Markus Hücker

What Pins Stripes in La2-xBaxCuO4?

Neutron Scattering Group

Electronic Liquid-Crystal Nature of Stripes Electronic Liquid-Crystal Nature of Stripes

Doping Phase Diagram of LBCO at Ambient PressureDoping Phase Diagram of LBCO at Ambient Pressure

Pressure Phase Diagram of LBCO at x=1/8Pressure Phase Diagram of LBCO at x=1/8

CMPMS (Brookhaven)

J. M. TranquadaG. D. GuC. C. Homes Z. J. XuJ. S. Wen

DESYM. v. Zimmermann

Washington University

M. DebessaiJ. S. Schilling

Competing Order in Strongly Correlated Electron Systems

CePd2Si2

Mathur et al. Nature 1998

heavy fermion superconductor

La2-xSrxCuO4

3DAF LTT

LTO

0.05 0.10 0.15 0.200

20

40

60

80

100

hole density (x)

T (

K)

SC

Tc

1/8-problem

Competing Order in Strongly Correlated Electron Systems

La2-xBaxCuO4

SG

stripes

HTT

Common Conception: LTT Phase Pins Stripes

La,Ba

Cu

OHTT

[010]

[100]

[001]

LTO

LTT

LTO phase

LTT phase

Cu-O-Cu

Stripe Order

Stripes: detected with neutrons, x-rays in LBCO, LNSCO

Stripe Order in LBCO

1.8 2.0 2.2

0

200

400

600

k (r.l.u.)

Int

(co

un

ts/m

in)

0.4 0.5 0.6100

200

300

400

500

k (r.l.u.)

Int

(co

un

ts/1

0se

c)

Tranquada et al. Nature (1995)

magnetism charge

Fujita et al. PRB (2004)

Electronic Liquid-Crystal

Kivelson et al. Nature (1998)

At ambient pressure symmetry broken by LTT structureAt ambient pressure symmetry broken by LTT structure

Hinkov et al., Science (2008)Ando et al., PRL (2002)Evidence in YBa2Cu3O6.45

Stripe phase of La2-xBaxCuO4:

Symmetry broken by orthorhombic structureSymmetry broken by orthorhombic structure

Stripe Order in LBCO at Ambient Pressure

p = 0 GPa

SO

0.100 0.125 0.1500

10

20

30

40

50

60

70

CO

SC

LTO

Tc

TLT

SCLTT

Tem

pera

ture

(K

)

hole doping (x)

Pressure Dependence of Tc

Ido et al. Physica C (1991)

0 GPa

2 GPa

0.120.1250.13

0.125SC

Tc

x=1/8

Tc~18K

sample

High Energy Single-Crystal X-ray Diffraction under Pressure

100 keVphotons

BW5 @ DESY, Hamburg

Review of Scientific Instruments 79, 33906 (2008)

LBCO

CGO

1 mm

p = 0 GPa

SO

0.0 0.5 1.0 1.5 2.0 2.5 3.00

50

100

150

200

250

LBCO (x=1/8)

pressure (GPa)

Tc

CO + DS

LTO

LTT + CO

HTT

Tem

pera

ture

(K

)

Tuning the Structure with Pressure

0.100 0.125 0.1500

10

20

30

40

50

60

70

CO

SC

LTO

Tc

TLT

SC

LTT

Tem

pera

ture

(K

)

hole doping (x)

Stripes in Tetragonal High Pressure Regime

c

(2, 0, 0)/(0, 2, 0) T~TLT

b

-0.01 0.00 0.010

1

2

3

4

5

6

7

8

9

1.72GPa

1.77GPa

0

0.6

0.77

1.15GPa

1.45GPa

p=2.7GPa

Inte

nsity

(ar

b. u

nits

)

q (r.l.u.)

