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Single-ion and exchange anisotropy effects in small single-molecule magnets*

Single-ion and exchange anisotropy effects in small single-molecule magnets*. Richard A. Klemm University of Central Florida, Orlando, FL USA and Dmitri V. Efremov Technische Universität Dresden, Dresden, Germany Quantum Coherent Properties of Spins-III, Dec. 20, 2010

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Single-ion and exchange anisotropy effects in small single-molecule magnets*

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  1. Single-ion and exchange anisotropy effects in smallsingle-molecule magnets* Richard A. Klemm University of Central Florida, Orlando, FL USA and Dmitri V. Efremov TechnischeUniversität Dresden, Dresden, Germany Quantum Coherent Properties of Spins-III, Dec. 20, 2010 *Phys. Rev. B 74, 064408 (2006); Phys. Rev. B 77, 184410 (2008).

  2. The giant spin approximation

  3. Eigenstates of giant spin model

  4. Does it work? For large-spin systems such as Mn12-ac It seems to work very well What about small-spin systems? Dimers & Tetramers

  5. Dimers (D2h, C2v, S2, C2)

  6. D2h, C2v, S2 symmetry

  7. Dipole-dipole exchange is physically different from single-ion interactions

  8. A. Sieber et al., Inorg. Chem. 44, 4315 (2005).D. N. Hendrickson et al., Polyhedron 24, 2280 (2005).

  9. Boskovicet al., JACS 125, 14046 (2003).

  10. Td and D4h

  11. C4h and C4v

  12. Lower-symmetry orthorhombic structures

  13. Single-spin quadratic Hamiltonian

  14. Group-symmetric Hamiltonian

  15. Quantization: is diagonal

  16. Two tetramer types Type I: Type II:

  17. Electric polarizations H. Katsura, N. Nagaosa, and A. V. Balatsky, PRL95, 057205 (2005). Multiferric behavior for S4, D2d

  18. AFM Heisenberg and DM only:Multiferroic behavior s1=1/2

  19. Multiferroic behavior

  20. AFM s1=1

  21. Phenomenological Hamiltonian

  22. Single-spin matrix elements Schwinger boson method using 6 non-interacting bosons

  23. Strong Exchange Limit

  24. AFM spin ½ level-crossing inductions

  25. Spin 1

  26. Strong exchange limit corrections

  27. Electron paramagnetic resonance For s1 > 1/2, EPR measurements of the 2nd excited state manifold (e.g., s = 4s1-2 for FM tetramers) can provide an independent determination of the three anisotropy Interactions,

  28. Summary and conclusions Exact single-spin matrix elements allow for analytic expressions for the strong exchange limit energies For FM tetramers, the three first-order anisotropy interactions can be determined from the 2nd excited state manifold by EPR For AFM tetramers, the level-crossing inductions provide a measure of the various Heisenberg, quartic, and anisotropy interactions

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