Time-resolved Diffuse Scattering:phonon spectoscopy with ultrafast x rays

David A. ReisPULSE Institute, Departments of Photon Science and

Applied Physics, Stanford UniversitySLAC National Accelerator Laboratory

Science at the Hard X-ray Diffraction Limit: Ultrafast Science… Cornell, June 20–21, 2011

phonons play defining role in materials properties

Superconductivity

materials with coupled degrees of freedom

Acoustic phonon “engineering”

Ferroelectricity

Electrical and thermal conductivity

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Why do physics in the time domain?

Spectra alone are sometimes inadequate

Based on slide from Phil Bucksbaum

01234567

294 330 349 392 440

beat

s

frequency [Hz]

Ultrafast Tickle and Probe

Separation of time-scales

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Sheu et al. unpublished Trigo et al. unpublished

Murray et al. PRB 72, 060301 (R) 2005.

a a

a

Coherent A1g Mode is strongly softened and chirped.

Peierls Distorted

Example: Photoexcited bismuth (all optical experiments)

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Low excitation (tickle regime)Pump-probe vs. Spontaneous Raman

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Collaboration with Roberto Merlin, UM

Jian Chen, Jinjing Li, unpublished

Subtle difference between the two…

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0 0( )0 0

tF e tF tt

( ) 0 02 2 2 2

cos( )sin[ ( )]( ) ( )( ) ( )

ttt t F e F e ttQ t e F d

Jian Chen, Jinjing Li, unpublished

Electronic Softening in Bi by femtosecond X-ray Diffraction

Johnson et al. PRL 2009.

Reis Physics Viewpoint 2009

D. M. Fritz et al. Science 315, 2007.

?

OpticalModes}

}1% e-

0% e-

AcousticModes

Murray et al. PRB 75 2007.

DFPT calculation

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Momentum and Time-resolved Phonon Spectroscopies virtually nonexistent

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Unobserved!

phonon-phonon and electron-phonon coupling, interatomic forces.

n(q,t) (q,t)

Ultrafast Tickle and Probe

x-ray diffuse scattering: measure deviations from average structure

d crystal + phonons

Example, diffuse scattering bythermal phononsVery weak, we need bright x-ray

pulses!

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(hkl)

Ghkl

(000)k0

ks

ks – k0 = Ghkl

Bragg scattering

Ultrafast Tickle and Probe 11

q

(000)

Ghkl

k0

ks

(hkl)Large detector

Diffuse scattering

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2d x-rayJoynson, Phys. Rev. 94, 851 (1954)……M. Holt et al., PRL 83, 1999.

Phonon Dispersion from TDS and limitations

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TDS: Limited to simple cases (# fit parameters low) and have a constraint (assumes Bose-Einstein distribution)

?

Simulation of InP impulse softening of TA by 20%

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Hillyard, Reis and Gaffney PRB 77, 195213 (2008).

Fourier transform of I(q,t) yields phonon dispersion (excited state)

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Alternatively, can use multiple coherent pulses

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2d

If you want to go really crazy, multiple colors, incidence angle, stimulated x-ray (electronic)Raman selected w & q…

Can we do x-ray 4-wave mixing, ala K. Nelson or S. Mukamel?

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100ps 1ns 5ns

10ns 18ns 25ns

50ns 75ns 100ns

Laser-melt and epitaxial regrowth of Bi on Sapphire

TDS

samplek0

ks

laser

Synchrotron data limited by time-resolution

17Trigo et al., unpublished

BioCARS beamline at APS~1% of LCLS photons/pulse but 100ps

Average of 5 shots

Advanced Photon Source

15 keV x-rays

~ 100 single x-ray Pulses

Equivalent to a single LCLS shot!

InP, 300K

Trigo et al. Phys. Rev. B, 82(23):235205, 2010.

Time-resolved x-ray diffuse scatteringwith 100ps resolution

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bright spots due to acoustic phonons near zone center

p-Polarization forbids scattering at 90o

High-symmetry directions, where acoustic branches are “soft”.

Beam stop shadow

“Bragg Rods” from surface scattering

Primarily TDS

19Ultrafast Tickle and Probe Trigo et al. Phys. Rev. B, 82(23):235205, 2010.

0.01

-0.005

0.005

0

[ I(400ps) −I(100ps) ] / I(off)

If processes were only thermal,

But, more than heating

20Ultrafast Tickle and Probe Trigo et al. Phys. Rev. B, 82(23):235205, 2010.

Similar to equilibrium

image

Sharp raise + exponential decay

Positive and negative

differential scattering

Delayed

Complex dynamics in the phonon populations due to the anharmoniccoupling between modes

time delay [ns]

U SVT

Interpretation by Singular Value Decomposition

Ultrafast Tickle and Probe 21Trigo et al. Phys. Rev. B, 82(23):235205, 2010.

LA TA

Brillouin zones

Contribution from acoustic phonon branches

Ultrafast Tickle and Probe 22Trigo et al. Phys. Rev. B, 82(23):235205, 2010.

Decay channel: LO TO + LA

k‐k

LO

TO

LA1.26 THz

9.24 THz

10.5 THz

LA

LO

TO

LA

Other phonons

Stimulated decay and emission of

TO + LAChen, Khurgin, Merlin, APL 80 2901, 2002.

Debernardi

Can we modify optical phonon lifetime?

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Will study anharmonic decay at LCLS this fall!

Acknowldegements

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Marino Trigo, Jian Chen, Mason Jian, Matthias Fuchs, Mike Kozina, Shambhu Ghimire, Vinayak Vishwanath, PULSE, SLAC, Stanford

Stanford PULSE Institute, SLAC National Accelerator LaboratoryYu-Miin Sheu,

Los AlamosTim Graber, Robert Henning,

CARS, U. Chicago

Supported by the U.S. Department of Energy, Office of Basic Energy Science

Lattice instabilities

25Lindenberg et al., Science 308, 2005;Gaffney et al., PRL 95, 2005; Hillyard et al., PRL 98, 2007.

Diffraction data consistent with complete softening

DFPT predicts instability first develops at X point

Model assuming uniform softeningGives similar results to inertial dynamics

formation of a nonequilibrium liquid

LCLS beamtime this fall to study Ultrafast diffuse scattering will measure evolution of interatomic forces and look for instability

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