T~TLT

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Tilt a

ng

le

(de

gre

e)

HTT

0 1 2 30.0

0.1

0.2

0.3

0.4

0.5

0.6

LTO

Pressure (GPa)

2(b-

a)/(

a+b)

at

TL

T (

%)

pc

T~10Ka

(1, 0, 0)

(2+2, 0, 5.5)

LTT HTT

LTO

[110]

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.10

0.20

0.30

0.40

Pressure (GPa)

Inte

grat

ed In

tens

ity I C

O (

coun

ts/s

ec)

0

1

2

3

4

Integrated Intensity I(100) (counts/sec)

LTT

[100][010]

High pressure: 4-fold symmetric planesHigh pressure: 4-fold symmetric planes

Charge stripes still develop Charge stripes still develop

Stripes spontaneously break SymmetryStripes spontaneously break Symmetry

What pins stripesWhat pins stripes

Charge Stripes on Square Lattice

PDF: Tilted Octahedra even in the HTT PhasePDF: Tilted Octahedra even in the HTT Phase

XAFS: Local Tilts around DopantsXAFS: Local Tilts around Dopants

PDF, XAFS

Haskel et al., PRB (2000)

Billinge et al., PRL (1994)

-0.01 0.00 0.01

0

25

50

75

100

2.7GPa

1.77GPa (x 0.1)

p=0GPa (x 0.01)

Inte

nsi

ty (

10

3 co

un

ts/s

ec)

q (r.l.u.)

(3/2 3/2 2)

0.0 0.5 1.0 1.5 2.0 2.5 3.00

50

100

pressure (GPa)

Tc

CO + DS

LTO

LTT + CO

HTT

Tem

pera

ture

(K

)

Diffuse scattering in High Pressure Regime

80Å

40Å

20Å

LBCO

-0.02 0.00 0.02

0

5

10

15

20

25

30

q (r.l.u) q (r.l.u)

p=1.77GPa

-0.02 0.00 0.02

0

5

10

15

p=2.7GPa

q (r.l.u)-0.02 0.00 0.02

0

10

20

30

40

(2+2,0,5.5)

p=0GPa

In

ten

sity

IC

O (

cou

nts

/sec

)

-0.02 0.00 0.02

0

5

10

15

20

25

30

q (r.l.u) q (r.l.u)

p=1.77GPa

-0.02 0.00 0.02

0

5

10

15

p=2.7GPa

q (r.l.u)-0.02 0.00 0.02

0

10

20

30

40

(2+2,0,5.5)

p=0GPa

In

ten

sity

IC

O (

cou

nts

/sec

)

0

50

100

0

2

4

6

0.00

0.05

0.10

0.15

0.20

0.25(1.5,1.5,2)

Inten

sity I(1.5 1.5 2) (105 co

un

ts/sec)

0.0 0.5 1.0 1.5 2.0 2.5 3.00

50

100

pressure (GPa)

Tc

CO + DS

LTO

LTT + CO

HTT

Tem

pera

ture

(K

)

Nematic Patches in High Pressure Regime

Commensurate patches of stripes and octahedral tilts Commensurate patches of stripes and octahedral tilts

Quenched disorder always a relevant pertubationQuenched disorder always a relevant pertubation

Dopant disorder leads to finite size domainsDopant disorder leads to finite size domains

E. Carlson et al., PRL (2006)

nematic patches

Summary

Stripes spontaneously break symmetry in HTT Stripes spontaneously break symmetry in HTT phase phase

Pinned by quenched dopant disorderPinned by quenched dopant disorder

Supports electronic liquid-crystal picture of Supports electronic liquid-crystal picture of HTSCHTSC

Outlook

c-axis correlationsc-axis correlations

What happens for xWhat happens for x1/8 Ba1/8 Ba

What happens at higher pressuresWhat happens at higher pressures

SO0.100 0.125 0.150

0

10

20

30

40

50

60

70

CO

SC

LTO

Tc

TLT

SCLTT

Tem

pera

ture

(K

)hole doping (x)

