Stripe Ordering in the Cuprates

Leland HarrigerHomework Project for Solid State IIInstructor: Elbio DagottoPhysics Dept., University of Tennessee at KnoxvilleSpring 2009

What is Stripe Ordering?

A periodic modulation of charge and spin.

Modulation of charge and spin are related by the phase boundary.

Result: Spin periodicity is twice that of charge periodicity

Why does Stripe Ordering Occur?

The Distance that Separates.

)(1

)(

copper

holesxnh

)(

)(1

copperN

holenh

a

LN

2

x

aLc 2

x

aLm

42 CuOSrLa xx

Scattering Basics (Preclude to testing for stripe ordering.)

if kkQ

Magnetic Scattering

0L

222

2

c

L

b

K

a

HQ

KH

ba

dQ

2

)0,,( HHQ

2

1H

Reciprocal Space of CuO4 in the Presence of Stripe Ordering. Big Circles are nuclear

Bragg peaks. Small plusses are

magnetic Bragg peaks. Other symbols are

incommensurate spreading of peaks due to stripe ordering.

Estimate of δ as a function of x.

x

aLc 2

x

aLm

xc ~

2c

m

Neutron Scattering

The triple axis spectrometer is very versatile for measurements of bulk solids.

Q-scans (ie: momentum transfer) Both elastic and inelastic Typically performed at a

fixed energy transfer. Energy Scans

Set E=0 for elastic scans Typically performed at a

fixed Q.

What Proof do We have of Stripe Ordering?

What does Stripe Ordering Mean for Superconductivity?

References

[1] J. Orenstein, et. al Science 288, 468 (2000) J. Tranquada, et. al. Nature 375, 561 J. Tranquada, et. al. Phys. Rev. Lett. 78, 338 S. Chi, et. al. Phys. Rev. Lett. 102 107005 Ph. Bourges, et. al. Physica C 424, 45 Yamada K. et. al. Phys. Rev. B 57 6165