Revealing Hidden Order and Dynamics with Soft Xray Resonant Scattering

1
Revealing Hidden Order and Dynamics with Soft
X-ray Resonant Scattering

• Paul G. Evans
• Department of Materials Science and Engineering
• University of Wisconsin, Madison
• evans_at_engr.wisc.edu

2
Outline

• Phases with long range order in solids
• Soft x-ray resonant scattering probes of ordered
  phases
• Novel Hole Crystal in SrCuO
• Magnetism, Soft Systems, Ferroelectricity
• What can coherent scattering bring to this?

3
Peierls Charge Density Wave

• Effective 1D chain of atoms.
• Peierls distortion leads to structural modulation
  with q2kf

Structural modulation leads to satellite peaks
around Bragg reflections from the lattice.
4
Fermi surface nesting in Cr

• ?(q) susceptibility, response of hypothetical
  non-magnetic system to magnetic perturbation with
  wavevector q

QSDW
Band structure of Cr Fermi surfaces nest with
Q(0,0,1-?), incommensurate with lattice.
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Cr in reciprocal space
Magnetic scattering appears near forbidden
lattice reflections.
Also Strain wave (CDW) reflections near allowed
lattice reflections.
K
H
L
SDW near (0 0 1)
CDW near (0 0 2)
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X-ray Scattering from CDWs
Canonical Example CDW phases in NbSe3 (Fleming
et al., 1978).
X-ray Studies of NbSe3 Crystallography of CDW,
Temperature Dependence of CDW Energy Gap, Several
Structural Phases, Distortion of CDW by Electric
Field
CDW structural information is the key to
understanding this material.
Problem Hard X-rays See ALL of the Electrons
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Origin of X-ray Reflections

• Peierls Distortion Moves the Atoms
• Intensity of reflections scales as Z2?q ?
• Structural distortions are easy to see with
  x-rays
• Magnetic Scattering can find the Magnetic
  Reflections
• Resonant and non-resonant scattering
• Weaker than structural modulations
• Modulations of Electron Density Without
  Structural Modulation
• Scattering is now from new lattice with charge
  ??Z
• Intensity is (?Z)2. Much weaker than scattering
  from structural distortion ((?Z)2)/Z2
  (10-2)2/(41)2 for NbSe3

8
Crystallization of holes in the spin ladder of
Sr14Cu24O41
Collaborators Peter Abbamonte, Brookhaven and
SUNY Stony Brook Andrivo Rusydi, Brookhaven and
U. Groningen Girsh Blumberg, Bell
Laboratories Adrian Gozar, U. Illinois and Bell
Labs Paul Evans, University of Wisconsin Theo
Siegrist, Bell Laboratories Luc Venema, U.
Groningen Hiroshi Eisaki, AIST, Tsukuba,
Japan Eric Isaacs, Argonne National
Laboratory George Sawatzky, University of British
Columbia Acknowledgements to Ian Affleck, Brad
Marston, Maurice Rice, Alexei Tsvelik, John
Tranquada, Young-June Kim, John Grazul, Shu Cheung
(to appear in Nature)
Funding U. S. Department of Energy, NWO (Dutch
Science Foundation)
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Sr14-xCaxCu24O41

• incommensurate and internally strained
• Sr2 , O2 ? Cu2.25
  isoelectronic to perovskite cuprates
• 6 holes / formula unit
• ladder has larger electronegativity 5.2
  holes on chain, 0.8 holes on ladder 1
• dchain 0.52 , dladder 0.057

1Osafune, PRL, 78, 1980 (1997) Nücker, PRB, 62,
14384 (2000)
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Spin Ladders
t, J

• Spin liquid (exponential decay in correlation)
• Singlets across the rungs

t?, J?
J? J

• Doped hole breaks a singlet (costs J?)

