XPCS Studies of Antiferromagnetic Domain f f m g mWall Dynamics in Elemental Chromium

Oleg ShpyrkoDepartment of Physics,

f l f University of California San Diego

“Crunchy” & “Squishy” Physics

Hard Condensed Matter “Crunchy”

Soft Condensed Matter “Squishy” CrunchySquishy

Gels, Colloids Metals, AlloysPolymers, FluidsLiquid CrystalsMembranes

Oxides (Insulators)SemiconductorsFerroelectricsMembranes

Bio-materialsFerroelectricsMagnets

XPCS and other spatio-temporal probes

Length Scale [Å] XPCS is the extension of dynamic light

S(q, ω) map:

Hz] E

R

INS

of dynamic light scattering probe (laser PCS)

quen

cy [H

Energy [e

Raman

Brillouin

IXS

Spin-Echo

Pros:• Smaller lengthscales• Non-transparent materials

Freq

eV]

XPCSlaserPCS

Spin Echo materials• Charge, Spin, Chemical and atomic structure sensitivity

[Å 1]

Cons:• Need fully coherent x-ray sources!

Scattering Vector Q [Å-1]

XPCS and other spatio-temporal probes

Length Scale [Å]S(q, ω) map:

Hz] E

R

INS

quen

cy [H

Energy [e

Raman

Brillouin

IXS

Spin-Echo

Freq

eV]

laserPCS

Spin Echo

???XPCS

Courtesy G. B. Stephenson

[Å 1]

New X-ray Sources(NSLS-II, LCLS)+Faster detectors!

XPCS

Scattering Vector Q [Å-1] +Faster detectors!

Mesoscale “Texture” in Strongly Interacting Fermi Systems

High-Tc cupratesCoexistence of multiple phases:superconducting and AF domains (stripes or checkerboards) in underdoped high-Tc cuprates

E. Dagotto, T. M. Rice, Science 271, 618 (1996).T H i t l N t 430 1001 (2004)

AF and FM domains in CMR manganites

AFM domains with orthogonal orientation of spin- and charge- density waves in Cr

CMR manganites

T. Hanaguri et al., Nature 430, 1001 (2004).p g y

What underlies such mesoscopic “texture”?

Is the texture (domain structure) frozen?

What are the effects of thermal and quantum fluctuations?

AFM chromium

P. G. Evans et al., Science (2002)

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

Brief Review - X-ray Speckle, the early years:

Speckle of (001) Cu3Au peak Speckle of the Fe3Al (1/2,1/2,1/2) l tti fl ti h i f i di d

M. Sutton et al., “The Observation of Speckle by Diffraction with Coherent X-rays” Nature 352, 608-610 (1991).

super-lattice reflection showing frozen-in disorder. b) Zoom of the central region in a) where the specklestructure is obvious. Grubel et al., ESRF News (1995)

Binary Alloys:

Cu3Au 3Sutton et al., Nature 1991, PRL 2005

Fe3AlBrauer et al., PRL 1995Mocuta et al., Science 2002

CoGa AlLi AlZn AlAgCoGa, AlLi, AlZn, AlAgStadler et al. 2004-7

Equilibrium: Non-equilibrium:

A. Fluerasu et al., Phys. Rev. Lett. 94, 055501 (2005)M. Sutton et al., Opt. Exp. (2003)

Quenched Cu3Au

Non-Equilibrium (aging) XPCS, cont’d:Non Equilibrium (aging) XPCS, cont d

CuPd binary alloy:

Ludwig et al., PRB 72, 144201 (2005)

Charge and Spin-ordered systems:

Nb3Se (classic CDW system)Sutton, Brock, Thorne et al., J. Phys. 2002, PRB 2001

Cr (CDW/SDW Antiferromagnet)Cr (CDW/SDW Antiferromagnet)Shpyrko, Isaacs et al., Nature 2007

Charge and Spin-ordered systems:

Ho films (helical AFM)Ho f lms (hel cal FM)Koning, Goedkoop, PRL 2007

Pr0 5Ca0 5MnO3 (Charge- & Orbital-Order)Pr0.5Ca0.5MnO3 (Charge & Orbital Order)Turner, Hill, Kevan et al., arxiv (?) 2008Nelson, Hill, Livet et al., PRB 2002

• Studies of antiferromagnets are more h ll i th th f f t challenging than those of ferromagnets

Net magnetic moment = 0

• Complex relationship between mesoscale phases (spin, charge, lattice) and physical properties

Spin domains in CrP. G. Evans, E. D. Isaacs et al.,

( )p y p p

Science 295 1042 (2002)

