Magnetic Excitations of Stripes E. W. Carlson D. X. Yao D. K. - - PowerPoint PPT Presentation

Magnetic Excitations of Stripes

• E. W. Carlson
• D. X. Yao
• D. K. Campbell

Stripes: Why?

HTSC Dilemmas

Superconductivity from a non-Fermi liquid High pairing scale despite strong repulsion

Metallic Charge Stripes: Spin-Charge Separation

Non-Fermi liquid normal state (Luttinger liquid) Pair the spin degrees of freedom, and avoid the Coulomb repulsion.

EC, V. Emery, S. Kivelson, D. Orgad in “Physics of Unconventional Superconductors”

• ed. Bennemann and Ketterson, (2004)

superconductivity

T

Josephson coupling Pairing

Inherent Competition

stripe fluctuations Static Stripes Good pairing Bad phase coherence Fluctuating Stripes Bad pairing Good phase coherence think think “ “stripe phonon stripe phonon” ” think local stripe order think local stripe order

EC, V. Emery, S. Kivelson, D. Orgad in “Physics of Unconventional Superconductors”

• ed. Bennemann and Ketterson, (2004)

Unidirectional modulation in charge and spin Charge: quasi-one-dimensional (rivers of charge) Spin: 2D Magnetic texture

Stripes

Stripes Have 2D Magnetic Texture

• Real Space

Reciprocal Lattice Vectors

2D spin waves disperse out of the reciprocal lattice vector positions

Neutron Scattering in Cuprates and Nickelates

Disappearance of (,) peak with doping Appearance of satellite peaks

AFM signal averages to zero

antiphase domain walls

• OR

OR site-centered site-centered bond-centered bond-centered

Neutron Scattering in Cuprates and Nickelates

• OR

OR site-centered site-centered bond-centered bond-centered

Charge Peaks related by X2

Checkerboards and Plaids?

Charge Peaks Antiphase Domain Walls in Antiferromagnetism Spin Peaks in Wrong Direction!

Hoffman et al., Science (2002) Vershinin et al., Science (2004)

Odd Spacing

Bond-centered

• Site-centered
• Magnetic

Reciprocal Lattice Vectors

Odd Spacing

Bond-centered

• Site-centered
• Intensities

Odd Spacing

Bond-centered

• Site-centered
• Observing

weight here rules out site-centered stripes

Magnetic Reciprocal Lattice Vectors

Even Spacing

Bond-centered Site-centered

Intensities

Even Spacing

Bond-centered Site-centered

Inelastic Response: Spin Waves

Site or Bond-Centered

Ja > 0 (AFM) Jb > 0 (AFM)

Jb Ja Jb

Ja > 0 (AFM) Jb < 0 (FM)

Ja

Site-centered p=3 Bond-centered p=3

Semiclassical Spin Waves

Low Energy Velocities

Spin wave cones may remain rather isotropic for bond-centered stripes, despite microscopic anisotropy.

site-centered bond-centered

1 2 3 1 2 3 1 1

Spin Wave Dispersions

• Bond-centered has one more band
• Bond-centered has weight at (0,π)
• Bands repel, do not cross

Resonance unlikely from crossings

Site-centered, p=3 Bond-centered, p=3

6

π π

5

Jb= 0.4 Ja Jb= - 1.0 Ja

Batista et al., PRB (2001) EC, Yao, et al., PRB (2004)

Data

YBCO6.6, S. Hayden et al., Nature 429, 531 (2004) Stripe-ordered LBCO, S. Hayden et al., Nature 429, 534 (2004)

Symmetrize

E=0.5J E=0.5Ja

a

E=1.5J E=1.5Ja

a

E=2.5J E=2.5Ja

a

E=3.5J E=3.5Ja

a

VB4 Jb = -.1 Ja

E=0.5J E=0.5Ja

a

E=1.0J E=1.0Ja

a

E=1.5J E=1.5Ja

a

E=2.0J E=2.0Ja

a

E=3.5J E=3.5Ja

a

E=4.0J E=4.0Ja

a

E=3.0J E=3.0Ja

a

E=2.5J E=2.5Ja

a

Vertical, Bond-centered, Spacing = 4

E=0.5J E=0.5Ja

a

E=1.0J E=1.0Ja

a

E=1.5J E=1.5Ja

a

E=2.0J E=2.0Ja

a

E=3.5J E=3.5Ja

a

E=4.0J E=4.0Ja

a

E=3.0J E=3.0Ja

a

E=2.5J E=2.5Ja

a

VB4 Jb = -.56 Ja

Vertical, Bond-centered, Spacing = 4

VS4 Jb = Ja

E=0.5J E=0.5Ja

a

E=1.0J E=1.0Ja

a

E=1.5J E=1.5Ja

a

E=2.0J E=2.0Ja

a

E=3.5J E=3.5Ja

a

E=4.0J E=4.0Ja

a

E=3.0J E=3.0Ja

a

E=2.5J E=2.5Ja

a

Vertical, Site-centered, Spacing = 4

Other Stripe Patterns

Diagonal

“DB4”

DB2 Jb= -.1 Ja

E=0.25J E=0.25Ja

a

E=0.5J E=0.5Ja

a

E=0.75J E=0.75Ja

a

E=1 J E=1 Ja

a

E=1.75J E=1.75Ja

a

E=2 J E=2 Ja

a

E=1.5 J E=1.5 Ja

a

E=1.25 J E=1.25 Ja

a

Diagonal, Bond-centered, Spacing = 2

Other Stripe Patterns

Staircase

• M. Granath, PRB (2004)

Smooth transition from diagonal to vertical peaks Fermi Surface Arcs

Globally diagonal Locally vertical Antiphase domain walls

SB2 Jb = -.1 Ja

E=0.4J E=0.4Ja

a

E=0.7J E=0.7Ja

a

E=1J E=1Ja

a

E=1.6 J E=1.6 Ja

a

E=3.6J E=3.6Ja

a

E=4.0 J E=4.0 Ja

a

E=2.6J E=2.6Ja

a

E=2.0 J E=2.0 Ja

a

Staircase, Bond-centered, Spacing = 2

Conclusions

2D magnetic texture

• Stripes produce 2D spin waves.
• Finite energy weight at (π, π) is natural from stripes,

but not from a pure antiferromagnet. Resonance peak

• Unlikely from crossing (bands repel)

Bond-centered stripes:

• Ferromagnetic coupling across domain wall
• One more band than site-centered
• Odd spacing has new elastic peaks,

forbidden for site-centered stripes

• Isotropic spin wave cones
• “Legs” of scattering

Comparison to Recent Cuprate Data

• Low energy could be semiclassical spin waves
• High energy is not