquid Mercury
Universal Phenomenon in Liquids:
Expand a liquid metal enough and it becomes an insulator.

For Hg~1500 C & ~ 1.5 kbar

15 mm Be, 200 m He (STP), 0.15 mm Sapphire~ 20 microns Hg
D. Ishikawa, M. Inui, K. Tamura, et al.
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“Fast Sound” at the Metal-Non-Metal Transitionin Liquid Hg
Universal Phenomenon in Liquids:
Expand a liquid metal enough and it becomes an insulator.

Ultrasonic
Velocity

Suggests a change in the microscopic
density fluctuations…
Probably general phenomenon…
but no confirmation yet.
(Next M-I transition under discussion)

D. Ishikawa, et al, PRL 93 (2004) 97801~2 months of beam time…
AQRB @ AOFSRR Cheiron School 2011

On Positive Dispersion
Very General feature:
As Q increases the phase velocity of theacoustic mode becomes larger than the
Low-Q (e.g. ultrasonic) sound velocity.
Casual explanation

Sette et al

For smaller length scales (high Q) and higher
frequencies, a liquid, locally, resembles a solid
which has a faster sound velocity.
Partial explanation in terms of a visco-elastic model…
Scopigno & Ruocco RMP 2005
Ruocco & Sette CMP 2008
Bryk et al JCP 2010
Hosokawa, et al

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Dynamical Distinction
Widom Line
Maximum in Cp

Supercritical
Argon

Simeoni et al NPhys 2010

Take the presence of Positive Dispersion
as the definition of liquid-like behavior
Gorelli et al, PRL (2006)
Simeoni et al, NPhys (2010)
Also Bencivenga et al EPL (2006)

AQRB @ AOFSRR Cheiron School 2011

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

Shear Wave -> Harder...
S (Q,! ) "# dte # dr # dr%$i!t

e iQ•( r$ r %) & (r%,t) &(r,t = 0)?

Weak, but significant, signal.
Hosokawa, et al, PRL (2009)

Next experiment: l-Cu
2.5 Days -> ?
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Elastic Inhomogeneity in a Glass
Ichitsubo, et al.

Pd42.5Ni7.5Cu30P20

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)
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Phonons in a Crystal
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.
-> 3R modes for any given q

AQRB @ AOFSRR Cheiron School 2011

MgB2 As An Example
Layered Material
Hexagonal Structure

B Layer

B-B Bond is Short& Stronger

Mg Layer

Mg-Mg Bond isLonger & Weaker3 Atoms/cell -> 9 modes / Q PointAQRB @ AOFSRR Cheiron School 2011

Acoustic and Optical Modes
Acoustic Modes are Continuum (Smooth) Modes

LA ModeCompression ModeTA ModeShear Mode

Optical Mode
Atoms in one unit cellmove against each-other

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Dispersion of an Optical Mode(0 0 0)(0.25 0 0)

(0.5 0 0)

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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
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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
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Superconductors @ BL35XU
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

From T. Fukuda

Dark Blue Line: Conventional, Phonon-Mediated Superconductors
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MgB2
High Tc (39K)

Phonon Structure

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

Simple Structure…
straightforward calculation.

Electronic Structure

Kortus, et al, PRL 86 (2001)4656

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

BCS (Eliashberg) superconductor with mode-specific electron-phonon coupling.
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Electron-Phonon Coupling in MgB2
Dispersion

SpectraLinewidth!!

M!

Clear correlation between
0
50
100!
linewidth & softening.
Excellent agreement with LDA Pseudopotential calculation.
PRL 92(2004) 197004: Baron, Uchiyama, Tanaka, ... Tajima
AQRB @ AOFSRR Cheiron School 2011

Carbon Doped Mg(CxB1-x)2
M

2%C, Tc=35.5K

12.5% C, Tc=2.5K

AlB2 (Not SC)!
Phonon structure correlates nicely with Tc for charge doping.
(Electron doping fills the sigma Fermi surface)
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More Superconductors
Similar types of results for
Mn Doped MgB2
CaAlSi
Boron Doped Diamond

Extrapolation to the High Tc Copper Oxide Materials….
1. Much More Complex
2. Calculations Fail so interpretation in difficult

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Phonons in the Cuprates…
Everyone has their favorite mode, or modes, usually focus on Cu-O planes(0 0)In-Plane Mode:(0.5 0)Stretching mode
Out of Plane Modes:
Buckling Mode
Apical ModeAt the level of phonon spectra, the anomaly of theBond Stetching Mode is very large
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Copper Oxide Superconductors
Remain Challenging…
C-axis modes

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

In-Plane Modes

Lines = Calculation
Points = IXSBeautiful Agreement
Shows Bond Stretching Anomaly
Is Huge (>> Buckling Anomaly)

Problems

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

Bohnen, et al.

