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

Inelastic X-Ray Scattering

Alfred Q.R. Baron
Materials Dynamics Laboratory (RIKEN)
Research 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
Resonant
Others (time permitting)

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Some References

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Scientific Information(from IXS)

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). Compton Scattering Rep. Prog. Phys. 48 415-481
Ament, L.J., et al, (2011). RIXS, Rev. Mod. Phys. 83 705-767

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Atomic Dynamics <-> Motions of atoms in a solid (phonons) or liquid.

Phase transitions, thermal properties, fundamental science (Atomic binding)Electron-phonon coupling, Magneto-elastic coupling
Superconductors, Ferroelectrics, multiferroics, etc

Electronic Dynamics <-> Motions/transitions of electrons
Chemical Bonding (Valence, etc)
Electronic Energy Levels (atomic/molecular)
Delocalized Electronic Excitations
Generalized Dielectric Response
Fermi-Surface Topology
Magnetic structure
Complex Materials
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Table Of IXS Techniques/Applications
Energy Scale

Information

X-Ray Raman(E)XAFS in Special Cases

Ein~10 keV
ΔE~100-1000 eV

Edge Structure, Bonding

ComptonOldestNote: Resolution Limited

Ein ~ 150 keV
ΔE ~ keVElectron Momentum Density
Fermi Surface Shape

Magnetic Compton

Weak But Possible

Ein ~ 150 keV
ΔE ~ keV

Density of Unpaired Spins

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

Electronic Structure

Exploding, Huge Instruments
Surface Sensitivity

0.1-1.5 keV
ΔE ~ 0.05 - 5 eVElectronic & Magnetic
Structure

Non-Resonant IXS

Low Rate
SimplerEin~10 keV
ΔE ~ <1-50 eV

Electronic Structure

IXS

Large Instrument

Ein~16-26 keV
ΔE ~ 1-100 meV

Phonon Dispersion

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

RIXS

Resonant IXSSIXSSoft (Resonant) IXSNRIXS

High-Resolution IXSNIS

Nuclear IXSAtom SpecificVia Mossbauer Nuclei(arb. units)

Comment

S(Q,omega)

Technique

Excitation Energy Scales
Elastic

Phonons
ComptonCore

QuasiElastic

-4
100!

Valence

Plasmon10-3 10-2 10-1 100
101
102
Energy Transfer to Sample [eV]103

Note: ΔE = Typical Energy Transfer (Not Resolution)
Note also: Limit to FAST dynamics (~10 ps or faster)

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AQRB @ AOFSRR Cheiron School 2014

Spectroscopy

Where We Are Measuring

Absorption vs. Scattering
Absorption
Spectroscopy

Measure absorption as you
scan the incident energy

Optical, IR, NMR

When energy hits a resonance,or exceeds a gap, or… get a change

Raman

Between the Bragg Peaks…
Conventional Diffraction
Linear Scale

Meas.

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

Scattering
Spectroscopy
IXS, INS

Optical Spect. NiONewman, PR 1959

SiliconE1 k1 e1

On Log Scale

Precession PhotoE2 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.
Energy scales PLUS spatial structure on scale of probe wavelength

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Calc

Holt et al

Ruby

Laue Photo

Bragg peaks

For IXS we are usually measuring between the
Bragg peaks where the intensity is weaker.
A strong signal is down by 107, weak by 1011

Why…?
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X-Ray Scattering Diagram

Resonant vs Non-Resonant

k1

E 1 = ω 1 =hc= ck 1
λ1

k 1 = k1 =Resonant:

Tune near an atomic transition energy
ie: K, L or M Edge of an atom
Generally High Rate
Complex interpretation
Energy fixed by resonance -> poorer resolution

NonResonant:Far from any atomic transition.
Small cross-section
Interpretation directly in terms of electron density
Choose energy to match optics -> good Resolution

!

