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Macroscopic quantum effects generated by the acoustic wave in molecular magnet

Macroscopic quantum effects generated by the acoustic wave in molecular magnet. 김 광 희 ( 세종대학교 ). Acknowledgements E. M. Chudnovksy (City Univ. of New York, USA) D. A. Garanin (City Univ. of New York, USA). M acroscopic Q uantum P henomena. M acroscopic Q uantum P henomena. N. H.

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Macroscopic quantum effects generated by the acoustic wave in molecular magnet

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  1. Macroscopic quantum effects generated by the acoustic wave in molecular magnet 김 광 희(세종대학교) Acknowledgements E. M. Chudnovksy (City Univ. of New York, USA) D. A. Garanin (City Univ. of New York, USA)

  2. Macroscopic Quantum Phenomena

  3. Macroscopic Quantum Phenomena N H H H microscopic, seen macroscopic, not seen

  4. Classical Dynamics Quantum Mechanics

  5. Why is Quantum Catnot seen? • - Rash answer • - maybe quantum mechanics does not hold for macroscopic bodies such as cats • - Careful answer • -Quantum mechanics is OK, but • - maybe states are not degenerate - maybe tunneling rate is too small DECOHERENCE!! - maybe temperature is too high - maybe the environmentsknow the states of the system

  6. What is a good candidate to show macroscopic quantum phenomena? • Josephoson junction-based system: phase difference of the order parameter • A. O. Caldeira and A. J. Leggett, Ann. Phys. (NY) 149, 374 (1983) • J. Clarke et al, Science, 239, 992 (1988) • Magnetic system:Magnetization S.C S.C

  7. Outline Review of magnetization reversal in magnet Giant spin approximation Stoner-Wohlfarth model in classical magnet Landau-Zener model in quantum magnet Rabi spin oscillations generated by ultrasound in solids Macroscopic quantum effects generated by the acoustic wave in molecular magnet Macroscopic quantum beats of magnetization Spintronics in molecular magnet Summary

  8. Magnet Molecular magnet

  9. Cobalt cluster of 3 nm HRTEM [110] direction, Fcc-structure, faceting Blue:1289-atoms truncated octahedron Grey: added atoms, total of 1388 atoms Truncated octahedron with 1289 atoms for diameters of 3.1nm

  10. Hystersis Loop in a Magnet (anisotropy energy +external field) M Ms H +1 -1 h -Ms

  11. [Wernsdorfer et al. PRL (2001)]

  12. [Zurek, QP 0306072]

  13. Classical vs Quantum

  14. Quantum Steps in Mn12 (uniaxial symmetry) At resonance, or H=0

  15. Quantum Steps in Mn12 = 0.44 T D = 0.60 K cf) 0.61 K [Sessoli et al. ’93] = 0.44 T

  16. Governed by Quantum dynamics !! [Barra et al. EPL (1996)]

  17. Phase interference Young experiment Aharovnov-Bohm effect Figure (interference) Source (coherent laser) and ……

  18. Is Aharonov-Bohm effect is expected in molecular magnets ?

  19. hard axis

  20. [Wernsdorfer and Sessoli, Science (1999)]

  21. To study quantum spin-rotation effects in solid, we need to estimate the magnetic field due to rotation . the phonon displacement field the local rotation of the crystal lattice

  22. Rabi Spin Oscillation (Cont’d) For displacement field in a surface acoustic wave, one obtains In the presence of deformation of the crystal lattice, local anisotropy axes defined by the crystal field are rotated by the angle. Laboratory frame Lattice frame

  23. Rabi Spin Oscillation (Cont’d) The lattice-frame Hamiltonian The Rabi oscillation between the two lowest states of sound wave

  24. Rabi Spin Oscillation (Cont’d) states Project the Hamiltonian on the “Rotating wave approximation” at

  25. Rabi Spin Oscillation (Cont’d) The probability to find the spin in the state

  26. Rabi Spin Oscillation (Cont’d) The expectation value of the projection of the spin onto the Z axis

  27. Rabi Spin Oscillation (Cont’d) The Rabi oscillations of have a wave dependence on coordinate !!

  28. Longitudinal Field Sweep. How can you obtain the global Rabi oscillations averaged over the whole sample ?

  29. Field sweep(cont’d) where

  30. Field sweep(cont’d) The field is changing at a constant rate g anda pulse of sound is introduced shortly before reaching the resonance between [G-H Kim and Chudnovsky, PRB (2009)]

  31. Molecular spintronics using molecular nanomanet To study the electronic and magnetic properties of a SMM and eventually to develop electronic devices [G-H Kim and T-S Kim, PRL (2004)]

  32. Idea is simple! But, dynamics is not simple!!

  33. What do we expect in the electronic devices? :Hamiltonian of SMM [J.A. Appelbaum, PRL, 1966; P.W. Anderson, PRL 1966 ] Direct tunneling between two electrodes Tunneling of electrons scattered by the spin of SMM Electric current ?

  34. Example: Fe8(cont’d) easy axis hard axis

  35. Molecular spintronics

  36. Summary • Classical vs. quantum dynamics in molecular magnet • Rabi oscillation generated by the ultrasound in molecular magnet • Applying a longitudinal magnetic field, we can generate quantum beats of the magnetization in molecular magnet • Possibility of molecular nanomagnet for molecular spintronics

  37. [T. W. Hansch , Nobel lecuture 2005]

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