Strain amplification of the 4k chain instability in Sr Cu O

Strain amplification of the 4k F chain
instability in Sr 14 Cu 24 O 41
Peter Abbamonte
University of Illinois at Urbana-Champaign
Fukuda, PRB, 66, 12104 (2002)
Collaborators:
Andrivo Rusydi, University of Hamburg
Serban Smadici, University of Illinois
Hiroshi Eisaki, AIST, Tsukuba
Yoichi Fujimaki, University of Tokyo
N. Motoyama, University of Tokyo
Michael Rübhausen, University of Hamburg
George Sawatzky, University of British Columbia
Shin-ichi Uchida,University of Tokyo
Acknowledgements:
S. van Smaalen (Beyruth), M. von Zimmermann
(DESY), A. Gozar (Brookhaven), M. Grüninger
(Köln), Girsh Blumberg (Bell Labs)
Funding: Office of Basic Energy Sciences, U.S.
Department of Energy #s DE-FG02-06ER46285 &
DE-AC02-98-CH10886

Sr 14-x Ca x Cu 24 O 41 (SCCO)
Fukuda, PRB, 66, 12104 (2002)
• Chains buckle to accommodate ladder:
c ≈ 7c L ≈ 10c c
1
c = 27.3 Å
• Sr 2+ , O 2– ⇒ Cu 2.25+
isoelectronic to perovskite cuprates
• 6 holes / formula unit. Most are in the
chain. 3
• Conductivity governed by ladders 2
CuO 2
Cu 2
O 3
• Spin gap at all temperatures 4 : Pairing
1 Etrillard, Physica C, 403, 290 (2004); Braden, PRB, 69, 214426 (2004)
2
Osafune, PRL, 78, 1980 (1997)
3 Nücker, PRB, 62, 14384 (2000); Piskunov, PRB, 72, 064512 (2005); Rusydi, PRB, 75, 10450 (2007)
4 Carter, PRL., 77, 1378 (1996); Takigawa, PRB, 57, 1124 (1998); Matsuda, PRB, 56, 14499 (1997)

Spin ladders
t, J
E. Dagotto, J. Riera, D. Scalapino, Phys. Rev. B, 45, 5744 (1992)
• Doped hole breaks a singlet; costs energy J
• No spin gap
• Holes bind into pairs, binding energy ~J
• Spin gap restored ⇔ Pairing
• Superconductivity, ∆ ~ d x2-y2 M. Sigrist, PRB, 49, 12058 (1994)
Unstable to the formation of “charge density waves”
S. White, I. Affleck, D. Scalapino, Phys. Rev. B, 65, 165122 (2002)
• δ rational ⇒ holes “crystallize” into insulating CDW
• δ irrational ⇒ metal with dynamic CDW correlations
• Reminiscent of ordered stripes vs. SC in High T c
Tranquada, PRL, 78, 338 (1997)

Spin ladders
t, J
E. Dagotto, J. Riera, D. Scalapino, Phys. Rev. B, 45, 5744 (1992)
• Doped hole breaks a singlet; costs energy ~J
• No spin gap
• Holes bind into pairs, binding energy ~J
• Superconductivity, ∆ ~ d x2-y2
• Spin gap restored ⇔ Pairing
M. Sigrist, PRB, 49, 12058 (1994)
Unstable to the formation of “charge density waves”
S. White, I. Affleck, D. Scalapino, Phys. Rev. B, 65, 165122 (2002)
• δ rational ⇒ holes “crystallize” into insulating CDW
• δ irrational ⇒ metal with dynamic CDW correlations
• Reminiscent of ordered stripes vs. SC in High T c
Tranquada, PRL, 78, 338 (1997)

Sr 14-x Ca x Cu 24 O 41 (SCCO)
• x = 13.6 ⇒ superconductivity T c = 12 K at
P = 3 GPa 1
• x = 0 ⇒ insulating with a CDW 2,3,4
1
M. Uehara, et. al.,
J. Phys. Soc. Jpn.,
65, 2764 (1996)
• Exhibits both predicted phases for ladder.
• Can tune between CDW and SC in one
system
3 Blumberg, et. al., Science, 297, 584 (2002)
1
Uehara, J. Phys. Soc. Jap., 65, 2764 (1996)
2
Gorshunov, PRB, 66, 60508 (2002)
4 Vuletić, PRL, 90, 257002 (2003)