E1 k1 e1

Q =k- k1

2π

E2 k2 e2

λ1

RIXS
SIXS

hc = 12.398 keV• Å

Two Main Quantities:
Energy Transfer

Momentum Transfer

E or ΔE = E 1 − E 2 ≡ ωQ ≡ k 2 − k1
Q≡ Q ≈

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

4π

λ1

IXS
NRIXS

( )

sin Θ
2

Periodicityd=Different Experimental Setups -> Modern Specialization

2π
Q

Nuclear Resonant & Compton Scattering -> Different
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AQRB @ AOFSRR Cheiron School 2014

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 k
d 2σ
2
I scattered ( Q, ω ) ∝= re2 e2* • e1
S ( Q, ω )dΩdωk1

σ T hom son = re

2

(

)

2
*
e2 •e1

Thomson Scattering
Cross Section
A Scale Factor

S(Q,ω )
Dynamic Structure Factor
The Science

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Different Views of S(Q, )2

S(Q,ω ) = ∑ pλ λ '
λ,λ '

∑ e

iQ•r jλ δ ( Eλ '−Eλ − ω )Transition between stateselectronsjFluctuations in electron density==

1∫ dt d 3r d 3r' e−iQ•r ρ(r',t = 0)ρ + (r + r',t )2π11Im{− χ (Q,ω)}π 1− e−ω /kBT

=

→

N∑
q

∑ ∑
Modes

d
Atoms
/Cell

1
1
1
Im{−ε −1(Q,ω)}π 1− e−ω /kBT v(Q)2fd (Q) −W d (Q)eQ •eqjd eiQ•x d δ(Q−q),τ Fqj (ω)
2M dGeneralized Response(e.g. Dielectric functions)

See Squires, Lovesy, Shulke, Sinha (JPCM 13 (2001) 7511)

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Kinematics

Why is it Better to Measurein Momentum/Energy Space?

Conservation of Energy

For diffraction (and diffractive/coherent imaging), one goes togreat lengths to convert from momentum space to real space.
If possible, a direct real-space measurement is preferred.

M
k1
!

E1 k1 e1

Q =k- k1
E2 k2 e2

So whyS(Q,ω )

Kinetic Energy Given to Sample:

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

f-sum rule:
Compton Form: λ 2 − λ 1 =AQRB @ AOFSRR Cheiron School 2014

The IXS Spectrometer
An Optics Problem
Main Components

λc = 2Q 2∫ dω ω S(Q,ω )=2M∫ dω S(Q,ω )h= 0.0243Å
m ec

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Basic Optical Concept(Hard x-rays)

k ′ E ′ eˆ'

Bragg’s Law : λ = 2d sin(ΘB)! =>!

Monochromator:
Modestly Difficult
Accepts 15x40 μrad2

Δθ = tan ⎛⎜⎝ Θ⎞ ΔE
B ⎟⎠ E

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

Sample Stages
Straightforward
Only Need Space

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

Analyzer:
Large Solid Angle
Difficulth(1 − cos Θ)Mcp2
 2Q 2=2M
k′2M
E′ eˆ 'ΔE E 1 N planes

The Goal: Put it all together and
Keep Good Resolution, Not Lose Flux

Note: small bandwidth means starting flux reduced by 2 to 3 orders of magnitude…
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AQRB @ AOFSRR Cheiron School 2014

High Resolution Analyzer Crystals
The more difficult optic…

Detector

Require:!
Correct Shape (Spherically Curved, R=9.8 m)!

SampleAnalyzer Crystal!

!

Not Strained (ΔE/E~few 10-8-> Δd/d<<few10-8)!

!
!

Analyzer
Crystal

Method: Bond many small crystallites to a curved substrate.
1. Cut!

3. Bond to !
Substrate!

2. Etch!

4. Remove Back!
X-Rays!

104 Independent!
Perfect Crystals!

Note: For resolution >300 meV, bending can be OK.
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A High (meV) Resolution Spectrometer

Spectrometer Photo
Spectrometer Photo

12 Chan. CZT Detector!

Not so easy…

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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

Sample!

Analyzer Array!

BL12XU

10m Arm & 12 Analyzers

3m Arm at BL12XU
BL12XU (Early)

Vacuum Flight Path!

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

BL11XU

BL43LXU

Shorter Possible(later, if time)10!E (meV)

Note difference between RIXS and NRIXS

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

Slit System!

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!

1

0.1

10

Granite Base w/Airpads!