How can we study mesoscale

Charge/spin densitywave domains

dynamics in the bulk?X-rays:• Scanning X-ray Microscopy

10 μm

Coherent x ray

10 μm

wave domainsg y py(slow dynamics)

• X-ray Photon CorrelationCoherent x-ray speckle

Spectroscopy or XPCS (faster)

Spin Density Wave (SDW) in Chromium:

Commensurate SDW (C-SDW)W f ll i di i f Wave follows periodicity of underlying atomic lattice

Incommensurate SDW (IC-SDW)Incommensurate SDW (IC SDW)Modulation period incommensurate with lattice periodicity

For chromium incommensurability parameter is δ=0.037 at room T y p(period is δ-1~28 times the lattice constant)

Charge, Spin and Lattice order parameters:R l Real Space:

Spin Spin Density

ChargeReciprocal

Space:

Chargedensity

Charge Density Wave satellites

Spin Density Wavesatellites

Bragg peak

Microscopic Magnetic Domains in Chromium:

Scanning X-ray Microscopy:

[0, 0, 2-2δ] Charge-density wave satellite

• bulk probe (micron-sized

10 μm

bulk probe (micron sized penetration depth)• spin, charge, latticeand chemical sensitivity

Domain Wall Fluctuations in Antif m n tsAntiferromagnets

Domain WallDomain Wall

Magnetic domain wall fluctuations in real and reciprocal space:in real and reciprocal space:

λ21

3

11

22

3

Real Space:l t l it hi bl k

1

Momentum Space:f f i i f elemental switching block,

w/ volume (λ/2)3, λ=3-4 nmtransfer of intensity from satellites 1 to 2 due to switch

Random Telegraph Noise in Cr (thin films):Chromium:Chromium:

Discrete steps in electrical resistivity

Slow (1 s -100 s)

δR/R ~ 10-5δR/R ~ 10 5

h d Is this domain switching?

R. Michel, M. Weissman, Phys. Rev. B 44, 7413 (1991).

Random Telegraph Noise in other materials:M n nit s (L C MnO ):Ruthenates (Sr RuO ): Manganites (La1-xCaxMnO3):Ruthenates (Sr2RuO4):

F. Kidwingira, D. J. Van Harlingen et al., Science 314, 1267 (2006)

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

Chromium:

R. D. Merithew et al., Phys. Rev. Lett. 84, 3442 (2000)R. Michel, Phys. Rev. B 44, 7413 (1991)

Random Telegraph Noise measurements:Focus on the Domain WallFocus on the Domain Wall

~100 nm

focused x-ray beam~100 nm (0.5 μm)

X-ray Photon Correlation Spectroscopy (XPCS):

…

t + 3Δtt + 4Δt10 μm

t + 3Δtt + 2Δt

t + Δtt

speckle pattern

…t + Δtt t + 2Δt t + 3Δt t + 4Δt

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

CCD camera

2(0,0,2 )Qaπδ= −

r

a

r'k

rkr

Control experiment: Bragg Speckle

Quasi-static Brag speckle(line scans from 2D image): X-ray Bragg speckle

(6-hr average)(6 hr average)

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

Bragg, 300K: (total 6 hrs) linescansx 1 0 6 D : \ b ra g g _ R T _ 1 5 x 4 0 _ 6 h rs \ b ra g g _ R T _ 1 5 x 4 0 _ 6 h rs _ 0 0 0 0 1 -0 7 0 1 0 . im m

L in e = 7 5 , F ra m e : 1 -1 4 0 1F ra m e : 1 4 0 2 -2 8 0 1

5

6F ra m e : 2 8 0 2 -4 2 0 1F ra m e : 4 2 0 2 -5 6 0 1F ra m e : 5 6 0 2 -7 0 0 1

CDW, 4K:6 hrs3

4

2 5

3

x 106 D:\cdw_4K_15x40_2\cdw_4K_15x40_2_00001-05010.imm

Line=70, Frame:1-1001Frame:1002-2001Frame:2002-3001Frame:3002-4001Frame:4002-5001

1

2

2

2.5

2 0 3 0 4 0 5 0 6 0 7 0 8 0

0

1

1.5

20 25 30 35 40 45 50 55 60 65 70

0.5

Autocorrelation function g2(t): Multiple relaxation timescales

1

17K,fit τ=3000sfit τ1=3300s τ2=40s

0.8

1

A

0.6

2 (q,t)

/S2 (q

,0)

40 s

g 2(t)

-1]/A

0.4

S[g

2

22

),(),()](/),([1),( τ

τtQItQIQStQSAtQg r

rrrrr +

=+=

0.2

3 000

2),(

ττQI

r

101

102

103

104

0

time [s]

