Spin waves in stripe ordered systems
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Spin Waves in Stripe Ordered Systems. E. W. Carlson D. X. Yao D. K. Campbell. Strong Correlations. nickelates manganites cuprate superconductors organic superconductors All show some evidence of real space order. Kinetic energy is minimized k-space structure

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Spin Waves in Stripe Ordered Systems

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Spin waves in stripe ordered systems

Spin Waves in Stripe Ordered Systems

E. W. Carlson

D. X. Yao

D. K. Campbell


Strong correlations

Strong Correlations

  • nickelates

  • manganites

  • cuprate superconductors

  • organic superconductors

    All show some evidence

    of real space order


Strong correlation

  • Kinetic energy is minimized

  • k-space structure

  • Real space homogeneity

  • Interaction energy is important

  • Real space structure

    • spin

    • charge

Strong Correlation

Fermi Liquid


Organic superconductors

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 superconductors1

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)


Cuprates and nickelates

Cu-O or Ni-O Planes

Other Layers

Layered structure  quasi-2D system

Cuprates and Nickelates

Layered structure  quasi-2D system


Cuprates and nickelates1

Cuprates and Nickelates

Dope with holes

(remove spins)

Topological Doping

Ni: S=1

Cu: S=1/2

Oxygen

Cu or Ni


Cuprates

Cuprates

Dope with holes

Superconducts at certain dopings

T

SC

AF

x

Oxygen

Cu or Ni


Neutron scattering in cuprates and nickelates

δ=0

δ=0

π

π

π

Neutron Scattering in Cuprates and Nickelates

Disappearance of (π,π) peak

with doping

Appearance of satellite peaks

AFM signal averages to zero

antiphase domain walls

π


Issues

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


Cuprates1

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

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


Site or bond centered

Ja

Ja

Jb

Jb

Bond-centered p=3

π

Both produce weight

at (π+ π/p, π)

π

Site or Bond-Centered

Site-centered p=3

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

  • Ja > 0 (AFM) Jb< 0 (FM)


Model and method

Ja

Jb

  • Bond-centered, p=3

  • Ja > 0 (AFM) Jb< 0 (FM)

Model and Method

Heisenberg model


Elastic response

Elastic Response


Magnetic reciprocal lattice vectors

π

π

Spacing p=3

Magnetic Reciprocal Lattice Vectors

Site-centered p=3

Bond-centered p=3


Magnetic reciprocal lattice vectors1

π

π

Spacing p=4

Magnetic Reciprocal Lattice Vectors

Site-centered p=4

Bond-centered p=4


Elastic neutron scattering

Elastic Neutron Scattering

f(n)

g(m)


Elastic neutron scattering p 3

f(n)

g(m)

π

π

Elastic Neutron Scattering p=3

Site-centered


Elastic neutron scattering p 31

f(n)

g(m)

Elastic Neutron Scattering p=3

Site-centered

π

π


Elastic neutron scattering p 32

π

π

Elastic Neutron Scattering p=3

Bond-centered

f(n)

g(m)


Elastic neutron scattering p 33

Elastic Neutron Scattering p=3

Bond-centered

f(n)

g(m)

π

π


Site vs bond centered p 3

Bond-centered p=3

f(n)

f(n)

g(m)

g(m)

π

π

π

π

Site vs. Bond-Centered p=3

Site-centered p=3


Site vs bond centered p 4

π

π

π

π

Site vs. Bond-Centered p=4

Site-centered p=4

f(n)

g(m)

Bond-centered p=4

f(n)

g(m)


Elastic peaks

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 peaks 3d antiphase domain walls

Elastic Peaks3D Antiphase Domain Walls


Inelastic response spin waves

Inelastic Response: Spin Waves


Model and method1

Ja

Jb

  • Bond-centered, p=3

  • Ja > 0 (AFM) Jb< 0 (FM)

Model and Method

Heisenberg model


Model and method2

Model and Method

Heisenberg model

Holstein-Primakoff Bosons

Up Spins:

Down Spins:


Model and method3

Fourier transformation + symplectic transformation

yield spectrum and eigenstates

Model and Method

Heisenberg model


Spin structure factor

Spin Structure Factor


Number of bands

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


Site centered s k w

π

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)


Bond centered s k w

π

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


Energy dependence on

S3

k=(π, π)

Energy dependence on λ=

k=(0,0)

S4


Energy dependence on1

Energy dependence on λ=

B2

k=(π, π)

k=(0,0)

B3

B4


Site centered velocities

||

AF

Site-centered velocities

v velocity along the stripe direction

v velocity perpendicular to the stripe direction

v velocity of pure 2D antiferromagnet


Bond centered velocities

Bond-centered velocities

||

AF

v velocity along the stripe direction

v velocity perpendicular to the stripe direction

v velocity of pure 2D antiferromagnet


Conclusions

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) bandsBond: (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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