15

20

25

30

35

40

E(keV)AQRB @ AOFSRR Cheiron School 2014

AQRB @ AOFSRR Cheiron School 2014

High Resolution Spectrometers

Other Spectrometers @ SPring-8

ESRF (ID28)

NRS Optics BL09

APS (Sector 30)

RIXS Spectrometer
2m Arm, BL11XU
Emission Spectrometerφ 1.5m Chamber

HRIXS~10m scale instruments

Compton Spectrometer BL08(~eV Resolution)
Hayashi, et al
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SPring-8 BL35XU

Disordered Materials

Atomic Dynamics: Systems and Questions
Disordered Materials (Liquids & Glasses):
Still
a new
Nearly allGoodnew data
is interesting.
20+
years
offield
IXS ->-> Slowing->
questionsneeded…
How do dynamical modes survive the cross-over from thelong-wavelength continuum/hydrodynamic regime toatomic length scales?

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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 2014l-Mg

(Kawakita et al)a-Se (Scopigno et al)l-Si (Hosokawa, et al)
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The IXS Advantage“Fast Sound” at the Metal-Non-Metal Transitionin Liquid Hg
INS
Diagram

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

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

Ultrasonic
Velocity

Glassy-Se

Water
Teixeira, et al
INS (1985)

Data of Foret et al

INS (1998)

Scopigno et al
IXS (2004)

Suggests a change in the microscopic
density fluctuations…
Sette et al
IXS (1996)+15 meV!

Also:

Probably general phenomenon…
but no confirmation yet.

-15 meV!

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

But:(Next M-I transition under discussion)<1 meV resolution is hard
Low Rates for Heavy Materials

On Positive Dispersion~2 months of beam time…
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Dynamical Distinction

Very General feature:

Widom Line
Maximum in Cp

As Q increases the phase velocity of theacoustic mode becomes larger than the
Low-Q (e.g. ultrasonic) sound velocity.
Casual explanation

Ishikawa, Inui, et al, PRL 93 (2004) 97801

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Supercritical
Argon

Sette et al

For smaller length scales (high Q) and higher
frequencies, a liquid, locally, resembles a solid
which has a faster sound velocity.

Simeoni et al NPhys 2010

Partial explanation in terms of a visco-elastic model…

Take the presence of Positive Dispersion
as the definition of liquid-like behavior

Scopigno & Ruocco RMP 2005
Ruocco & Sette CMP 2008
Bryk et al JCP 2010
Hosokawa, et al

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Gorelli et al, PRL (2006)
Simeoni et al, NPhys (2010)
Also Bencivenga et al EPL (2006)

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

Liquid Excitations = Solid + Disorder?

Shear Wave -> Harder...
S (Q,ω ) ≈Giordano & Monaco, PNAS (2010)∫ dte ∫ dr ∫ dr′−iωte iQ•( r− r ′) ρ (r′,t) ρ(r,t = 0)

IXS from Na: Above & Below TM

0.4
liquid Ga
40°C-1

Q (nm ) =

?

2DHO
0.3
residual x2

Black = Polycrystalline NaBlue = Liquid Na

10.6

1DHO

S(Q,ω)/S(Q) (meV-1)

0.2

Red = Polycrystal + Scaling by
Density, T, & Blurring…

2DHO
0.1
9.2
1DHO
0.0

Weak, but significant, signal.
-20

0
ω (meV)

20

Hosokawa, et al, PRL (2009)

Not bad …

Next experiment: l-Cu
2.5 Days -> ?
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Phonons in a Crystal

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MgB2 As An Example

Normal Modes of Atomic Motion = Basis set for small displacements

Layered Material
Hexagonal Structure

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

B Layer

B-B Bond is Short& Stronger

Mg Layer

Mg-Mg Bond isLonger & Weaker3 Atoms/cell -> 9 modes / Q PointAQRB @ AOFSRR Cheiron School 2014

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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

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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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MgB2

Superconductors

High Tc (39K)

Systems Investigated 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

Phonon Structure

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

Simple Structure…
straightforward calculation.

