1. Symmetry Issues E NRIQUE DEL B ARCO, C HRISTOPHER R AMSEY (UCF) 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) Nature Physics 4, 277-281 (2008)

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

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

4. SYMMETRY RULES and DM 7/2 7/2 Wernsdorfer, arXiv:0804.1246v1 a - Experiment invalid b - Dimer model not valid c - DM interaction not possible Wernsdorfer, PRB (2008) a - Dimer model identically used in a Mn 6 wheel (CI) b - DM interaction used to explain results Wernsdorfer, PRL (2008) (accepted) a - Dimer model used in an “identical” Mn 12 wheel b – DM interaction used to explain results, v2 perhaps invalid, v3 clearly existing Rejected by NP: See our response in arXiv:0806.1922

5. SYMMETRY RULES and DM 2 2 2 2 2 2 5/2 d1d1 center of inversion middle point D *  * D  x y z 2 2 2 2 2 2 5/2 d1d1 center of inversion middle point D  D *  * x y z 7/2 middle point center of inversion D = 0

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

7. 2 2 2 2 2 2 5/2 d1d1 center of inversion D  middle point D *  * x y z SYMMETRY RULES and DM 2 2 3/2 center of inversion middle point x y z D  D *  * (d’ >J) (d,J)(d,J)

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

9. NEW TOPOLOGICAL EFFECT Quantum Tunneling Spin Fe 8 : Wernsdorfer & Sessoli, Science (1999) Mn 12 : del Barco et al., PRL (2003) EXPERIMENTTHEORY Loss et al., PRL (1992) Von Delft et al., PRL (1992) Garg, EPL (1993) Coupled Tunneling Spins SINGLE SPIN Classical spin precession i.e. Wagh et al., PRL (1998) Pancharatnam (1956) (light interference) Berry (1954) (quantal systems) Aharanov and Anandan (1987) (generalization Hilbert space). INTERACTING SPINS Classical coupled-spins precession Sjoqvist, PRA (2000) THEORY (none yet?) Mn 12 wheel: Ramsey et al., Nature Physics (2008) EXPERIMENT QUESTION 2

10. SYMMETRY RULES and QTM [NEt 4 ] 3 [Mn 3 Zn 2 (salox) 3 O(N 3 ) 6 Cl 2 ] 2 2 2 (S=6)

11. SYMMETRY RULES and QTM

14. H HHAHA

15. H HHAHA

16. H H

17. H

18. QUESTION 3