X-ray Scattering Studies ofDynamics in Strongly CorrelatedElectron Systems
From Femto-seconds to Minutes
J.P. Hill
Brookhaven National Laboratory

Collaborators
Cuprate work:
Y-J. Kim, D. Ellis, S. Wakimoto (U. Toronto, Canada)
R.J. Birgeneau (U. C. Berkeley, USA)
T. Gog (APS, USA)
D. Casa (APS, USA)
G. Blumberg (Lucent Technologies, USA)
Manganite work
J.J. Turner, S. Kevan (U. Oregon, USA)
M. A. Pfeifer (U. Latrobe, Australia)
K.J. Thomas (BNL, USA)
K. Chesnel (ALS, USA)
Y. Tomioka (CERC, Japan)
Y. Tokura (CERC, Japan)

Outline
1. Dynamics in the Energy Domain- Resonant Inelastic X-ray Scattering- Recent results in the cuprates

2. Dynamics in the Time Domain- Coherent x-ray Scattering- Recent results in the manganites

3. Future- NSLS-II- Instrumentation

1. Dynamics in the Energy Domain
Inelastic X-ray Scattering
wi, kiwf, kfq=ki-kf
w=wi-wf

Elastic scattering (w = 0) gives static properties.
Inelastic scattering ( " ! 0) gives dynamic properties.

Electronic Excitations
1) Excitation spectrum determines the dynamic responseof material.
2) Excitation spectra provide stringent test of theory.
3) “High-energy physics” of strongly correlated electron
systems controls their behavior:t ~ 1 eV, U ~ 8 eV, D ~ 2eVCharge Transfer
Phonons

50 meV

Magnons

500 meVd-d

1.5 eV

2 eV

EnergyNeed a momentum and energy resolved probe

IXS

Resonant Inelastic X-ray Scattering
But….IXS from electronic excitations is weak (unlike thecase for phonons)d 2)% f | H int | n"% n | H int | i"
& % f | H int | i" + !
d'd(Ei $ En + i#|n "Non-resonant scattering(weak)

2Resonant scattering(strong at Ei=En)

Kao et al, PRB 1996, NiO

Resonant IXS is > 100 x Non-Resonant IXS

10 years of RIXS Progress: CuGeO3

1999

1 cps

1500 meV X21, NSLS

2002

6 cps 300 meV

9IDB, APS

2006

50 cps 115 meV

30IDB, APS

2007

600 cps 90 meV 30IDB, APS

Figure of merit = count rate/resolution, increased by 104!

La2CuO4
DE=120 meV

DDE = 120 me

9IDB, APS

Something New at 500 meV…
La2CuO4

12 counts/minq=(p,0)On resonanceOff resonanceDifference

Characteristics of 500 meV mode:• Strongly peaked around (p,0)• Strongly doping dependent• Present only for e parallel to c
• Rotates polarization of photon.

JPH, G. Blumberg, Y-J. Kim, D. Ellis et al., Phys. Rev. Lett (2008)

2-Magnon Scattering?
Single Magnon Dispersion Surface

R. Coldea (PRL, 2001)

Calculated 2-magnon DOS

2-magnon DOS has strong peaks at(p,0) at ~500 meV

Calculated energy and momentum behavior, and doping dependence allresemble two-magnon scattering
N.B. Predicted by Tsutsui, Tohyama and Maekawa (1999)

Summary: Cuprates
Used resonant inelastic x-ray scattering to look at
excitations in mid-IR region of the cuprates• Observed a new peak at 500 meV• Peak occurs at (p,0). Softens, and broadens, away fromthere. Strongly doping dependent. Rotates the photon
polarization• Consistent with it being due to 2-magnon scattering.
• Future experiments will study the temperature dependence
and detailed q-dependence to make the assignment
unambiguous.

2. Dynamics in the Time Domain
Coherent X-ray ScatteringCoherent Scattering: Dynamic Speckle
Speckle pattern characteristic of domain
structure:xl /aTransverse
coherence lengthlRxt ~(2ps h)Longitudinalcoherence length

l2xl ~(2Dl )Coherent flux

F ~ B l Dl

An Orbital Glass?
Pr0.5Ca0.5MnO3Normalized counts

ξorb ~ 375 Åξmag 780 Å

x~300 A
H/K (r.l.u.)
S. Grenier, JPH, et al. PRB 69 134419 (2004)
K.J. Thomas, JPH, et al. PRL 92 237204 (2004)

Orbital Speckle Observed

Mn LIII edge
10 mm pinhole

Pr0.5Ca0.5MnO3
J.J. Turner et al., New Journal of Physics (2008)

Speckle Patterns are Largely StaticSpaceT = 205 K

T = 232 KTime

Some Dynamics Close to Transition
Correlations between images at fixed temperature drop off slightly
near the orbital ordering transition temperature:

J.J. Turner et al., New Journal of Physics (2008)

Summary: Manganites
Used soft x-ray coherent scattering (correlationspectroscopy) to look at orbital domains in a half-doped
manganite.
• Observed “orbital speckle”• The speckle was static at low temperatures – therefore thedomains are static at low temperatures• Even very close to the transition, (correlation length has
halved to ~ 100A), the speckle was still largely static• BUT, there is a small component close to the transition
that is dynamic. Time constant is ~ 5 mins

3. National Synchrotron Light Source-II
Operational: June 2015

E=3.0 GeV
I=500 mA
e=0.6 nm-rad

Brightness will be used to study dynamics:- Better energy resolution- Faster time scales

Inelastic X-ray Scattering Beamline

1 meV

0.1 meV
NSLS-II: Yong Cai

Hard X-ray Coherent Scattering

B = 20 x APSTime scales = 400 x faster

NSLS-II: Andrei Fluerasu

Conclusions
Strongly correlated electron systems exhibit
dynamics over a wide range of time and spacescales.
Inelastic x-ray scattering is a powerful probe of thevery fast dynamics:– Now– NSLS-II~2 meV – 10’s eV
0.1 meV – 10’s eV

Coherent x-ray scattering is a powerful probe oflong length scale, slow dynamics– Now– NSLS-II

ms to minutes
ms to minutes