Electronic Structure

From T. Fukuda

Kortus, et al, PRL 86 (2001)4656

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

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

Dark Blue Line: Conventional, Phonon-Mediated Superconductors
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Electron-Phonon Coupling in MgB2
SpectraDispersion
100

E2g

(2.27, 0, - 0.01)

(meV)

300K
44K
16K

(2.23, 0, - 0.03)

A2u

40

20

0

Points: Measurements at BL35

10Γ!

(2.19, 0, 0.03)

!

20

0

E1u

M

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

30

FWHM

Energy (meV)60

More Superconductors
Linewidth(2.31, 0, 0.01)

B1g
80

A

AQRB @ AOFSRR Cheiron School 2014-1!-M (Å )M!

(2.15, 0, 0.01)

Extrapolation to the High Tc Copper Oxide Materials….
1. Much More Complex
2. Calculations Fail so interpretation in difficult(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.
PRL 92(2004) 197004: Baron, Uchiyama, Tanaka, ... Tajima
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AQRB @ AOFSRR Cheiron School 2014

Copper Oxide Superconductors
Remain Challenging…

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)C-axis modes

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

In-Plane Modes

Lines = Calculation
Points = IXSStretching 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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Iron-Pnictide Superconductors
High-Tc demonstrated February 2008 (Hosono’s group)(Tc saturated within months…)

Beautiful 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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Phonons in the Iron Pnictides
1111 Materials -> 8 Atoms/cell-> 24 Modes (6 mostly oxygen)
Magnetism -> 16 Atoms / 48 Modes
No ab mirror plane-> Complex motions appear quickly
as one moves away from gamma.

Phonon response, in itself, is remarkably plain:
NO very large line-widths
NO obvious anomalies
Several families: Fe with Tetrahedral As (or Se)
Proximity to Magnetic Order
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NO asymmetric Raman lines

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Some Examples of Measured Spectra:

Basic DFT (GGA) for PrFeAsO(No Magnetism)

In-PlaneC-axisSome agreement, but details are poor
Also, fails to get correct As height
above the Fe planes.
Fe-As Bond Length
Expt: 2.41 Å
GGA: 2.31 - 2.33 Å

Parent100

B1g
80Energy (meV)

Estimateof modemotions
based on
calc

60

300K
44K
16K

E2g
A2u

40

E1u
20

0

M

Clear differences in measured spectra (with doping, temperature)-> interpretations requires modeling…

ΓA

Points: Measurements at BL35
Lines: Calculations by Bohnen et al.

A Better Model is Needed

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Symbol size: Measured Intensity
Line Thickness: Calculated Intensity
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Different Models:Compare dispersion with various models

Original: Straight GGA for Tetragonal stoichiometric PrFeAsO

Magnetic Orthorhombic: LSDA for LaFeAsO withstripe structure of De la Cruz (16 atoms/prim. cell, 72 Ibam)

Red =Data (SC)In-Plane

O7/8: Super cell 2x2x1 with one oxygen removed
and softened Fe-As NN Force constant(31 atoms/prim cell, Tetragonal, No Magnetism)

Blue =
Calc.

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

Original ab-initio Calculations: Nakamura & Machida

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C-axisSoft: As Original but soften the FeAs NN Force constant by 30%

Size:
Intensity

Over all: Better fit with magnetic calculations
And best fit with either “clipped” or “IP Soft” model

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Comments

Towards A Better Model?

Of the straight ab-initio calculations, magnetic models do better thannon-magnetic due to softening of ferrmagnetically polarized modes
However, they get details wrong, including too high an energy for AF
polarized modes & predicting splitting that is not observed

Of the modified calculations, the in-plane soft generally seems best,
but still data-calc difference are larger than doping/T effects.
Many people have suggested some sort of fluctuating magnetism, especiallywhen magnetic calculations were seen to be better than non-magnetic
calcs for the (non-magnetic) superconducting materials.
However, phonon response of parent and SC are nearly the same, and it
seems unlikely that fluctuating magnetism is the answer
in the parent material which shows static magnetism.

Fitting of full spectra: intensity vs energy transfer.
Zeroth Approximation: All Samples are the Same
Doping and Temperature Dependence are Weak
Differences between samples is generally much smaller
than between any calculation and the data-> Fit all spectra to a common modeland then fit subsets of the data to determine
effects of doping or phase transitions.

