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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. 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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  1. Spin Waves in Stripe Ordered Systems E. W. Carlson D. X. Yao D. K. Campbell

  2. Strong Correlations • nickelates • manganites • cuprate superconductors • organic superconductors All show some evidence of real space order

  3. Kinetic energy is minimized • k-space structure • Real space homogeneity • Interaction energy is important • Real space structure • spin • charge Strong Correlation Fermi Liquid

  4. 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

  5. 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)

  6. Cu-O or Ni-O Planes Other Layers Layered structure  quasi-2D system Cuprates and Nickelates Layered structure  quasi-2D system

  7. Cuprates and Nickelates Dope with holes (remove spins) Topological Doping Ni: S=1 Cu: S=1/2 Oxygen Cu or Ni

  8. Cuprates Dope with holes Superconducts at certain dopings T SC AF x Oxygen Cu or Ni

  9. 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

  10. 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

  11. 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)

  12. 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

  13. 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)

  14. Ja Jb • Bond-centered, p=3 • Ja > 0 (AFM) Jb< 0 (FM) Model and Method Heisenberg model

  15. Elastic Response

  16. π π Spacing p=3 Magnetic Reciprocal Lattice Vectors Site-centered p=3 Bond-centered p=3

  17. π π Spacing p=4 Magnetic Reciprocal Lattice Vectors Site-centered p=4 Bond-centered p=4

  18. Elastic Neutron Scattering f(n) g(m)

  19. f(n) g(m) π π Elastic Neutron Scattering p=3 Site-centered

  20. f(n) g(m) Elastic Neutron Scattering p=3 Site-centered π π

  21. π π Elastic Neutron Scattering p=3 Bond-centered f(n) g(m)

  22. Elastic Neutron Scattering p=3 Bond-centered f(n) g(m) π π

  23. 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

  24. 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)

  25. 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

  26. Elastic Peaks3D Antiphase Domain Walls

  27. Inelastic Response: Spin Waves

  28. Ja Jb • Bond-centered, p=3 • Ja > 0 (AFM) Jb< 0 (FM) Model and Method Heisenberg model

  29. Model and Method Heisenberg model Holstein-Primakoff Bosons Up Spins: Down Spins:

  30. Fourier transformation + symplectic transformation yield spectrum and eigenstates Model and Method Heisenberg model

  31. Spin Structure Factor

  32. 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

  33. 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)

  34. 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

  35. S3 k=(π, π) Energy dependence on λ= k=(0,0) S4

  36. Energy dependence on λ= B2 k=(π, π) k=(0,0) B3 B4

  37. || AF Site-centered velocities v velocity along the stripe direction v velocity perpendicular to the stripe direction v velocity of pure 2D antiferromagnet

  38. Bond-centered velocities || AF v velocity along the stripe direction v velocity perpendicular to the stripe direction v velocity of pure 2D antiferromagnet

  39. 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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