New results in an old metal: slow dynamics using X-ray speckle Eric D. Isaacs Center for Nanoscale Materials, Argonne National Laboratory The James Franck.

New results in an old metal: slow dynamics using X-ray speckle

Eric D. IsaacsCenter for Nanoscale Materials, Argonne National

LaboratoryThe James Franck Institute, The University of Chicago

Advanced Photon Source

Center for Nanoscale Materials

Outline

Texture and multiphase coexistenceFluctuations of domain wallsWider implications

– ‘quantum’ soft matter– domain wall resistivity

Sandpiles (10-3-10 m)

Avalanches(10-103 m)

tectonic plates (102-106 m)

Abrikosov vortexlattice (10-7 m)

100km

1 km

1 m

1 mm

1 m

1 nm

1Å

Liquid dropletspinned on roughsubstrates(10-4 – 10-2 m)

Magnetic domains(10-8-10-4 m)

Charge-, Spin-density waves(10-10-10-7 m)

Collective dynamics in the presence of quenched disorder

Jamming, shear flow in granular materials, colloids (10-9–10-2 m)

S. Mori et al., Nature 392, 473 (1998)M. Uehara et al., Nature 399, 560 (1999)

CMR manganites

Mesoscale Structure in Strongly Interacting Fermi Systems

M. Bode, et al., Nature (2006)

AF iron

engineering antiferromagnets

No need to look at complicated material to find complexity

Chromium and its common alloys are ‘simple’ bcc metals, exhibiting complex behaviors including:

• Only elemental material w/SDW.

• Spin-density wave ground state at 311 K due to Fermi-surface nesting.

•Spin-flip transition at 123 K.

• Quantum critical behavior: drive TN to zero by doping with V or by applying pressure.

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Feng, et al.

magnetic and charge x-ray contrast in chromium

Spin Density Wave satellites

Charge Density Wave satellites

Real Space:

Reciprocal Space:

Bragg peak

Spin Density

Chargedensity

Texture and multiphase coexistence

For science & engineering, need to image individual domains & walls between them - but visible light does not couple & neutrons average over a large sample

Atomic-scale light - X-rays

outermost zone

1992: 0.5 m

2007: 30 nm

Force Radiation

-eE electric dipole“Thomsonscattering”

-eEmagnetic quadrupole

After F. de Bergevin and M. Brunel, Acta Cryst. A 37 314 (1981).

EE

EH

e-

-e

Magnetic X-ray Scattering (Classical Picture)

electric dipole)( H⋅∇ H E

e-

.

.

.

€

I ∝ hωmc 2( )

2

r02 ≤10−4 r0

2Magnetic scattering is very weak:

e-

€

I ∝ r02

100

Evans et al., Science 295, pp. 1042-1044 (2002)

8.6

8.7

0

5

10

110 120 130 140

2

3

41

H=2 kG

H=0

T (K)

10 m 2

4 3

1

10 m 10 m 10 m

10 m 10 m 10 m 140 K 130 K 125 K 120 K

110 K 119 K 115 K ≤1

≥4

Q || (001) and S⊥Q

Q ⊥ (001) or S||Q

Magnetic domain nucleation

Q-domains

10 m

3-4 nm

REAL SPACE:

RECIPROCAL SPACE:

Domain Dynamics using Coherent X-rays - Simulation

X-ray Coherence

Young’s double slit experiment.Intensity varies as

Advanced Photon Source: • 10 x 40 m2 slits• X-ray flux ~ 3x109 ph/s• Coherence factor: A ~ 15 %

coherence factor

€

I = I0 1+ Acos 2πLsin θ( ) /λ( )[ ]

Speckle Pattern

10 m

Q~10-2 Å-1

Resolution:

€

~ π /ΔQ

~ 50nm

X-ray Photo Correlation Spectroscopy (XPCS)

…

€

g2(r

Q ,t) = 1+ A[S(r

Q ,t)/ S(r

Q )]2 =I(

r Q ,t )I(

r Q ,t +τ )