SC

Tc

supplemental slides

High Energy Single-Crystal X-ray Diffraction under Pressure

Different Models for the Stripe Phase

Fermi surface nesting; SDW/CDW

B. Shraiman, E.D. Siggia, PRL 62, 1564 (1989) Hasselmann et al. PRB 69, 14424 (2004)Shushkov et al. PRB 70, 245023 (2004)

Spiral spin order

Mason et al. PRL 77, 1604 (1996)

Electronic micro phase separationJ. Zaanen et al. PRB 40, 7391 (1989)V. Emery et al., PRL 64, 475 (1990)S.R. White et al., PRL 80, 1272 (1998)

Question of Dimensionality (1D Stripes, 2D Pattern)

V. Hinkov et al., Nature 450, 650 (2004)

Magnetic excitations in detwinned YBa2Cu3O6+x

“Checkerboard” electronic state in Ca2-xNaxCuO2Cl2T. Hanaguri et al., Nature 430, 1001 (2004)

hole concentration of 1/8 crucialhole concentration of 1/8 crucial

Maeno et al. PRB, 7753 (1991)Maeno et al. PRB, 7753 (1991)

Competing order in La2-xBaxCuO4

Ba – doping

Kimura et al., PRB 70, 134512 (2004)

SCCO

Tc=31K

100% Ba 100% Sr

Competing order in La1.875Ba0.125CuO4

Ba-doping is crucial

Doping dependence

LTO

[110]

LTT

[100][010]

average structure

local distortions

electronic correlations

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

100

200

300

400

LTT

LTO

HTT

Tem

pera

ture

(K

)

Nd - content (y)

1.216 1.212 1.208 1.204 1.200 1.196 1.192

<rave

> (A)

0.0045 0.0050 0.0055 0.0060

o

o

(A2)

Average Structure and Cation Size Variance

McAllisten et al. PRB (2002)

La1.85-yNdySr0.15CuO4

Büchner et al. (1992)Wagener et al. PRB (1997)

L1.85-yMyCuO4

0.0

0.5

1.0(1, 0, 0)

(2.24, 0, 5.5)

Inte

grat

ed I

nten

sity

1.20

1.25

1.30

ab

T (K)0 10 20 30 40 50 60 70

1.25

1.30

1.35

1.40

c

Detection of Charge and Spin Stripe Transition

TSO

WFM

TSO

H||ab

H||c

spin

spin

La1.875Ba0.125CuO4

TCO

charge peak

LTOLTT

charge

spin

SCpressure

?

?

T

I

SO

0.100 0.125 0.1500

10

20

30

40

50

60

70

CO

SC

LTO

Tc

TLT

SCLTT

Tem

pera

ture

(K

)

hole doping (x)

Stripe Order in LBCO at High Pressure?

Traveling-Solvent Floating-Zone Technique

feedrod

crystal

liquidzone

0.5mm/h

La2-xBaxCuO4 with x=1/8(G.D. Gu)

Charge correlations along the c-axis

c

-1.0 -0.5 0.0 0.5 1.0

0

50

100

150

200

L (r.l.u.)

Int

(co

un

ts/m

in)

similar result:La1.48Nd0.4Sr0.12CuO4 , x-rays, T. Niemoeller et al., EPL (1998)La1.875Ba0.075Sr0.05CuO4 , neutrons, H. Kimura et al., PRB (2003)

1D charge stripes

2D charge grid

(0, 2+2, L)

c

c

M. Vojta et al., cond-mat/0408461

h

k

(0 2 ½)

Results for LBCO consistent with 1D-stripe model

0.4 0.5 0.6100

200

300

400

500

k (r.l.u.)

Int (

cou

nts

/10

sec)

0.55 0.60 0.65100

200

300

400

500

h (r.l.u.)

Int (

cou

nts

/10

sec)

0.4 0.5 0.6100

200

300

400

500

h (r.l.u.)

Int (

cou

nts

/10

sec)

+++

+++

+++

(½ ½ 0)

1.7 1.8 1.9 2.0 2.1 2.2 2.3

0

200

400

600

k (r.l.u.)

