1. Internal Degrees of Freedom and Quantum Tunneling of the Magnetization in Single-Molecule Magnets E NRIQUE DEL B ARCO Department of Physics – UCF Orlando In collaboration with: Steve Hill (FSU & NHMFL) and David N. Hendrickson (UCSD) SPONSORED BY: 1

2. SMMs and Giant Spin Approximation GSA failure / multi-spin description / low-nuclearity SMMs A low nuclearity SMM: Mn 4 EPR and QTM Characterization Asymmetric Berry Phase Interference Symmetry Considerations Motion of Berry Phase Patterns Internal Degrees of Freedom OUTLINE 2

3. SMMs and the GSA MODEL 8  Mn III (S=2) = 16 -4  Mn IV (S=3/2) = 6 ~ S = 10 3

4. SMMs and the GSA MODEL ~ S = 10 up down x y z 4

5. SMMs and the GSA MODEL ~ S = 10 up down x y z Magnetic field 5

6. SMMs and the GSA MODEL ~ S = 10 up down x y z on-resonance QT on (fast relaxation) QT off (non relaxation) off-resonance on-resonance 6

7. SMMs and the GSA MODEL 7

8. FAILURE of the GSA MODEL Anomalous term Barra et al. (1997) Low-lying excited states Mukhin et al. (2001) QTM btw. different spin lengths Ramsey et al. (2008) observed before in AF molecules Carreta et al. (2007) 8

9. MULTI-SPIN DESCRIPTION LOW NUCLEARITY SMMs Connection between D mol and d ion Higher-order molecular anisotropy Consequences of weak coupling and spin frustration Internal degrees of freedom and QTM: (Symmetry lowering effects) (Spin selection rules) S. Hill et al., Dalton Transactions (2010). Ni 4 (S = 4)Mn 6 (S = 4,12)Mn 3 (S = 2,6) 9

10. MULTI-SPIN DESCRIPTION THE CASE OF Mn 4 SMM [Mn 4 (Bet) 4 (mdea) 4 (Hmdea) 2 ] (BPh 4 ) 4 K. J. Heroux et al., unpublished. S = 9 (at low-T) Mn II (S = 5/2) Mn III (S = 2) 10

11. MULTI-SPIN DESCRIPTION THE CASE OF Mn 4 SMM 11

12. MULTI-SPIN DESCRIPTION THE CASE OF Mn 4 SMM ( ) 12 test: k=1?

13. MULTI-SPIN DESCRIPTION THE CASE OF Mn 4 SMM ( ) 13

14. MULTI-SPIN DESCRIPTION THE CASE OF Mn 4 SMM TIME REVERSAL INVARIANCE OF THE SPIN-ORBIT INTERACTION =ODD =EVEN 14

15. MULTI-SPIN DESCRIPTION THE CASE OF Mn 4 SMM Second order anisotropy (symmetries): a)3 mutually orthogonal two-fold rotation axes b)3 mutually orthogonal mirror planes c)Inversion center (b) Guarantees invariance w.r.t. reversal of H T IMPOSES SYMMETRIC BPI PATTERNS WHETHER H L =0 or H L  0 xy-mirror symmetry must be broken TO ALLOW ASYMMETRIC BPI PATTERNS W.R.T. H T REVERSAL TRI GUARANTEES THE TWO PATTERNS TO BE MIRROR IMAGES 15

16. MULTI-SPIN DESCRIPTION THE CASE OF Mn 4 SMM 16

17. MULTI-SPIN DESCRIPTION Euler angles: 17

18. MULTI-SPIN DESCRIPTION (z - easy axis) (x - hard axis) CENTRAL ION (2) EXTERNAL IONS (1,3) 18

19. SOME RELAXATION ISSUES 19

20. SOME RELAXATION ISSUES 20

21. SOME RELAXATION ISSUES 21

22. SOME RELAXATION ISSUES 22

23. 23 ACKNOWLEDGEMENTS STUDENTS: Hajrah M. Quddusi and Simran Singh (UCF) Junjie Liu (FSU) Katie Heroux and Chris Beedle (UCSD)