τ

I(r

Q ,τ )τ

2

t + Δt

…

t

t + 2Δtt + 3Δt

t + 4Δt10 m

autocorrelation function

CDW domains in real space

150K

O. G. Shpyrko et al., Nature (2007)

Autocorrelation function, g2(t)

150K100K

Autocorrelation function, g2(t)

150K100K

70K

Autocorrelation function, g2(t)

150K100K

70K40K

Autocorrelation function, g2(t)

150K100K

70K

40K

30K

Autocorrelation function, g2(t)

30K

17K

Autocorrelation function, g2(t)

30K

17K

4K

Autocorrelation function, g2(t)

Compressed exponentialexp[-(t/s)] with ~1.5

But why?

Bragg speckle

Autocorrelation function, g2(t)

Classical Arrhenius model

1 1( ) expS RB

ET

k T − − ⎛ ⎞

= −⎜ ⎟⎝ ⎠

Quantum Tunneling model:

1 1 1( ) expS QM RB

ET

k T − − − ⎛ ⎞

= + −⎜ ⎟⎝ ⎠

Barrier E~ 250KRelaxation frequency R

-1 ~ 0.1 Hz

1 2

Real Spaceelemental switching block,

w/ volume (/2)3, =3-4 nm

2

1

1

1

22

3

3

Momentum Spacetransfer of intensity from

satellites 1 to 2 due to switch

1 2

Where could this come from?

Wider implications…’Soft’ quantum matter

Jamming (similar to Glass Transitions)

Repulsive Interactions:

J. Liu and S. Nagel, Nature 396, 21 (1998)

U

100 m

Fluid Solid

Slow Dynamics in Soft matter

Final relaxation: “compressed exponential”

exp[-(t/ f)] with ~1.5

Onion gel

L. Ramos and L. Cipelletti, Phys. Rev. Lett. 87, 245503 (2001)

B. Chung et al., “Microscopic Dynamics of Recovery in Sheared Depletion Gels”Phys. Rev. Lett. 96, 228301 (2006)

R. Bandyopadhyay et al., “Evolution of Particle-Scale Dynamics in an Aging Clay Suspension”, Phys. Rev. Lett. 93, 228302 (2004)

Aging in Soft Matter with XPCS (gels and clays):internal stress speeds up relaxation

g2(q,t) exp[-(t/f) 3/2], f q-1

Source of Stress in Hard Matter - Spin/Charge Density Wave Pinning Defects

H. Fukuyama and P. A. Lee, Phys. Rev. B 17, 535 (1978)P. Littlewood and T. M. Rice, Phys. Rev. Lett 48, 44 (1982)

Phase elasticity Pinning potential

summary• X-ray photo correlation spectroscopy (XPCS) allows

measurement of dynamics of antiferromagnets at nanometer length scales (finite-q).

• Dynamics are strongly reminiscent of ‘glassy’ collective behavior in disordered systems seen universally in soft matter near jamming transition, but, …

• … in solid-state system, quantum tunneling provides additional channel for relaxation.

• Antiferromagnetic domain walls give rise to measurable electron scattering: need full calculation of 3D resistivity tensor.

X-ray Revolution (Future is Bright!)

incandescent light sources (incoherent)

lasers (coherent)

Moore’s law for X-ray Sources

18 ordersof magnitudein 5 decades!

12 ordersof magnitudein 6 decades

(Energy Recovery Linacs)

Developments for Nanoscience

1. Nano-scale focusing - CNM’s Hard X-ray Nanoprobe @ the APS

2. Coherence (X-ray “Lasers”)• Lens-less imaging• X-ray photo correlation spectroscopy

Proposed Energy Recovery Linac at Cornell, Argonne

X-ray Free Electron X-ray Free Electron Laser at SLAC Laser at SLAC (opening in 2009)(opening in 2009)

Hard x-ray spot size vs. year

Spo

t si

ze (

nm)

WSi2/Si

Zone plate Multi-layer Laue lens

CNM/

M. A. Pfeifer et al., Nature 442, 63–66 (2006).E.D. Isaacs, News&Views, Nature 442 (2006).

O. Shpyrko, et al Nature 447, 68–71 (2007)

X-ray photo correlation spectroscopy (XPCS) - dynamics with high spatial resolution

Two things we can do with coherent x-rays

Structure of non-periodic structures - we can invert speckle pattern, solving the phase problem for ‘lens-less’ imaging. Long-range order no longer required.