Still some missing ingredient(s) in the calculation-> Interpretation Difficult
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AQRB @ AOFSRR Cheiron School 2014

Phonons in a Quasicrystal

Mostly like a solid but some glassy character.
Building a Quasicrystal (Zn-Mg-Sc)

Ferroelectrics
Develop spontaneous polarization over macroscopic (>~um) domains when T is below
the ferroelectric transition temperature (T0). The origin is a displacement (offcentering) of ions. This is switchable by an external (electric) field.
Zeroth Approximation -> Two types of transitions“Displacive” transition where there is a “continuous” below T“Soft Mode” transition Examples: BaTiO3, KTaO3, Gd (MoO4)3

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

Soft Mode
Nomenclature

Compare to crystalline approximant &Simulation (2000 atoms/cell)Lines & Glass“Order-Disorder” transition where displacements occur firstmetastably and then condense. No soft mode.

General Trend: Blurring out
past a cutoff energy
Pseudo-Brillouin zone size

Examples KH2PO4(KDP), NaNO2, OrganicsA

De Boissieu, et al.
Nature Materials, Dec 2007

Ferrodistortive transition involves softening of gamma point mode
(ferroelectric modes)
Antiferrodistortive involves softening of zone boundary mode
(unit cell size increases)

Red: Fits, Blue: Simulation
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B

Perovskite structure (ABO3) popular as it is relatively simple
and the cubic structure is inherently unstable.. Why?
(3 atoms & one lattice constant)
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Multiferroic EuTiO3Other Multiferroicss

Perovskite – Similar to SrTiO3

Katsufuji& Takagi ,PRB,2001

But with magnetism & coupling ofmagnetic & dielectric response

Sr1-xBaxMnO3

TbMnO3
Cycloidal spin structure coupled todevelopment of polarization below 28K

Phase transition just below RT – putativerotation oxygen octahedra.
Calculations say disorder-order.
Bussman-Holder, PRB, 20111mm

No observed phonon softening may suggest
a different (magnetic) driving force

Classical ferroelectric softmode

IXS -> Phonon Softening-> Displacive

Sakai, et al. PRL 2011 (Tokura-lab)Kajimoto, et al. PRL 2009 (Tokura-lab)

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IXS under High
Pressure

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High Pressure & Temperature for Geology

Specific: elastic properties in extreme (geological) conditions
based on IXS sound velocity measurements
MgO Single Crystal in Ambient Conditions
135GPa,2000-3500K

Often: Just want the sound velocity
Precision/Accuracy 0.2/0.8% using
Christoffels Eqn & 12 Analyzer Array

Vp, Vs (km/sec), (g/cm3)

General Viewpoint: Just another thermodynamic variable.

Vp, Vs Known
Need T, ρ,
Composition

H. Fukui, et al., JSR~1 Order Improvement in Precision
Over Previous IXSICB, 330GPa,
5000~7000K

One Scan with 12-Analyzers
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Earth’s Center, 365 GPa
6000~8000 K

Needed: Lab measurements relating T, Density & Composition to V
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IXS Data for Iron at 167 GPa

Diamond Anvil Cells
P > 200 GPa
T > 5000K (Laser Heating)

So far with IXS:
170 GPa or 3000K

Very clear iron peak, but significant backgrounds(Note diamond background can be tricky-> careful orientation is required)

Std Cell
Laser

Sine fit gives velocity (Vp)

Diamonds: 2 x 1.5mm Thk
Sample: ~ Φ20 μm x 5μm Thk
Also Gasket & Pressure Medium
P increases -> Smaller Sample & Gasket Hole

Cell with Internal Heating

Small samples, Signal low, Poor signal to noise
AQRB @ AOFSRR Cheiron School 2014

Sound Velocity in Pure Iron
Birch’s Law: Linear relation between density and velocity.
SIMPLE, in principle

AQRB @ AOFSRR Cheiron School 2014

Novel Uses of The Phonon Intensity
Phonon Cross Section:

But 3 Facilities ->mostly different results
SP8 is faster than ESRF
and similar to APS
ESRF recently became
faster than before
Pure Iron to 170 GPa
Ohtani et al, submitted

T-Dependence:
APS is sensitive.
SP8 and ESRF are not.
WIP
AQRB @ AOFSRR Cheiron School 2014

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 2014

Using Thermal Diffuse Scattering(TDS)

Atomic -> Electronic Dynamics

Phonon Intensity ~ 1/ -> In simple materials can use intensity togain insight about phonon frequencies

AtomicDynamics

Long history… at least to Colella and Batterman PR 1970 (Va dispersion)More sensitive -> See Kohn anomalies when
phonons span the Fermi surface

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

Electronic excitations similar: Orbitons...?