Chain buckling in Sr 14 Cu 24 O 41
Z. Hiroi, PRB, 54, 15849 (1996)
(1,-1,0) zone
Fukuda, PRB, 66, 12104 (2002)
c = 27.3 Å
Conjecture: Interplay between
chain buckling and a chain CDW

X-ray & Neutron scattering – chain CDW?
Charge density wave in the chain layer
T. Fukuda, PRB, 66, 12104 (2002)
D. E. Cox, PRB, 57, 10750 (1998)
Matsuda, PRB, 54, 12199 (1996)
Matsuda, PRB, 56, 14499 (1997)

X-ray & Neutron scattering – chain CDW?
Charge density wave in the chain layer
T. Fukuda, PRB, 66, 12104 (2002)
D. E. Cox, PRB, 57, 10750 (1998)
Matsuda, PRB, 54, 12199 (1996)
Matsuda, PRB, 56, 14499 (1997)
All just Bragg peaks from the structure
S. van Smaalen, PRB, 67, 26101 (2003)

X-ray & Neutron scattering – chain CDW?
Charge density wave in the chain layer
T. Fukuda, PRB, 66, 12104 (2002)
D. E. Cox, PRB, 57, 10750 (1998)
Matsuda, PRB, 54, 12199 (1996)
Matsuda, PRB, 56, 14499 (1997)
All just Bragg peaks from the structure
S. van Smaalen, PRB, 67, 26101 (2003)
Higher harmonics appear only at low T
Etrillard, Physica C, 403, 290 (2004)
Braden, PRB, 69, 214426 (2004)

X-ray & Neutron scattering – chain CDW?
Charge density wave in the chain layer
T. Fukuda, PRB, 66, 12104 (2002)
D. E. Cox, PRB, 57, 10750 (1998)
Matsuda, PRB, 54, 12199 (1996)
Matsuda, PRB, 56, 14499 (1997)
All just Bragg peaks from the structure
S. van Smaalen, PRB, 67, 26101 (2003)
Higher harmonics appear only at low T
Etrillard, Physica C, 403, 290 (2004)
Braden, PRB, 69, 214426 (2004)
Harmonics come from thermal contraction
M. v. Zimmermann, PRB, 73, 115121 (2006)
Still unclear if there is a CDW in the chain of Sr 14
Cu 24
O 41

Resonant soft x-ray scattering (RSXS)
valence band
• Resonant elastic scattering, E i = E s
– not RIXS
• Periodic DOS modulation gives
“Bragg” peak
• | g(k,ω) | 2 where ω = E - E F
• Same as STS for V > 0
E i
E s = E i
Hanaguri, Nature,
Core level
430, 1001 (2004)
Bulk-sensitive → can study anything (214’s, heterostructures)
Full T-dependence → 18 K < T < 500 K (pushing to 12 K)
Not much k → Can reach (π,0) in cuprates but not (π,π)
Radiative broadening ~ 200 meV

Unoccupied density of states (k=0)
O K edge (1s → 2p) Cu L edge (2p → 3d)
•, • Sr 14
Cu 24
O 41
(SCO)
δ c
= 0.32 1 or δ c
=0.5 2
δ L
= 0.2 1 or δ L
=0.07 2
• La 6
Ca 8
Cu 24
O 41
(LCCO)
δ c
= 0.056 3
δ L
= 0 3
1
A. Rusydi, PRB, 75, 104510 (2007), 2 N. Nücker, PRB, 62, 14384 (2000), 3 A. Rusydi, cond-mat/0611730

“Hole crystal” in the ladder
T=28K
Abbamonte, Nature, 431, 1078 (2004)
T=28K
• Density of states modulation: A Wigner crystal
• L L = 0.200 ± 0.009 r. l. u. ⇒ λ = 5.00 ± 0.24 c L
• Commensurate with Ladder: Does not index to
27.3 Å unit cell.

