# Presentation: 562822

## Crystallization of holes in the spin ladder of Sr14Cu24O41

- Peter Abbamonte
*Brookhaven National Laboratory / SUNY Stony Brook*

**Collaborators:**
- 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

*Crystallization of holes in the spin ladder of Sr**14**Cu**24**O**41*

**Funding: ***DOE, NSF, NWO (Dutch Science Foundation)*

- (to appear in Nov. 4 issue of *Nature*)

## Spin ladders

- Singlets across the rungs

*Spin ladders*

- E. Dagotto, J. Riera, and D. Scalapino, *Phys. Rev. B*, **45**, 5744 (1992)
- E. Dagotto and T. M. Rice, *Science*, **271**, 618 (1996)

*t**||*, *J**||*

*t*, *J*

*J* >> *J**||*

-  Holes bind into pairs
-  Superconductivity without phonons,
-     ~ *d*x2-y2 [M. Sigrist, *PRB*, **49**, 12058 (1994)]

-  Doped hole breaks a singlet (costs ~*J*)

## Spin ladders

- 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)

*Superconductivity not automatic *– models also reveal a “charge density wave”

-  *x* rational  holes “crystallize” into a CDW
* **x* irrational  power law correlations 1/|n-n|*K*+. Friedel oscillations easily induced.
-  Reminiscent of ordered stripes vs. SC in perovskite cuprates
* **Not high T**c**, but worthy of study in its own right*

## 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
-  *chain* = 0.52 , *ladder* = 0.057

- 1Osafune, *PRL*, **78**, 1980 (1997); Nücker, *PRB*, **62**, 14384 (2000)

## Sr14-xCaxCu24O41

-  *x* = 13.6  superconductivity Tc = 12 K at P = 3 GPa 2
-  *x* = 0  insulating with a CDW 3
-  m* ~ 50   (103 – 104 more typical) 4
-  Exhibits characteristics of *both* phases predicted by Dagotto (1992)

- 2Uehara, *J. Phys. Soc. Jap.*, **65**, 2764 (1996)
- 3Blumberg, *Science*, **297**, 584 (2002); Gorshunov, *PRB*, **66**, 60508 (2002)
- 4Vuletić, *PRL*, **90**, 257002 (2003)

## Study with x-ray scattering?

- modulation wavelength (commensurate?)
- coherence length
- form factor (sinusoidal?)
- (T) (mean field or no?)

- R. M. Fleming, D. E. Moncton, and D. B. McWhan, *Phys. Rev. B*, **18**, 5560 (1978)

- NbSe3

- T. Fukuda, *PRB*, **66**, 12104 (2002)
- [refinement of study by D. E. Cox, *PRB*, **57**, 10750 (1998)]

- S. van Smaalen, *PRB*, **67**, 26101 (2003)

*Conclusion: no obvious evidence for a structural CDW in Sr**14**Cu**24**O**41*

## Two types of CDWs

- Scattering from Wigner crystal *nominally* weaker by ~ 10-7
*CDW predicted by Dagotto et. al. is Wigner, not Peierls (viz. “hole crystal”) *
*Could a hole crystal be responsible for the transport properties of Sr**14**Cu**24**O**41**?*

***Peierls CDW***

***Wigner crystal ***
- [E. Wigner, *Phys. Rev.*,** 46**, 1002 (1934)]

*Examples*
*Mechanism*
*Effective mass*
*Charge modulation*
*Cross section*
*Bottom line*

- NbSe3, K0.3MoO3
*H**ep*
- ~ 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

## Resonant soft x-ray scattering

- P. Abbamonte, L. Venema, A. Rusydi, G. A. Sawatzky, G. Logvenov, and I. Bozovic, *Science*, **297**, 581 (2002)

*I*normal ~ | **(**q**) |2
*I*RSXS ~ | **(**q**) +  *n*(**q**) |2            *n**i* = ** *c*†*i*** *c**i***  – 1	    ~ 102

## Edge structure in Sr14Cu24O41

- N. Nücker, *et. al*., *PRB*,** 62**, 14384 (2000)

*Edge structure in Sr**14**Cu**24**O**41*

- chain    ladder

- UHB

## X-ray scattering in vacuum

-  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 / Au·CsI cathode

## Sample prep. for low energy scattering – the surface is everything

-  Traveling solvent floating zone technique*
-  Polish with dry, diamond film, 30 m  10 m  ... 0.1 m
-  Anneal at 120 °C in O2 for ~1 day
-  No bragg peaks!  Orient with Ge(111) reference sample and use surface reflection

- * T. Osafune, N. Motoyama, H. Eisaki, S. Uchida, *PRL*, **78**, 1980 (1997)

- Surface roughness

## Valence modulation in Sr14Cu24O41

-  *L* = 0.200 ± 0.009 r. l. u.   = 5.00 ± 0.24 *c**L*.
-  *Does not index to 27.3 Å unit cell.*
* *c = 255 Å, a = 274 Å
-  No measurable off-resonant signal  purely electronic phenomenon

- Photon Energy (eV)

- Total fluorescence yield
- (relative units)

- T=28K

- T=28K

## Resonance properties

-  Disappears of OK prepeak –*cannot be structural*
-  Visible at Cu*L*2,3 – still at L=0.2
-  Coherent, bulk phenomenon
-  No harmonic at L=0.4 – sinusoidal

-  Resonates *only* with ladder feature
-  Resonates at Cu*L*3, not *L*3 (just electrostatic)

*Simplest explanation: *hole crystal in the ladder, as predicted by Dagotto* et. al.*

- T=28K

## Temperature dependence

-  (T) non–MFT (crossover)
- Agrees with Vuletić et. al. [PRL, 90 257002, (2003)]
-  c is T–independent

- Simplest explanation: phase fluctuations from impurities

- S. Girault, A. H. Moudden, J. P. Pouget, J. M. Goddard, *PRB*, **38**, 7980 (1988)

## Does the wavelength  = 5.00 cL make sense?

-  0.8 holes in 7 rungs   ** = 0.8 / 14 = 0.057
-  Spin gap  bosonic pairs
-  Expected  = 1/ = 17.54 *c**L* – *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?

## Summary

-  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.*)
* *(T) and c(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 Vuletić *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

*Summary*