Speckle Pattern and Spatial Resolution

Q~10-2 Å-1

Spatial resolution:

€

~ π /ΔQ ~ 50nm

Resolution is coherent flux-limited:IBragg ~ 1/q2

Current resolution: ~ 50 nm we need factor of 100 in coherent flux to achieve 5 nm.

= smallest object that can contribute to speckle

Can we image disorder directly?

M. A. Pfeifer et al., Nature 442, 63–66 (2006).

Autocorrelation Function and Temporal Resolution

Resolution is coherent flux-limited:g2(t) ~ intensity-intensity correlations

Statistics:5% error bars 1 second resolution

we need factor of 100 in coherent flux to achieve msec resolution. spatial + temporal: need 10,000 x

Can we image single quantum rotor directly?

Coherent (lens-less) X-ray Imaging

Can we invert speckle of embedded, irregular structures to obtain 3D real-space images? (ptychography)

1. Reveal internal CDW phase information (topological defects, phase strain) with ~ 50 nm resolution currently

2. 3D movies of nanoscale fluctuations (FEL, ERL)

3D speckle (momentum space):

conclusions• Complex behavior in simple substance

– Textures– Quantum fluctuations - slow [and fast seen

w/neutrons]– Beginning of AFM domain wall engineering

• Future: collective dynamics using bright coherent sources

10 m

‘Quantum’ Speckle Collaborators

Dr. Oleg Shpyrko, Center for Nanoscale Materials, Argonne National LabJonathan Logan, Clarisse Kim, U. Chicago

Rafael Jaramillo, Dr. Yejun Feng, Prof. Tom Rosenbaum, U. Chicago

Prof. Paul Evans, U. Wisconsin, Madison

Dr. Paul Zschack, Dr. Michael Sprung, Dr. Alec R. Sandy(Advanced Photon Source, Argonne)

Prof. Gabriel Aeppli, Prof. Ian Robinson(University College, London)

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XPCS and other spatio-temporal probes

Scattering Vector Q [Å-1]

Length Scale [Å]

Freq

uen

cy [

Hz] E

nerg

y [e

V]

Raman

Brillouin

XPCSlaserPCS

IXS

Spin-Echo

INS

Advantages• Shorter lengthscales• Non-transparent materials• Charge, Spin, Chemical and atomic structure sensitivity

Disadvantages• Need coherent x-ray sources!

S(q, ) map:

Aging of Soft Matter systems undergoing ‘jamming’ transitions (using laser speckle PCS)

Colloidal particles gel

100 101 102 103 104 1050.00

0.25

0.50

0.75

1.00

q (cm-1)2493384596188331133152820582782375650666745

C:\Backup Penn\Arnie\lucacip\doc\Papers\PRL_GELPoly\Fig2

(sec)

0 2x1011 4x1011-2

-1

0

(q)3/2 (cm-1sec)3/2100 101 102 103 104 105 1060.0

0.2

0.4

0.6

0.8

C:\lucacip\Origin\DLS CCD\000709_F108_000329B

21 deg 45 deg 80 deg g2OKbaselin

g2OKbaselin g2OKbaselin StretchedExp simulation

t (sec)t

f(q,

t)Micellar polycrystal Conc. Emulsion

f(q,) exp[-(t/f) 3/2], f q-1

review: Cipelletti et al., Faraday Discuss. 123 (2003)

What is the relationship between bulk properties (eg, transport) and mesoscale structure?

Michel et al., PRB 44, 7413 (1991)

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Time (sec)

B. Raquet et al., Phys. Rev. Lett. 84, 4485 (2000).

La1-xCaxMnO3 films

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D. van Harlingen, et al., 2006

underdoped YBCO nanowires

chromium films

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