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Density functional study of magnetic solids Spin exchange interactions and magnetic properties

Density functional study of magnetic solids Spin exchange interactions and magnetic properties M.-H. Whangbo Deparetment of Chemistry North Carolina State University. NCSU: Yuemei Zhang Chuan Tian Jinhee Kang Dr. Changhoon Lee Dr. Erjun Kan Dr. Fang Wu

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Density functional study of magnetic solids Spin exchange interactions and magnetic properties

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  1. Density functional study of magnetic solids Spin exchange interactions and magnetic properties M.-H. Whangbo Deparetment of Chemistry North Carolina State University

  2. NCSU: Yuemei Zhang Chuan Tian Jinhee Kang Dr. Changhoon Lee Dr. Erjun Kan Dr. Fang Wu FU: Prof. Hongjun Xiang UTK: Prof. Janice Musfeldt EWU: Prof. Jamie Manson ANL: Dr. John Schlueter KHU: Prof. Hyun-Joo Koo MPI-Stuttgart: Dr. Reinhard Kremer Prof. Jürgen Köhler DOE: $, NERSC NCSU: HPC

  3. Na3Cu2SbO6 F-AF vs. AF-AF chain? Ca3CoMnO6 Ising magnetism vs. JT distortion Sr3Fe2O5 Magnetic dipole-dipole & 3D order Cs2CuCl4 Cause for 2D spin lattice Bi4Cu3V2O14 Diamond chain? Cu3(CO3)2(OH)2 Diamond chain? YbAl3C3 Phase transition & spin gap [Cu(HF2)(pyz)2]BF4 Magnetoelastic interaction CuF2(H2O)2(pyz) Jahn-Teller axis switching under P

  4. Magnetic solids: Low-energy excitations Pair-wise spin exchange Spin exchange parameter Jij • Experiment: Fitting parameters, Unique? • Theory • Formal: Excitation spectrum in terms of J’s • Computational: Numerical values of J’s • Ordered spin states • DE (spin Ĥ): J’s  DE (electronic Ĥ): DFT+U calc.

  5. Na3Cu2SbO6 & Na2Cu2TeO6 Inorg. Chem. 47, 128 (2008) J1: Cu-O-Cu, F or AF? J2: Cu-O…O-Cu, AF J1-J2 chain F-AF or AF-AF chain?

  6. kBK Na3Cu2SbO6 Na2Cu2TeO6 Neutron scattering: spin wave dispersion F-AF model !

  7. Ca3CoMnO6: Ising magnetism vs. JT distortion Phys. Rev. B79, 054432 (2009) CoO6 TP : Co2+ (HS, d7) at high T MnO6 OCT: Mn4+ (HS, d3)  Collinear  : No inversion symmetry  ferroelectric polarization Ising magnetism?

  8. High spin Co2+ (d7, L = 2, S = 3/2) at TP (2, -2)  (x2-y2, xy) (1, -1)  (xz, yz) 0  z2 1 -1 -1 1 2 -2 2 -2 z-axis // the 3-fold rotational axis 0 0 Unevenly filled degenerate level Ising magnetism  J = 7/2, Jz = 7/2, DJz = 7 > 1

  9. Jahn-Teller (JT) instability: Unevenly filled degenerate level  JT distortion JT distortion  Removal of Ising magnetism?

  10. DFT+U+SOC calculations meV/ FU The  state undergoes a JT distortion.

  11. Ca3CoMnO6  Loss of the C3 symmetry JT distortion  state Partial quenching of µLby JT distortion

  12. Why  ? JNNN , strongly AFM meV t2g t2g

  13. Neutron diffraction at low T Low spin Co2+ (d7, L = 1, S = 1/2) at TP ? -1 1 Low spin? Low spin? Large? 1 -1 -1 1 2 -2 2 -2 2 -2 0 0 0 Ising magnetism: J = 3/2, Jz = 3/2, DJz = 3 > 1 DFT+U calc: High-spin << Low-spin !

  14. Spin orientation & 3D order Spin orientation, Local Collinear, Non-collinear Canting Weak, Any consequence?

  15. MDD interactions Cause for spin orientation & 3D magnetic order MDD  S2 Spin ice systems: Dy2Ti2O7  Dy3+ (f9) Ho2Ti2O7  Ho3+ (f10) Transition-metal analog?

  16. Sr3Fe2O5: MDD & 3D order? Fe2+ (S = 2, d6) Inorg. Chem. 48, 9051 (2009)       3D AFM structure (2a, 2b, c) supercell    

  17. kBK J1, J2, J5 (2a, 2b, c) //ab AFM slab Inter-slab  (J2, J4, J4), (J5, J4, J4) frustrated Monte Carlo  No 3D order TN 280 K !

