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Symmetry Issues

E NRIQUE DEL B ARCO , C HRISTOPHER R AMSEY (UCF). Nature Physics 4 , 277-281 (2008) . S TEPHEN H ILL ( NHMFL and Physics Department, FSU – Tallahassee ) S ONALI J. S HAH , C HRISTOPHER C. B EEDLE AND D AVID N. H ENDRICKSON ( Chemistry Department, UCSD – La Jolla-San Diego ).

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Symmetry Issues

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  1. ENRIQUEDEL BARCO, CHRISTOPHER RAMSEY (UCF) Nature Physics4, 277-281 (2008) STEPHEN HILL (NHMFL andPhysics Department, FSU – Tallahassee) SONALI J. SHAH, CHRISTOPHER C. BEEDLEAND DAVID N. HENDRICKSON (Chemistry Department, UCSD – La Jolla-San Diego) Symmetry Issues

  2. QUANTUM TUNNELING BTW. STATES OF DIFFERENT SPIN LENGH SYMMETRY RULES and DM

  3. b) Dzyaloshinskii–Moriya interaction SYMMETRY RULES and DM ANTI-SYMMETRIC TERM NEEDED a) Hyperfine interaction / state mixing NOT ALLOWED ON A DIMER MODEL DUE TO INVERSION SYMMETRY c) Tilts of easy axes?

  4. , v3 Wernsdorfer, arXiv:0804.1246v1 , v2 a - Experiment invalid b - Dimer model not valid c - DM interaction not possible perhaps invalid clearly existing 7/2 7/2 Wernsdorfer, PRB (2008) Wernsdorfer, PRL (2008) (accepted) a - Dimer model identically usedin a Mn6 wheel (CI) b - DM interaction used to explain results a - Dimer model used in an “identical” Mn12 wheel b – DM interaction used to explain results SYMMETRY RULES and DM Rejected by NP: See our response in arXiv:0806.1922

  5. z y   7/2 2 2 5/2 5/2 5/2 5/2   x 2 2 center of inversion d1 d1 5/2 5/2 2 2 z center of inversion center of inversion   * * y middle point middle point 5/2 5/2 2 2 middle point 7/2 2 2   * * x 5/2 5/2 2 2 5/2 5/2 D = 0 D D D D SYMMETRY RULES and DM

  6. The Hamiltonian of the coupled half-wheels: 7/2 Each half-wheel: center of inversion middle point Exchange coupling: 7/2 Symmetric exchange: D  0 parallel to z-axis (Ramsey, Nature Physics) D  0 tilted (Wernsdorfer, PRL) Antisymmetric exchange (DM interaction): SYMMETRY RULES and DM

  7.  z 2 5/2 y 5/2   2 d1 5/2 2 x center of inversion z   * * (d,J) 2 5/2 y 2 middle point 2   * * 3/2 5/2 2 5/2 D D D D x center of inversion 3/2 middle point (d’<d,J’>>J) 2 SYMMETRY RULES and DM

  8. y The Hamiltonian of 4 coupled quater-wheels:  Each quarter-wheel: hard x-axis D  Exchange coupling: ~30o z  * (d,Jw) 2 Symmetric exchange: y x  * 3/2 D D x center of inversion Center of inversion symmetry imposes: Antisymmetric exchange (DM interaction): 3/2 middle point (d’<d,Js>>Jw) 2 SYMMETRY RULES and DM QUESTION 1

  9. SINGLE SPIN INTERACTING SPINS Classical spin precession Classical coupled-spins precession Sjoqvist, PRA (2000) i.e. Wagh et al., PRL (1998) Pancharatnam (1956) (light interference) Berry (1954) (quantal systems) Aharanov and Anandan (1987) (generalization Hilbert space) . . . Quantum Tunneling Spin Coupled Tunneling Spins THEORY THEORY Loss et al., PRL (1992) Von Delft et al., PRL (1992) Garg, EPL (1993) (none yet?) EXPERIMENT EXPERIMENT Fe8: Wernsdorfer & Sessoli, Science (1999) Mn12: del Barco et al., PRL (2003) Mn12 wheel: Ramsey et al., Nature Physics (2008) NEW TOPOLOGICAL EFFECT QUESTION 2

  10. 2 2 2 (S=6) SYMMETRY RULES and QTM [NEt4]3[Mn3Zn2(salox)3O(N3)6Cl2]

  11. SYMMETRY RULES and QTM

  12. SYMMETRY RULES and QTM

  13. SYMMETRY RULES and QTM

  14. SYMMETRY RULES and QTM H H HA

  15. SYMMETRY RULES and QTM H H HA

  16. SYMMETRY RULES and QTM H H

  17. SYMMETRY RULES and QTM H

  18. SYMMETRY RULES and QTM QUESTION 3

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