Int (

cou

nts

/min

)0.20 0.25 0.30

-100

0

100

200

300

400

500

600

h (r.l.u.)

Int (

cou

nts

/min

)

2.1 2.2 2.3

0

200

400

600

k (r.l.u.)

Int (

cou

nts

/min

)

magnetism charge

Search for non-1D-Correlations

[100]

La,Ba

[010]

[110]

Cu

O

[001]

h

k

L=0

L=0

21

L=5.5

HTT

LTO

LTT

LTT-phase LTO-phase

k

L=2

a b

c d

L=6

1

2

h

2

1

1 2

L=0

L=2

[110]

[100][010]

a c

(1, 0, 0) T~10K (1.5, 1.5, 2) T~10K(2+2, 0, 5.5) T~10Kb

-0.002 -0.001 0.000 0.001 0.002

0

100

200

300

400

2.7GPa

1.77GPa

1.72GPa

p=0GPa (x 0.1)

1.64GPa

Inte

nsity

(co

unts

/sec

)

k (r.l.u.)-0.02 -0.01 0.00 0.01 0.02

-5

0

5

10

15

20

25

30

35

2.7GPa

1.77GPa

p=0GPa

Inte

nsity

(co

unts

/sec

)

k (r.l.u.)-0.01 0.00 0.01

0

25

50

75

100

2.7GPa

1.77GPa (x 0.1)

p=0GPa (x 0.01)

Inte

nsi

ty (

103 c

ou

nts

/se

c)

q (r.l.u.)

0 20 40 60 80 100

0.0

0.1

0.2

e

2.7GPa1.77GPa

1.72GPa

1.62GPa

p=1.45GPa

2(b-

a)/(

a+b)

(%

)

Temperature (K)

0 10 20 30 40 50 60 70

0.00

0.05

0.10

0.15

0.20

0.25

1.15GPa (x0.2)

2.7GPa

1.77GPa

p=0GPa (x0.1)

Inte

grat

ed In

tens

ity (

coun

ts/s

ec)

Temperature (K)0 10 20 30 40 50 60 70

0.0

0.5

1.0

1.5

2.0

dc

ba

(1.5, 1.5, 2)

(2+2, 0, 5.5)(1, 0, 0)

2.7GPa

1.77GPa

1.15GPap=0GPa

Inte

nsity

I CO (

coun

ts/s

ec)

Temperature (K)

0 20 40 60 80 1000.00

0.01

0.02

0.03

TDS p=0GPa

2.7GPa

1.77GPa

(1.5, 1.5, 2)

FW

HM

(r.

l.u.)

Temperature (K)0 20 40 60 80 100

0

2

4

6

8

10

12

THT

=235K

TLT

THT

TLT

2.7GPa

1.77GPa

p=0GPa (x0.1)

Pea

k In

tens

ity (

105 c

ount

s/se

c)

Temperature (K)

Temperature dependence

0.0

0.5

1.0(1, 0, 0)

(2.24, 0, 5.5)

Inte

grat

ed I

nten

sity

1.20

1.25

1.30

ab

T (K)0 10 20 30 40 50 60 70

1.25

1.30

1.35

1.40

c

Detection of Charge and Spin Stripe Transition

TSO

WFM

TSO

H||ab

H||c

spin

spin

La1.875Ba0.125CuO4

TCO

charge peak

LTOLTT

Yamada et al. JSSC (1989)

Bozovic et al. PRL (2002)

LSCO thin filmLSCO bulk

Gao et al. PRB (1994)

Hg-1223 bulk

Pressure and Superconductivity

Pressure: affects crystal structure and electronic band structure

buckled

flat

0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

0.125

0.12

x=0.14

T

C

(K)

pressure (GPa)

ARPES

Stripes vs. CDW

T. Valla et al., Science (2007)

ARPES

T. Valla et al., Science (2007)