• Holes bind into pairs
• Superconductivity without phonons,
• D dx2-y2 M. Sigrist, PRB, 49, 12058 (1994)

E. Dagotto, J. Riera, and D. Scalapino, Phys.
Rev. B, 45, 5744 (1992) E. Dagotto and T. M.
Rice, Science, 271, 618 (1996)
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Ordering of Holes on Spin Ladders
Superconductivity not automatic models also
reveal a charge density wave
E. Dagotto, J. Riera, and D. Scalapino, Phys.
Rev. B, 45, 5744 (1992) S. White, I. Affleck, and
D. Scalapino, Phys. Rev. B, 65, 165122 (2002) S.
Carr, A. Tsvelik, Phys. Rev. B, 65, 195121 (2002)

• holes crystallize, drive system insulating
• Particularly stable for d rational
  (commensurate)
• Almost a CDW power law correlations
• 1/n-n?Kr. Friedel oscillations easily
  induced.
• Reminiscent of ordered stripes vs. SC in
• perovskite cuprates
• Not high Tc, but worthy of study in its own right

Some evidence in electrical and optical transport
measurements. Blumberg, Science 297, 584 (2002).
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Prediction Charge Ordering Due to Coulomb
Repulsion of Holes
CDW predicted by Dagotto et. al. is Wigner, not
Peierls (viz. hole crystal)
Wigner crystal E. Wigner, Phys. Rev., 46, 1002
(1934)
Peierls CDW
NbSe3, K0.3MoO3 Hep 103 104 Z 101
102 Z2 102 104 Easy to measure
4He surface, 2DEG, (Mott state!)
Coulomb ??? 10-2 (White et. al.)
10-4 Hard to measure
Examples Mechanism Effective mass Charge
modulation Cross section Bottom line
Weaker by 107
Could a hole crystal be responsible for the
transport properties of Sr14Cu24O41?
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Resonant soft x-ray scattering
Semi-classical susceptibility (SI units)
c(q) - (re l2 / p) n(q) n electron
density This changes at an absorption resonance.
LaSrCuO P. Abbamonte, L. Venema, A. Rusydi, G.
A. Sawatzky, G. Logvenov, and I. Bozovic,
Science, 297, 581 (2002)
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Edge structure in doped Sr14Cu24O41
Pre-edge x-ray absorption features at O K edge
are linked to hole concentration.
chain ladder
increasing hole concentration
absorption
photon energy (eV)
N. Nücker, et. al., PRB, 62, 14384 (2000)
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UHV Soft X-ray Scattering

• He flow cryostat
• 5 Tesla magnet (vertical field)
• Base pressure 5 10-10 mbar
• National Synchrotron Light Source, X1B

• 1.2 m vacuum chamber
• 4 circle geometry
• Multilayer fluorescence rejection
• Channeltron / AuCsI cathode

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The surface is everything

• Traveling solvent floating zone technique
• Polish with dry, diamond film, 30 mm ? 10 mm ?
  0.1 mm
• Anneal at 120 C in O2 for 1 day
• Transfer orientation from hard x-ray
  measurements using a Ge(111) reference sample.

T. Osafune, N. Motoyama, H. Eisaki, S. Uchida,
PRL, 78, 1980 (1997)
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Valence modulation in Sr14Cu24O41
T28K
Total fluorescence yield (relative units)
T28K
Photon Energy (eV)

• L 0.200 0.009 r. l. u. ? l 5.00 0.24 cL.
  
• Does not index to 27.3 Å unit cell.
• xc 255 Å, xa 274 Å
• No measurable off-resonant signal ? purely
  electronic phenomenon

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Resonance properties
T28K

• Disappears of OK prepeak cannot be structural
• Visible at CuL2,3 still at L0.2
• Coherent, bulk phenomenon
• No harmonic at L0.4 sinusoidal

• Resonates only with ladder feature
• Resonates at CuL3?, not L3 (just electrostatic)

Simplest explanation hole crystal in the ladder,
as predicted by Dagotto et. al.
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Temperature dependence

• D(T) nonMFT (crossover)
• Agrees with Vuletic et. al. PRL, 90 257002,
  (2003)
• xc is Tindependent

Simplest explanation phase fluctuations from
impurities
S. Girault, A. H. Moudden, J. P. Pouget, J. M.
Goddard, PRB, 38, 7980 (1988)
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Does the wavelength l 5.00 cL make sense?