Orbiton Movie
S. Maekawa

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… use it to learn where to look…

1 electron-> Very Weak

Calculated Orbiton Dispersion
Ishihara

Key is to see momentum dependence (dispersion).
First Attempt via IXS: NJP 2004

AQRB @ AOFSRR Cheiron School 2014

d-d Excitations in NiOAQRB @ AOFSRR Cheiron School 2014

Orientation DependenceFirst 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, ΔE~300 meV

Orbitals
Results of Wanneir function
analysis of LDA+U calcsof Larson et al PRL (2007)
Larson, et al., PRL 99 (2007) 026401

Cai, et al, BL12XU, UnpublishedAQRB @ AOFSRR Cheiron School 2014

Cluster calculations
Haverkort, et al PRL (2007)

ScatteredIntensity
AQRB @ AOFSRR Cheiron School 2014

Momentum Resolved Optical
SpectroscopyLarger Energy Range

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

Hiraoka et al
AQRB @ AOFSRR Cheiron School 2014

AQRB @ AOFSRR Cheiron School 2014

The Orbiton Story

Calculated Orbiton
Dispersion(One, mostly experimental, viewpoint)

Orbital order exists -> there should be an equivalent excitation
Essential picture is of a correlated d-d excitation – change in electronic
wave function on one atom is correlated with change at other atoms.

2001

LaMnO3

Khaliullin & Okamoto (PRL 2002)

But some dissent:

Two phonon peak?
Gruninger (n), Kruger (prl), Marin-Carron (prl)And also corroboration
Calculated Dispersion

Oles, Feiner, Zaanen (PRB 2000)

Saitoh et al, (N 2001)

Raman spectra from different materials
AQRB @ AOFSRR Cheiron School 2014

van den Brink (PRL 2001)

Still Some Debate:
Ishihara (PRB 2004)
Energy scale?
Coupling to phonons and/or spin?
Linewidth small or large?
AQRB @ AOFSRR Cheiron School 2014

Resonant IXS (RIXS)

Recent Work

Soft x-ray RIXS (SRIXS)

K-Edge RIXS (d-d excitations)

Ulrich, Ament, et al (PRL 2009)At SLS/ADDRESS

May, 2012

L3 in YTiO3, 55 meV Resolution at 450 eVHigh Energy Excitation in Sr2CuO3

LaMnO3 Inami, et al (prb 2003)

KCuF3 Ishii, et al (PRB 2011)2-orbiton signal at 250 meV...

Resolution Improving:
1000 -> 250 meV -> 70 meV

2011: STILL NO DISPERSING EXCITATIONSFirst attempt non-resonant (6 meV res) -> No Signal

AQRB @ AOFSRR Cheiron School 2014

Resonant IXSAQRB @ AOFSRR Cheiron School 2014

Fluorescence Lines(RIXS/SIXS)

Ne: K 0.848
Ar: K 2.96
Kr: K 12.6
Fig: Ament et al, RMP 2011

Fig: Ament et al, RMP 2011

Direct RIXS

L 1.59

Xe: K 29.8 L 4.1
Rn: K 84.8 L 11.7

InDirect RIXSK Lines: Stronger, easier to reach for transition metals
L Lines: Weaker, lower energy
Photons: Orbital angular momentum change, Δl=1, dominates: s-> p or p->d
Science: Most interest is in d-orbitals
AQRB @ AOFSRR Cheiron School 2014

