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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 3: Vanadates: Competing nn and nnn interactions yield Incommensurate order Competing anisotropies yield complex field dependent phase diagrams Ni and Co have very different magnetic structures Theoretical tools introduced in pervious lectures suffice to explain most features

  3. General outline: Cuprates Vanadates Lecture 3

  4. Buckled Kagome S=3/2 S=1

  5. Buckled Kagome

  6. ? Cross-tie is FRUSTRATED Crystal Structure of Ni3V2O8 Only magnetic (S=1) Ni ions are shown b a c Cross-tie Spine

  7. H || a H || b 5 5 5 H || c 0 0 0 Magnetic Field (T) 0 2 4 6 8 10 Temperature (K)

  8. Specific heat Weak ferromagnetism in C phase Neutron scattering intensities in C, LTI and HTI Incommensurate wave vector

  9. MAGNETIC PHASE DIAGRAM OF Ni3V2O8 Paramagnetic HTI = High Temperature Incommensurate Phase LTI = Low Temperature Incommensurate Phase CAF = Antiferromagnetic + weakly ferromagnetic CAF’ = Incommensurate?

  10. MAGNETIC PHASE DIAGRAM OF Ni3V2O8

  11. Theory Step I: Main interactions along spines: Superexchange, Ni—O—Ni and Ni—O—O--Ni O O O Ni Ni Ni Ni Explain HTI, LTI, CAF

  12. Incommensurability? -- simplest model: HTI LTI (q locked in) At low T, anisotropy wins again  CAF

  13. Step II: Anisotropy comes from spin orbit interactions Spin-orbit interaction generates Antiferromagnetic bond-dependent spin anisotropy Also Dzyaloshinskii-Moria antisymmetric exchange O Bilinear coupling between staggered Moment along a and ferromagnetic Moment along c Ni Ni Oxygen tilted along z D along y, AFM along x FM along z

  14. Step III: spin on cross-tie NI? Pseudodipolar interactions y x y x II II I2 I1 I1 I2

  15. More recent results: Multiferroic behavior Ferroelectric moment along b, only in LTI phase! Can switch ferroelectric moment with magnetic field!

  16. 5 0 5 0 5 0 PHASE DIAGRAM SPONTANEOUS POLARIZATION b a H || a P( mC/m2) T=4K Magnetic Field (T) P || b H || c H || c T=5K 0 0.5 1 1.5 2 2.5 3 3.5 0 2 4 6 8 10 Temperature (K) Magnetic Field (T)

  17. THIS DOES NOT WORK!! WE DO NOT BELIEVE IN ACCIDENTAL DEGENERACY (TP = TM). ALSO BOTH M AND P DEPEND STRONGLY ON H, SO THEN, WHEN WE MINIMIZE WITH RESPECT TOP, PAPPEARS ONLY WHENMIS NONZERO: LANDAU THEORY WITH TWO ORDER PARAMETERS

  18. MAGNETOELECTRIC COUPLING where x,y are LTI or HTI and t = x,y,z s(q) = s(-q)* is an order parameter In the HTI phase we have a single order parameter which has a node at some lattice site. About this site there will be inversion symmetry. So I s(q) = s(-q) = s(q)* I = inversion operator = 0 ( IH = H)

  19. Thus the trilinear magnetoelectric interaction is of the form H = sHTIsLTI P + d P2 So, after we minimize with respect to P: P = const sHTIsLTI = const sLTI MANETOELECTRIC INTERACTION This qualitatively explains the dependence of P on T and H

  20. Can arise from DM and PD interactions Confirm mean field trilinear term from microscopic Hamiltonian

  21. Spine-spins (a-axis) Cross-tie b-axis Mode Number: 64 B2u-phonons Mode Energy: 69.24 meV (experimental value is about 80 meV!) Connected to V Dipole Moment: 0.4612 (One of the largest dipole moment!) Mode Description: Two oxygen atoms connected to cross-tie Ni moves along b-axis, significantly effecting the Ni-O-Ni bond angle for the spine spins (see the animations; side and top views).

  22. Phys. Rev. B, in press

  23. (Spins along spine parallel to each other)

  24. FM, d=0 AFM, d=1/2

  25. Theory x(J3)

  26. Quartic terms Higher harmonics Lock-in Lock-in

  27. Dielecric constant Ferroelectricity???

  28. Conclusions: Vanadates are almost frustrated; interesting phase diagrams Can explain incommensurate phases by competing interactions Multiferroics!

  29. THE END

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