• 0.8 holes in 7 rungs ? d 0.8 / 14 0.057
• Spin gap ? bosonic pairs
• Expected l 1/d 17.54 cL what is going on?

• Possible explanations
• Hole density from Nücker et. al. incorrect
• Umklapp strong enough to draw extra charge from
  chains (Marston Troyer)
• 3rd harmonic stabilized instead of 1st
• Coherent across 50 neighboring ladders.
  Two-dimensional?

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Summary Sr14Cu24O41

• We see a standing wave in the hole density in
  Sr14Cu24O41
• commensurate / resonates with ladder ?
  originates in ladder
• no (measurable) lattice distortion ? Driven by
  many-body interactions
• No visible harmonics ? sinusoidal (weak-coupling
  c.f. White et. al.)
• D(T) and xc(T) ? impurities (sample
  inhomogeneity)
• Confirmation of Dagotto, Riera, Scalapino (1992)
• of hole crystallization in doped spin ladders.
• Conclusions
• Explains observed CDW in transport with no
  Peierls distortion
• Explains low effective mass estimated by Vuletic
  et. al.
• Low-dimensional precursor to stripe phases in
  high Tc superconductors
• Supports picture that superconductivity in
  copper-oxides occurs in close
• proximity (in the RG sense) to charge order

So far Statistical description with averages in
both time and configuration.
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What can be gained using coherent soft x-ray
scattering?

• Advantages
• Resonant energies in useful range for transition
  metals, C, O, N, and other elements.
• Chemical, magnetic, and orbital dependence of
  cross sections
• Higher coherent flux for given source size and
  distance from the source (transverse spatial
  coherence length z?/2?d)
• Disadvantages
• Large ?? means low photon momentum, limited range
  of spatial frequencies.
• Limited penetration into solids.

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Two Ways to Use Coherence

• Oversampling/Inversion of the Diffraction Pattern
• Dynamics Intensity Correlation Spectoscopy

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E.
Nagler, L. E. Berman, G. A. Held, and G. B.
Stephenson, Nature 352 606 (1991).
Applied to a wide variety of structural problems
using hard x-rays.
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Examples Holes in Sr14Cu24O41
Incoherent Illumination
Coherent Illumination 1) Speckle from individual
domains of hole order. 2) Can the dynamics help
to explain the temperature dependence of the
order parameter?
mean coherence length of hole modulation 50
ladder lattice constants
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Soft Materials and the C edge ? Resonance
??CC
C. Morin, et al., J. Electron Spectroscopy and
Related Phenomena 121 203 (2001).
(Potentially) Particularly Useful in
Differentiating Materials with a Small Density
Contrast
Example Aromatic Block Copolymer
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Polarization Switching in Ferroelectric Devices
Stored polarization can be switched by an applied
E-field.
Can we use image inversion (or just intensity
correlation spectroscopy) to watch the domains
move?
27
Quantitative Diffuse XRMS
Normalized Intensity (a.u.)
-6 -3 0 3 6
-2 0 2 4 6 -2 0 2
4 6
Azimuthal Transverse Angle, W (degrees)
J. F. MacKay, C. Teichert, D. E. Savage, and M.
G. Lagally, Phys. Rev. Lett. 77, 3925 (1996).
J.J. Kelly IV, B.M. Barnes, F. Flack, D.P.
Lagally, D.E. Savage, M. Friesen, and M.G.
Lagally, J. Appl. Phys. 91, 9978 (2002).
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Conclusions

• Resonant scattering with soft x-rays allows a
  range of previously invisible ordering phenomena
  to be probed.
• Hole ordering in ladders of Sr14Cu24O41
• Wavelength, T dependence, resonance energy, etc.
• Coherence can add even more information for a
  variety of systems.