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La1.48Nd0.4Sr0.12CuO4
Phonon anomaly (blurring) is highly localized in
momentum space…
Expt done by a neutron scatterer because
he could not get good enoughresolution using neutrons
Forces a reinterpretation of some Neutron
data (Reznik, Nature, 2006)

Note:
D. Reznik, et al, Accepted

IXS Q Resolution
Analyzer array
Count rate limited.

2.5 days
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The Iron-Pnictide Superconductors
High-Tc demonstrated February 2008 (Hosono’s group)-> Research Explosion

Fe Planes with Tetrahedral As
Parent (non SC) Shows Mag. Order & Tetragonal-> Orthorhombic Transition at ~140 K
AQRB @ AOFSRR Cheiron School 2011Materials

Zhao, Nmat

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SamplesSingle Crystals of PrFeAsO1-y~100!m

Superconductor: Tc (onset) ~ 45 K
Parent: Resistivity Change at ~145 K
Typically “reasonable” crystal quality~1 degree mosaic
Measurements
3 to 6 hours / spectrum (Fe&As!)
Wide variety of Q and T<=300K
Many small changes with doping & T

PrFeAsO1-y
20 um Thick
Transverse: ~0.1 to ~0.5 mm

Ishikado, Kito, & Eisaki(at AIST)AQRB @ AOFSRR Cheiron School 2011

Some Examples of Measured Spectra:

ParentIn-PlaneC-axisGenerally: Differences in measured spectra (doping, temperature)are smaller than difference between DFT calculations and Data…
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Different Models:
Original: Straight GGA for Tetragonal stoichiometric PrFeAsO
Soft: As “Original” but soften the FeAs NN Force constant by 30%
Soft O7/8: Super cell 2x2x1 with one oxygen removed
and softened Fe-As NN Force constant(31 atoms/prim cell, Tetragonal, No Magnetism)

Magnetic Orthorhombic: LSDA for LaFeAsO withstripe structure of De la Cruz (16 atoms/prim. cell, 72 Ibam)
Magnetic Tetragonal: LSDA for LaFeAsO with stripes
Force a=b (to distinguish effects of structure vs magnetism)
Clipped: Mag. Ortho. with cut force constantSoft IP: “Original” but soften FeAs NN In Plane components
Calculations: Nakamura & Machida
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Compare dispersion with models

Red = Data (SC)Blue = Calc.

Area/Height: Intensity

Over all: Better fit with magnetic calculations
And best fit with either “clipped” or “IP Soft” model
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But: No evidence of magnetic anisotropy
in the phonon spectra
Parent, 10 K
(110)

Magnetic
Model

Splitting along the (110) direction ispredicted but not observed, even in theparent materials…

AQRB @ AOFSRR Cheiron School 2011

Soften In-Plane Fe-Fe Force-ConstantSoftening the in-plane componentsof the force-constant matrix
Avoids the anti-crossing

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Phonons in a Quasicrystal

Mostly like a solid but some glassy character.
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

Red: Fits, AQRB
Blue:@Simulation
AOFSRR Cheiron School 2011

SmRu4P12

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

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

Sm Mode confirmed by (Sm specific)
Nuclear Inelastic Scattering
Anti-Crossing Subsequently Confirmed
Christensen et al, Nature Materials

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

2.0x10

25 K

1.0

0.0

-10

0

10

20

30

Energy (meV)AQRB @ AOFSRR Cheiron School 2011

Elastic Constants in Geological Conditions
Required for Modeling Earths Interior & Interpreting Seismic Data (v->T)… but this is difficult to measure for samples in a DAC

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

Precision/Accuracy 0.2/0.8% using
Christoffel’s Eqn & 12 Analyzer Array
H. Fukui, et al., JSR~1 Order Improvement Over Previous IXSOne Scan with 12-Analyzers

AQRB @ AOFSRR Cheiron School 2011

Liquid Surfaces
Surface Dynamics are different than bulk…
Surface Sensitivity (~5nm) is possible at Extreme Grazing Incidence
e.g. Surface Layering… (fig. Spyrko, et al)

Liquid Indium (ESRF)

Reichert, et al, PRL 2007

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

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Novel Uses of The Phonon Intensity
Phonon Cross Section:

