x-ray scattering studies of dynamics in strongly...
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X-ray Scattering Studies ofDynamics in Strongly Correlated
Electron Systems
From Femto-seconds to MinutesJ.P. Hill
Brookhaven National Laboratory
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CollaboratorsCuprate 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 workJ.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)
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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
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1. Dynamics in the Energy Domain
q=ki-kfw=wi-wf
Elastic scattering (w = 0) gives static properties.
Inelastic scattering ( ) gives dynamic properties.0!"
wi, kiwf, kf
Inelastic X-ray Scattering
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Electronic Excitations
50 meV 500 meV 2 eV1.5 eV
PhononsMagnons d-d
Charge Transfer
Energy
Need a momentum and energy resolved probe IXS
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 ~ 2eV
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Resonant Inelastic X-ray Scattering
2
|
intintint
2 |||||| !
" #+$
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' n ni iEE
iHnnHfiHf
dd
d
(
)
Non-resonant scattering(weak)
Resonant IXS is > 100 x Non-Resonant IXS
Resonant scattering(strong at Ei=En)
But….IXS from electronic excitations is weak (unlike thecase for phonons)
Kao et al, PRB 1996, NiO
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10 years of RIXS Progress: CuGeO3
Figure of merit = count rate/resolution, increased by 104!
1999 1 cps 1500 meV X21, NSLS
2002 6 cps 300 meV 9IDB, APS
2007 600 cps 90 meV 30IDB, APS
2006 50 cps 115 meV 30IDB, APS
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DDE = 120 me
La2CuO4
DE=120 meV
9IDB, APS
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Something New at 500 meV…La2CuO4
On resonance
Off resonance
q=(p,0)
Difference
JPH, G. Blumberg, Y-J. Kim, D. Ellis et al., Phys. Rev. Lett (2008)
12 counts/min
Characteristics of 500 meV mode:
• Strongly peaked around (p,0)• Strongly doping dependent• Present only for e parallel to c• Rotates polarization of photon.
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2-Magnon Scattering?Single Magnon Dispersion Surface
R. Coldea (PRL, 2001) 2-magnon DOS has strong peaks at(p,0) at ~500 meV
Calculated 2-magnon DOS
Calculated energy and momentum behavior, and doping dependence allresemble two-magnon scattering
N.B. Predicted by Tsutsui, Tohyama and Maekawa (1999)
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Summary: Cuprates
Used resonant inelastic x-ray scattering to look atexcitations 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 photonpolarization• Consistent with it being due to 2-magnon scattering.• Future experiments will study the temperature dependenceand detailed q-dependence to make the assignmentunambiguous.
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2. Dynamics in the Time DomainCoherent X-ray Scattering
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Coherent Scattering: Dynamic Speckle
x
l /a
Speckle pattern characteristic of domainstructure:
Transversecoherence length
Longitudinalcoherence length
l R(2psh)
xt ~
l 2
(2Dl )xl ~
Coherent flux l DlF ~ B
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H/K (r.l.u.)
Nor
mal
ized
cou
nts
An Orbital Glass?
x~300 A
Pr0.5Ca0.5MnO3
S. Grenier, JPH, et al. PRB 69 134419 (2004)K.J. Thomas, JPH, et al. PRL 92 237204 (2004)
ξorb ~ 375 Åξmag 780 Å
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Orbital Speckle Observed
Pr0.5Ca0.5MnO3
Mn LIII edge10 mm pinhole
J.J. Turner et al., New Journal of Physics (2008)
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T = 205 K
T = 232 K
Speckle Patterns are Largely StaticSpace Time
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Some Dynamics Close to TransitionCorrelations between images at fixed temperature drop off slightlynear the orbital ordering transition temperature:
J.J. Turner et al., New Journal of Physics (2008)
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Summary: Manganites
Used soft x-ray coherent scattering (correlationspectroscopy) to look at orbital domains in a half-dopedmanganite.
• 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 hashalved to ~ 100A), the speckle was still largely static• BUT, there is a small component close to the transitionthat is dynamic. Time constant is ~ 5 mins
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3. National Synchrotron Light Source-II
E=3.0 GeVI=500 mAe=0.6 nm-rad
Operational: June 2015
Brightness will be used to study dynamics: - Better energy resolution- Faster time scales
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Inelastic X-ray Scattering Beamline
0.1 meV
1 meV
NSLS-II: Yong Cai
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Hard X-ray Coherent Scattering
NSLS-II: Andrei Fluerasu
B = 20 x APSTime scales = 400 x faster
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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 ~2 meV – 10’s eV– NSLS-II 0.1 meV – 10’s eV
Coherent x-ray scattering is a powerful probe oflong length scale, slow dynamics– Now ms to minutes– NSLS-II ms to minutes