“Hole crystal” in the ladder
OK edge intensity
T = 20 K
Forms only on
rational fractions.
τ
τ
1/3
1/5
= 1.652 =
5
3
U ~ 1/R
Pair density wave:
Tesanovic, PRL, 93, 217004 (2004)
Chen, PRL, 93, 187002 (2004)
Rusydi, PRL, 97, 016403 (2006)

Everything makes sense but …
What about the chain?

Chain and ladder orders
A. Rusydi, cond-mat/0611730
Z. Hiroi, et. al., PRB, 54, 15849 (1996)

Chain and ladder orders
A. Rusydi, cond-mat/0611730
Z. Hiroi, et. al., PRB, 54, 15849 (1996)

Chain and ladder orders
A. Rusydi, cond-mat/0611730
Z. Hiroi, et. al., PRB, 54, 15849 (1996)

Temperature dependence

Strange energy dependence
x40

Separating charge and strain with RXS
P. Abbamonte, PRB, 74, 195113 (2006)
Structure factor
Form factor
Absorption related to f(ω)
Strain scattering follows:
Charge scattering follows:
RXS line shape gives
W = v 0
/u 0
and phase φ
W ~ 0 Supermodulation (Bragg)
W ~ 1 A -1 Peierls CDW in K 0.3
MoO 3
W ~ 10 A -1 “stripes” in LBCO

Lattice and hole form factors

Fits
Sr 14
Cu 24
O 41
W = 1.13 Å -1
φ= -23.1º
La 6
Ca 8
Cu 24
O 41
W LCCO
= 0.065 Å -1
φ LCCO
= -90.1
Q = n c
4k F modulation
stabilized by
supermodulation

Fits
lattice
holes
Sr 14
Cu 24
O 41
W = 1.13 Å -1
φ= -23.1º
La 6
Ca 8
Cu 24
O 41
W LCCO
= 0.065 Å -1
φ LCCO
= -90.1
Q = n c
4k F modulation
stabilized by
supermodulation
Interference “dip”

The Upshot
• LCCO has a simple misfit supermodulation with period
27.3 Å. q = 0.3 r.l.u. commensurate
• Add holes (δ c ~ 0.3) → Supermodulation amplifies &
stabilizes 4k F instability of the chain
• 4k F instability feeds back, shifting supermodulation to
incommensurate value q = 0.318 r.l.u.

Conclusions
• RSXS allows determination of W, φ
• Sr 14 Cu 24 O 41 has two distinct, coexisting charge density waves
1. Ladder HC is mainly electronic, W ~ ∞ (immeasurably large)
2. Chain CDW is 4k F stabilized by misfit strain, W = 1.13 Å -1
(W = 0.065 Å -1 if you take the holes out)
• Transport is an amalgem of both
• A CDW can form by straining a sample in the right way.

Fits
W SCO
= 1.13 Å -1 , φ SCO
= -23.1º

Resonant soft x-ray scattering (RSXS)
• 1.2 m vacuum chamber: Pumped with Turbos and TSPs, 2 × 10 -9 mbar
• Diffractometer: 10 motor axes working in a 6-circle geometry, in-vacuum
step motors, ceramic bearings, vacuum lubricants.
• Photon counting detector: Channeltron, braking voltages, Au/CsI cathode
• Helium cryostat: Indirect cooling with copper braids (OFHC), T=18 K
• 5 Tesla Magnet: Under commissioning.
• Current: NSLS X1B; Forthcoming: APS Sector 28

Resonance profile or |g(k,ω)| 2
Supermodulation in Bi 2
Sr 2
CaCu 2
O 8+δ
ZR
singlets
McElroy, Nature, 422, 592 (2003)

Quantum melting
“Melting”
Wigner
crystal
L L = 1/3: ξ c
= (1580 ± 70) Å and ξ a
= (1615 ± 70) Å
L L = 1/5: ξ c
= (255 ± 40) Å and ξ a
= (274 ± 40) Å
Interaction strength grows with decreasing hole spacing

Spectroscopic details
Note core
level shift

Correlation with metal-insulator transition
Kojima, J. Elect. Spect.
Rel. Phen., 237, 117
(2001)
Note this
phase
boundary.

Structural characterization
• Grain broken from same sample as chain studies
• All 603 reflections index to known structure
• 198 arise from incommensurate structure (chain buckling)

Oxygen stoichiometry

Self-absorption effects