In principle, the phonon polarization is complex, but in some cases, it can be
simple, or smooth, letting one get information aboute.g.
the form factor from frequency resolved measurements or
sharp frequency changes from integrated measurements
AQRB @ AOFSRR Cheiron School 2011

Using Thermal Diffuse Scattering(TDS)
Phonon Intensity ~ 1/w -> In simple materials can use intensity togain insight about phonon frequencies
Long history… at least to Colella and Batterman PR 1970 (Va dispersion)More sensitive -> See Kohn anomalies when
phonons span the Fermi surface

Zn,
TDS from SiliconHolt, et al, PRL 1999

Bosak et al, PRL 2009

Detailed Phonon/FS behavior in SIMPLE materials
More generally very useful, but not so detailed
Learn where to look…
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Atomic -> Electronic Dynamics
AtomicDynamics
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

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

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d-d Excitations in NiOFirst something simple…

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

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

Non-Resonant IXS, !E~300 meV

Larson, et al., PRL 99 (2007) 026401

Cai, Hiraoka, et al, BL12XU
UnpublishedAQRB @ AOFSRR Cheiron School 2011

Orientation Dependence

Orbitals
Results of Wanneir function
analysis of LDA+U calcsof Larson et al PRL (2007)

ScatteredIntensity

Cluster calculations
Haverkort, et al PRL (2007)

AQRB @ AOFSRR Cheiron School 2011

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
AQRB @ AOFSRR Cheiron School 2011

“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 2011

NRIXS

MgB2 Collective Excitation

Excitation repeats from one zone to the next…
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Larger Energy Range

Hiraoka et al
AQRB @ AOFSRR Cheiron School 2011

RIXS & NRIXS
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

Slightly Different Experimental Setup
AQRB @ AOFSRR Cheiron School 2011

RIXS -> 2 Orbiton
This is different…

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

AQRB @ AOFSRR Cheiron School 2011

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 2011

AQRB @ AOFSRR Cheiron School 2011

X-Ray Raman Scattering

Nagasawa, et al, J. Phys. Soc. Jpn. 58 (1989) pp. 710-717
AQRB @ AOFSRR Cheiron School 2011

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.

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Nuclear Inelastic ScatteringFirst Demonstrated (Clearly) by Seto et al 1995

Mössbauer Resonances Exist in Different Nuclei…

Resonances have relatively long lifetimes so that if one has apulsed source, one can separate the nuclear scattering by using afast time resolving detector.
Nuclear Scattering
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NIS Setup
1. Ein = Eres
2. Ein + Ephonon = Eres
3. Ein - Ephonon = Eres

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

$E ~ eVHigh Heat Load
Monochromator

Sample$E ~ meVHigh Resolution
Monochromator

Forward Detector(NFS)
Incoherent Detector(NIS)

Element- Specific!
Projected!
Phonon DOS!
Time Domain!
Mossbauer Spectroscopy!
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NIS Gives the Partial Projected DOS
Example of the Fe-As Superconductors

Partial= Element SpecificCalculation: Boeri et al

Projected= Weakly Directional

I ~ ! •k1

Measurement: Higashitaniguchi et al

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NIS: Good and Bad
Important things to note:
1. Element and isotope selective.
2. Gives Projected Density of states NOT Dispersion(But it does this nearly perfectly)

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Surfaces by NIS
The large nuclear cross section allows sensitivity even tomonolayers with relatively low backgrounds

In-Situ Deposition@ ESRF
Stankov et al, JP 2010

57Fe on W(110)

Stankov et al PRL (2007)

Also: Multilayers - Cuenya et al, PRB 2008

57Fe with 56Fe
Slezak et al PRL 2007

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NIS Example: Biological Macro-Moleculese.g.

Where element specificity
can help a lot.

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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,! ) =From Shülke

Typical: Q~100Å-1
E>100 keV
Ie: Compton scattering projects
out the electron momentum
density.
Typical of incoherent scattering…
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Three-Dimensional Momentum Density
Reconstruction
Three-dimensional momentum density, n(p), can bereconstructed from ~10 Compton profiles.

J(p z ) = !! n(p)dp x dp y
Reconstruction:
・Direct Fourier Method
・Fourier-Bessel Method
・Cormack Method
・Maximum Entropy Method

Momentum density, n(p)From Y. Sakurai

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Fermi surfaces of Cu and Cu alloys

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) 

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Spin Polarization by Magnetic Compton
Scattering
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

C. Utfeld et al., PRLAQRB @ AOFSRR Cheiron School 2011