3,000 s

time [s]10 100 1,000 10,000

Autocorrelation data:

Bragg specklegg p

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

Classical Arrhenius model1 1( ) expS R

ETτ τ− − ⎛ ⎞Δ= −⎜ ⎟

Quantum Tunneling model:E⎛ ⎞Δ

( ) expS RB

Tk T

τ τ ⎜ ⎟⎝ ⎠

1 1 1( ) expS QM RB

ETk T

τ τ τ− − − ⎛ ⎞Δ= + −⎜ ⎟

⎝ ⎠

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

Slow Dynamics in Soft Matter

1 .0Onion gel

0 .6

0 .8

f(t,q

) β-relaxation(cage)

0 .2

0 .4f

α-relaxation(collective)compressed exponential

1 0 -7 1 0 -5 1 0 -3 1 0 -1 1 0 1 1 0 3 1 0 50 .0

t (sec )

exponential

t (sec )

Final relaxation: compressed exponentialf(q,t)=exp[-(t/τf)β] with β~1.5 and τf ∝ q-1(q, ) e p[ ( /τf) ] w β . d τf q

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

Aging of Soft Matter under jamming transition(using Laser speckle PCS)

reviewed in L. Cipelletti et al., Faraday Discuss. 123 (2003)

Colloidal gels1.00

0.8

Micellar polycrystal

1 0

Concentrated Emulsions

0.50

0.75q (cm-1)

24933845961883311331528

f(q,τ

) 0.4

0.6

g2(t

) - 1

21 deg 45 deg 80 deg

q,t) 0.5

1.0

f(q,t)

100 101 102 103 104 1050.00

0.2520582782375650666745

f

( )

100 101 102 103 104 105 1060.0

0.2

C:\lucacip\Origin\DLS CCD\000709_F108_000329Bt (sec)t

f(q

101 102 103 104

0.0

t (sec)τ (sec) t (sec)

f(q,τ) ∝ exp[-(t/τf)1.5], τf ∝ q-1

What does next generation of (NSLS II) b i ? sources (NSLS-II) bring us?

Brightness=Coherent Fluxbrightness=1021 Photons/sec/mm2/mrad2/0.1%BW or

=Flux/emittance/0.1% BW

Ratio of source emittance to diffraction limited emittance λ2/4π is coherent fraction

1 E h d i l l i (f h l 1. Enhanced spatial resolution (for the same temporal scale) – scales as Δrmin~1/√I

2. Enhanced temporal resolution – scales as Δτmin~1/I2

Intensity~2-3 x 10-3 Å-1

~10-2 Å-1

QQQBragg

Intensity~2-3 x 10-3 Å-1

x30I ~ (ΔQ)-2

x30increase in coherent flux (brightness)

~10-2 Å-1

Q~5x10-2 Å-1~5 fold increasein ΔQ (resolution) Q

QBragg

in ΔQ (resolution)

Instead of π/10-2Å-1 ~30 nm, resolution becomes ~6 nm

Enhanced time resolution:For CDW in Cr we could get reasonable statistics at <1

d ibl d tsecond, possibly down to~100 ms

With x30 factor enhancement in brightness (NSLS-II vs. APS) temporal resolution is APS), temporal resolution is improved by a factor x(30)2=1,000

Could get into sub-1 ms regime

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

(in theory – need detectors!)

Other Order Parameters:Other Order Parameters:

Magnetic (non-resonant) scatteringMagnetic (non resonant) scatteringFor Cr SDW satellite at APS ~ 1 ct/sec (coherent flux)Factor of 30 helps, but realistically need a factor of ~103+ (!)

Orbital Order: Second Order Phase Transitions:Phase Transitions:

Orderparameterparameter

Nelson, Hill et al., PRB 66, 134412 (2002) T emperaturePressure, Magnetic field

Chromium Work -”X-ray Speckle” Collaboration:X-ray Speckle Collaboration:

Oleg Shpyrko and Prof. Eric Isaacs (Center for NanoscaleMaterials, Argonne and Physics Dpt., University of Chicago)Yejun Feng, Rafael Jaramillo, Jonathan Logan and Clarisse Kim Prof Thomas Rosenbaum (University of Chicago)Prof. Thomas Rosenbaum (University of Chicago)Paul Zschack, 33-IDMichael Sprung, 8-IDp g,Suresh Narayanan, 8-IDAlec R. Sandy, 8-ID(Advanced Photon Source, Argonne)( anc hoton Sourc , rgonn )Gabriel Aeppli(U. College London)