Internal Degrees of Freedom and Quantum Tunneling of the Magnetization in Single-Molecule Magnets E NRIQUE DEL B ARCO Department of Physics – UCF Orlando.

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Presentation transcript:

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

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

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

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

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

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

SMMs and the GSA MODEL 7

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

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

MULTI-SPIN DESCRIPTION THE CASE OF Mn 4 SMM [Mn 4 (Bet) 4 (mdea) 4 (Hmdea) 2 ] (BPh 4 ) 4 K. J. Heroux et al., unpublished.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

MULTI-SPIN DESCRIPTION THE CASE OF Mn 4 SMM 11

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

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

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

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

MULTI-SPIN DESCRIPTION THE CASE OF Mn 4 SMM 16

MULTI-SPIN DESCRIPTION Euler angles: 17

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

SOME RELAXATION ISSUES 19

SOME RELAXATION ISSUES 20

SOME RELAXATION ISSUES 21

SOME RELAXATION ISSUES 22

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