Transition metals (Sc-Zn) -> L= soft x-ray
AQRB @ AOFSRR Cheiron School 2014

X-Ray Raman Scattering

Spin Waves Possible

Nagasawa, et al, J. Phys. Soc. Jpn. 58 (1989) pp. 710-717
Tohji&Udagawa, PRB 39 (1989) 7590
AQRB @ AOFSRR Cheiron School 2014

X-Ray Raman Scattering

AQRB @ AOFSRR Cheiron School 2014

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

Suppose you would like to measure the structure of the oxygen kedge (at 532 eV) of a sample inside of complex sample environment…

Mössbauer Resonances Exist in Different Nuclei…

Diamond:labs < 0.5 um 500 eVlabs ~ 2 mm 10 keV
Easier at 10 keV than 0.5 keVSupercritical
Water
Ishikawa, et al,

Resonances have relatively long lifetimes so that if one has apulsed source, one can separate the nuclear scattering by using afast time resolving detector.
Tetrohydrofuran Clathrate
Conrad, et al, PRL (2009) 218301

Nuclear Scattering
AQRB @ AOFSRR Cheiron School 2014

AQRB @ AOFSRR Cheiron School 2014

NIS Setup

NIS: Good and Bad
1. Ein = Eres
2. Ein + Ephonon = Eres
3. Ein    = Eres

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

ΔE ~ eVHigh Heat Load
Monochromator

Sample

ΔE ~ meVHigh Resolution
Monochromator

Important things to note:
1. Element and isotope selective.
2. Gives Projected Density of states NOT Dispersion(But it does this nearly perfectly)
3. Resolution given only by monochromator(analyzer is ~ueV)
Easier optics but setup not optimized(compensated by large cross section)

Forward Detector(NFS)
Incoherent Detector(NIS)

Single Photon
Creation

Element- Specific!
Projected!
Phonon DOS!

Two Photon
Annihilation

-40

-30

-20

Y

Single Photon
Annihilation
PhononCreation +Annihilation

-10

0

10

Two Photon
Creation

20

30

5

40

Energy (meV)

10
15
20
25
30
Time After Excitation [ns]35Time Domain!
Mossbauer Spectroscopy!
AQRB @ AOFSRR Cheiron School 2014

Surfaces by NISAQRB @ AOFSRR Cheiron School 2014

Example (NRVS/NIS/NRIXS) In Biology
S. Cramer, et al, JACS

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

Measurement to determine the products of biological reactions via site-selective
vibrational spectroscopy and comparison against calcs and model compounds
A compound in the nitrogen cycle…
Is X present? How many irons?

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

Toxicity of Nitric Oxide (NO)-> Reaction products previously believed to bemononuclear are dinuclear

57Fe with 56Fe
Slezak et al PRL 2007

AQRB @ AOFSRR Cheiron School 2014

AQRB @ AOFSRR Cheiron School 2014

Three-Dimensional Momentum Density
Reconstruction

Compton Scattering
For very large Q and ΔE<<E one can takem∫∫ dp x dp y ρ (p z = pQ )Q
m≡J(pQ )
Q

S(Q,ω ) =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)Note: a bulk probe that is tolerant of sample imperfections.

Typical of incoherent scattering…
AQRB @ AOFSRR Cheiron School 2014

From Y. Sakurai

AQRB @ AOFSRR Cheiron School 2014

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) 

AQRB @ AOFSRR Cheiron School 2014

AQRB @ AOFSRR Cheiron School 2014

Reducing the Two-Theta Arm Size

Temperature Gradient Analyzer(Ishikawa & Baron, JSR 2010)

Dispersion Compensation: Houtari, et al JSR (2005)dLonger Arm: T~0.1C

l=150 to 200mm

Short Arm: T: 1 to 10C

Animation
D. Ishikawad =4R 2 ΔE
p E

5 meV at 16 keV
R=2m, p=0.1 -> d=50 mm
AQRB @ AOFSRR Cheiron School 2014

~ meV resolution at 3m

A Nano-Volt Spectrometer
Rayleigh Scattering of Synchrotron Mossbauer Radiation (RSSMR)~5 meV at 1m

AQRB @ AOFSRR Cheiron School 2014

Beyond Plane Waves
Usual Measurement is a
two-point correlation function:

