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Spin Waves in Stripe Ordered SystemsPowerPoint Presentation

Spin Waves in Stripe Ordered Systems

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Strong Correlations

- nickelates
- manganites
- cuprate superconductors
- organic superconductors
All show some evidence

of real space order

- Kinetic energy is minimized
- k-space structure
- Real space homogeneity

- Interaction energy is important
- Real space structure
- spin
- charge

Fermi Liquid

Organic Superconductors

q -(ET)2 X

(TMTST)2PF6

From S. Lefebvre et al., Physica B 312: 578-583 (2002)

From E. Dagotto, cond-mat/0302550

Organic superconductors

CDW, SDW

Bond Order

- BCSDW (Campbell)

D. Chow et al., Phys Rev Lett 85 1698 (2000)

(Mazumdar, Clay, and Campbell, Synth. Met. 137, 1317 (2003)

Other Layers

Layered structure quasi-2D system

Cuprates and NickelatesLayered structure quasi-2D system

Cuprates and Nickelates

Dope with holes

(remove spins)

Topological Doping

Ni: S=1

Cu: S=1/2

Oxygen

Cu or Ni

δ=0

π

π

π

Neutron Scattering in Cuprates and NickelatesDisappearance of (π,π) peak

with doping

Appearance of satellite peaks

AFM signal averages to zero

antiphase domain walls

π

Issues:

nature – static vs. dynamic

orientation – vertical vs. diagonal

spacing – commensuratevs. incommensurate

width – one atom vs. two ...

location of holes – site-centered vs.

bond-centered

Cuprates

stripes: interleaved charge and spin density

(Kivelson, Emery)

(Zaanen)

(Castro Neto, Morais-Smith)

bond-ordered charge density

(Sachdev)

from Almason and Maple (1991)

2D magnetic/current textures:

DDW (Marsten, Chakravarty, Morr); Staggered flux (Lee); Loops (Varma)

Scattering Probes

Energy, Momentum

Phase Information?

Yes in certain cases

Goals:

- Phase-sensitive information from diffraction probe
- Guidance for microscopic theories of superconductivity in cuprates, organics

Ja

Ja

Jb

Jb

Bond-centered p=3

π

Both produce weight

at (π+ π/p, π)

π

Site or Bond-CenteredSite-centered p=3

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

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

Elastic Peaks

2D Antiphase Domain Walls

Site-centered: never weight at

Bond-centered: no weight at for p=EVEN

generic weight at for p=ODD

The presence of weight at with incommensurate peaks at is positive evidence of a bond-centered configuration

Elastic Peaks3D Antiphase Domain Walls

Fourier transformation + symplectic transformation

yield spectrum and eigenstates

Model and MethodHeisenberg model

Number of Bands

Site-centered p=4

p-1 spins per unit cell

Spin up/Spin down degeneracy

) (p-1)/2 bands

3 bands for p=4

Bond-centered p=4

p spins per unit cell

Spin up/Spin down degeneracy

) p/2 bands

4 bands for p=4

π

Site-Centered: S(k,w)Jb=0.4 Ja

Jb=1.0 Ja

Jb=2.5 Ja

p=3

p=4

kx

N.B. Site-centered consistent with F.Kruger and S. Scheidl, PRB 67, 134512 (2003)

π

Bond-Centered: S(k, w)Jb= - 0.1 Ja

Jb=-0.56 Ja

Jb=-1.0 Ja

p=2

- Note the elastic weight for p=3

p=3

p=4

kx

AF

Site-centered velocitiesv velocity along the stripe direction

v velocity perpendicular to the stripe direction

v velocity of pure 2D antiferromagnet

Bond-centered velocities

||

AF

v velocity along the stripe direction

v velocity perpendicular to the stripe direction

v velocity of pure 2D antiferromagnet

Conclusions

Elastic:

For both 2D and 3D antiphase domain walls, bond-centered p=ODD stripes show new peaks, forbidden for site-centered

Inelastic:

- Number of bands distinguishes site- or bond-centered
Site: (p-1) bands Bond: (p) bands

- Qualitatively different spin wave spectra
Site: all bands increase with J_b

Bond: lower bands independent of J_b

top band ~ 2 J_b

- Velocity anisotropy
Bond-centered is rather isotropic over a large range of parameters

Extensions:

- Diagonal spin waves
- Other spin textures

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