  18. c y • z2 xz, yz • = 90 • Spin: a • //c or //b? b x          

  19. meV/ 8 FUs       b   c   SOC: Local interaction Cannot remove the inter-slab spin frustration MDD : Long-range interaction Removes the inter-slab spin frustration 3D AFM ordering

  20. Cs2CuCl4: Cause for 2D spi lattice Isolated (CuCl4)2- ions Inorg. Chem. 48, 4185 (2009) 4 3 2 c 1 b a 2D triangular antiferromagnet //bc: J2/J1 1/3

  21. kBK

  22. Spin dimers (CuCl4)2 J1 J2 J4 J3 Symmetrical Asymmetrical

  23. without Cs 6p with Cs 6p Selective participation of the Cs+ 6p orbitals

  24. Bi4Cu3V2O14: Diamond chain? Inorg. Chem. 47, 4779 (2008)

  25. meV Not a diamond chain An AFM chain made up of AFM trimers

  26. Azurite, Cu3(CO3)2(OH)2 Frustrated or unfrustrated diamond chain? J. Phys.:Condens. Matter, 21, 392201 (2009)

  27. Double peaks!

  28. J2, J1, J3 > 0: Frustrated diamond J2, J1 >0, J3 < 0: Unfrustrated diamond Double peaks in c vs T Neutron scattering Phys. Rev. Lett. 100, 117202 kBK

  29. J4 Jm

  30. kBK J1 J3: frustration within a diamond chain J2 dimer & (-J2-J4-)∞ chain  J2 dimer &(-J4-)∞ chain? -()- -()- -()- -()- -( )- -( )- -( )- -( )-

  31. g-factor anisotropy Hb: 2.02, 2.12 H//b: 1.86, 2.14

  32. (CuCl)LaNb2O7 CuCl4O2 octahedron: Axial elongation  CuCl2O2 square plane linear Cl-Cu-Cl linear O-Cu-O c O-Cu-O

  33. 2D net of the Cu2+ ions Projection view: CuCl2O2 square planes along the c-axis Zigzag chains : Cl-corner-sharing CuCl2O2 Axially-elongated CuCl4O2 octahedron Spin-dimer behavior: 3rd nearest-neighbor spin exchange

  34. Cu-Cl…Cl-Cu exchange interaction Spin-dimer behavior c Strong Negligible

  35. YbAl3C3 : phase transition & spin gap Yb3+ (f13), Al3+, C4- YbC6 octahedra CAl5 trigonal bipyramids

  36. T* = 77 K: Antiferroquadrupolar order? J. Phys. Soc. Jpn. 74, 2413 (2005) Spin gap, dimer-like LuAl3C3: Lu3+ (f14), Cp anomaly at 110 K! Phase transition at T*: structural in origin? J. Phys. Soc. Jpn. 76, 123703 (2007)

  37. Below T*: Orthorhombic (Pbca) J. Phys. Soc. Jpn. 77, 103601 (2008) Model 1 Model 2 a a Cooperative second-order Jahn-Teller distortion?

  38. eV/FU kBK 2 J2-J1 AFM chains, AFM coupled via J3  AFM-coupling of FM chains 1 Effect of magnetic field J. Phys. Soc. Jpn. 78, 014709 (2009) T*= 110 K at 30 T: Field  reduction of spin frustration AFM-coupling of FM chains?  27Al NMR line broadening below T*: More different Al-environments below T* 3 4

  39. [Cu(HF2)(pyz)2]BF4: Magnetoelastic interaction IR spectra under magnetic field Phys. Rev. Lett. 103, 157301 (2009) Out-of-plane pyz ring bend J/kB = 6.1 K DE = EAF - EF = 4J Out-of-plane pyz C-H bend

  40. AFM FM FM J  4t2/U How to reduce t? pyz: Out-of-plane bending Relaxed FM 4J 4J AFM How constant are J’s?

  41. Pressure-induced switching of the Jahn-Teller axis CuF2(H2O)2pyz (pyz = pyrazine) CuF2O2N2 octahedron Linear N-Cu-N O-Cu-O F-Cu-F Cu-Lax > Cu-Leq Cu-N > Cu-O > Cu-F JT-axis switching under pressure? a b c

  42. Phase II 1D AFM chain Phase I 2D AFM square lattice

  43. N-Cu-N  O-Cu-O  F-Cu-F Successive switching of the Jahn-Teller axis

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