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Magnetic Interactions and Order-out-of-disorder in Insulating Oxides

Magnetic Interactions and Order-out-of-disorder in Insulating Oxides. Amnon Aharony. Ora Entin-Wohlman, A. Brooks Harris, Taner Yildirim Robert J. Birgeneau, Marc A. Kastner, Koichi Katsumata R. Ramirez, C. Broholm, J. W. Lynn TAU, BGU, U Penn, NIST, MIT, RIKEN, Lucent, JHU.

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Magnetic Interactions and Order-out-of-disorder in Insulating Oxides

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  1. Magnetic Interactions andOrder-out-of-disorderin Insulating Oxides Amnon Aharony Ora Entin-Wohlman, A. Brooks Harris, Taner Yildirim Robert J. Birgeneau, Marc A. Kastner, Koichi Katsumata R. Ramirez, C. Broholm, J. W. Lynn TAU, BGU, U Penn, NIST, MIT, RIKEN, Lucent, JHU Les Houches summer school on Quantum Magnetism, June 2006

  2. Lecture 2: Generalized superexchange: add spin-orbit and involve all 10 d orbitals Tetragonal lattice: bond dependent anisotropies, Remove frustration by spin wave zero-point energy; Order out of disorder Orthorhombic lattice: Dzyaloshinskii-Moriya, dependence on Cu—O—Cu bond angle Interplanar coupling: Shender mechanism, Pseudo-dipolar anisotropies

  3. LCO, 214 YBCO, 123 What determines the easy axes for the spins (in plane and between planes)?

  4. Simple theory: Super-exchange Hubbard Hamiltonian: Perturb in t, keep low energy states Heisenberg Hamiltonian: ordered moment: 2 1 (the manifold, each site has only a single electron)

  5. Superexchange: No phase transition in the 2D isotropic Heisenberg model?? Order arises due to small anisotropies plus weak interplane coupling Plus quantum fluctuations!

  6. Theory On Cu Cu---O---Cu On Cu

  7. cuprates: full Hamiltonian full Coulomb interaction; spin-orbit interaction; hopping among all 5 d-orbitals; further hopping processes;

  8. Tetragonal symmetry: Spin-orbit anisotropy y 3 z x 2 1

  9. Orthorhombic symmetry: Also Dzyaloshinskii-Moriya antisymmetric exchange O Cu Cu Oxygen tilted along z D along y, AFM along x FM along z

  10. Moriya's anisotropic superexchange interaction, frustration, and Dzyaloshinsky's weak ferromagnetism, L. Shekhtman, O. Entin-Wohlman and AA, Phys. Rev. Lett. 69, 000836 (1992)

  11. For a 90 degrees Cu—O—Cu bond, electrons must hop from each Cu ion to two orthogonal orbitals on the oxygen, and then Hund’s rule turns the superexchange ferromagnetic. Superexchange then turns antiferromagnetic as the bond angle increases towards 180 degrees.

  12. NNN NN

  13. Tetragonal symmetry: y f 3 z x 2 1 Mean field theory: Frustration!

  14. f 3 z x 2 1 Order out of disorder!

  15. 2342 The “Shender” mechanism: 3 2 1 3 1 2 2122

  16. Pseudodipolar interactions y x y x II II I2 I1 I1 I2

  17. Interplane interactions 1 2 Also explain : need Nd-Cu and Pr-Cu interactions

  18. Order determined by delicate competition With quartic spin anisotropies on the Pr or Nd

  19. 2342 Fits to magnetic moment versus Direction of magnetic field yield Many of the interesting parameters

  20. Spin wave theory for 2342 Shender 4-fold

  21. ESR: in plane anisotropy gap in 2122 and 2342, In and out of plane gaps for CuII at low T

  22. Spin chains, ladders: same interactions as in 2342?

  23. Conclusions: Cuprates: taylored 2D and 1D S=1/2 AFMs Hubbard + spin-orbit effective magnetic anisotropies Pseudodipolar, Dzyaloshinskii-Moriya Fluctuations: Shender, in-plane 4-fold Explain structures of many cuprates 2342: measure many anisotropies, useful for chains and ladders Relevance to ladders, chains, nickelates, cobaltates, titanates…

  24. THE END (More tomorrow)

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