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Spin Waves in Stripe Ordered Systems: Insights into Strongly Correlated Superconductors

This paper investigates spin waves in stripe-ordered systems, focusing on materials like nickelates, manganites, and cuprate superconductors. These systems exhibit strong correlations manifesting in unique k-space structures and minimized kinetic energy. We discuss the impact of real-space structures, including charge and spin density configurations. Techniques such as neutron scattering reveal critical phenomena, including the disappearance of peaks with doping and evidence of bond-ordered charge densities. The findings guide microscopic theories in superconductivity.

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Spin Waves in Stripe Ordered Systems: Insights into Strongly Correlated Superconductors

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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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