xpcs studies of antiffmgerromagnetic domain wall dynamics ... · xpcs studies of...
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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
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“Crunchy” & “Squishy” Physics
Hard Condensed Matter “Crunchy”
Soft Condensed Matter “Squishy” CrunchySquishy
Gels, Colloids Metals, AlloysPolymers, FluidsLiquid CrystalsMembranes
Oxides (Insulators)SemiconductorsFerroelectricsMembranes
Bio-materialsFerroelectricsMagnets
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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]
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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!
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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)
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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)
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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
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Equilibrium: Non-equilibrium:
A. Fluerasu et al., Phys. Rev. Lett. 94, 055501 (2005)M. Sutton et al., Opt. Exp. (2003)
Quenched Cu3Au
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Non-Equilibrium (aging) XPCS, cont’d:Non Equilibrium (aging) XPCS, cont d
CuPd binary alloy:
Ludwig et al., PRB 72, 144201 (2005)
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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
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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
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• 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)
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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)
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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
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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
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Domain Wall Fluctuations in Antif m n tsAntiferromagnets
Domain WallDomain Wall
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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
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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).
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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)
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Random Telegraph Noise measurements:Focus on the Domain WallFocus on the Domain Wall
~100 nm
focused x-ray beam~100 nm (0.5 μm)
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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)
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CCD camera
2(0,0,2 )Qaπδ= −
r
a
r'k
rkr
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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)
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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
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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
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Autocorrelation data:
Bragg specklegg p
O. G. Shpyrko et al., Nature 447, 68 (2007)
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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)
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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)
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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
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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
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Intensity~2-3 x 10-3 Å-1
~10-2 Å-1
QQQBragg
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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
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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!)
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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
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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)