S (Q,ω ) =12π

∫ dt e−iωt∫ dr ∫ dr′

x e iQ•( r− r ′) ρ (r′,t) ρ(r,t = 0)Complete picture includes higher order correlation functions

I(Q,t)I(Q',t') ∝ ρ(r',t) ρ (r,0) ρ(s',t') ρ (s,0)
Ps Scales
XFEL
Or
XFELO
(A) Autocorrelation at One Q(B) Cross-Correlation, Different Q
Wochner et al, PNAS (2009)

Masuda, Mitsui, Seto, et al, JJAP (2008, 2009)
AQRB @ AOFSRR Cheiron School 2014

AQRB @ AOFSRR Cheiron School 2014

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

For meV Resolution at 20 keV

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

NSLS-II(Not Proven)New
Beamline

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

?
ERL
(~$1B,
Not Funded)

Present
Status
Source & BL
Improvements

Machine Barrier

Expected
Upgrades

ESRF

Improvements

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

AQRB @ AOFSRR Cheiron School 2014

AQRB @ AOFSRR Cheiron School 2014

Quantum NanoDynamics Beamline(BL43LXU)

Medium resolution: 10-100 meVHigh resolution spectrometer: <1 to 6 meV-1
2m Arm, Large Q Acceptance
10 m Arm, Good Q Resolution, to 12 ÅGood tails using (888)
Large (42 element) analyzer array.

AQRB @ AOFSRR Cheiron School 2014

AQRB @ AOFSRR Cheiron School 2014

Using a 2D Analyzer Array(Cubic Crystal, a=4Å, 22 keV)

Baron, et al, J. Low Temp Phys,

BL43, First ID(a) Array of 12 x Φ10 cm analyzer crystals(b) Using the array for a longitudinal mode(c) Using the array for a transverse mode

Thanks for Your Attention!

When count rates are very low parallel data collection is crucial.

AQRB @ AOFSRR Cheiron School 2014

AQRB @ AOFSRR Cheiron School 2014

Medium Resolution Spectrometer

Range of Momentum Transfer

Momentum Transfer [Å-1]30

125.7 keV
21.7 keV
17.8 keV
15.8 keV

20
0.5(13 13 13)

10
5
0

(888)
0

30

Thomson Factor

Based on a 2m Arm & 3x3 Array Of Analzyers:
Energy resolution: ~10 to 100 meV (mono dependent)
Analyzers at Si(888) at 15.816 keV (reduced tails compared to lower order)
Dispersion compensation with Temperature Gradientkeeps high resolution with large space near sample.
Maximum momentum transfer ~15 Å-1 (phase plate needed @ 90 Deg.)
Solid Angle Gain: x25/Analyzer compared to high res spectrometer
Commissioning to begin late in 2012

Thomson Factor
Polarizer Efficiency

60

90

120

150

180

0

Scattering Angle [deg]AQRB @ AOFSRR Cheiron School 2014

AQRB @ AOFSRR Cheiron School 2014

Liquid Surfaces
Surface Dynamics are different than bulk…
Surface Sensitivity (~5nm) is possible at Extreme Grazing Incidence
100

e.g. Surface Layering… (fig. Spyrko, et al)-1

q (nm )
10.3

-1

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

10

10-2
10-3
3.6

10-1
10-2
10-3
-15 -10Liquid Indium (ESRF)

-5

0

5

! (meV)

10

15

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

Gate Valve
Residual Gas
Analyzer
Sputter Ion Gun
TMP Linear Transfer
Mechanism
Ionization
Gauge
X-ray Window

Electrode Feedthrogh

AQRB @ AOFSRR Cheiron School 2014

NIS Example: Biological Macro-Molecules

Ion Pump

Reichert, et al, PRL 2007

Vibration Isolation Table

AQRB @ AOFSRR Cheiron School 2014

SmRu4P12

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

e.g.

Where element specificity
can help a lot.

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

Sm Mode confirmed by (Sm specific)
Nuclear Inelastic Scattering
AQRB @ AOFSRR Cheiron School 2014

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 2014

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

IXS Q Resolution
Analyzer array
Count rate limited.

2.5 days
AQRB @ AOFSRR Cheiron School 2014