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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:. OUTLINE.
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Internal Degrees of Freedom and Quantum Tunneling of the Magnetization in Single-Molecule Magnets ENRIQUE DEL BARCO Department of Physics – UCF Orlando In collaboration with: Steve Hill (FSU&NHMFL) and David N. Hendrickson (UCSD) SPONSORED BY:
OUTLINE SMMs and Giant Spin Approximation GSA failure / multi-spin description / low-nuclearity SMMs A low nuclearity SMM: Mn4 EPR and QTM Characterization Asymmetric Berry Phase Interference Symmetry Considerations Motion of Berry Phase Patterns Internal Degrees of Freedom
SMMs and the GSA MODEL 8MnIII(S=2) = 16 ~ S = 10 -4MnIV(S=3/2) = 6
SMMs and the GSA MODEL ~ S = 10 z up y x down
SMMs and the GSA MODEL Magnetic field ~ S = 10 z up y x down
SMMs and the GSA MODEL ~ S = 10 z up y x down on-resonance off-resonance QT on (fast relaxation) on-resonance QT off (non relaxation)
FAILURE of the GSA MODEL Anomalous term Low-lying excited states QTM btw. different spin lengths Ramsey et al. (2008) observed before in AF molecules Carreta et al. (2007) Mukhin et al. (2001) Barra et al. (1997)
MULTI-SPIN DESCRIPTION LOW NUCLEARITY SMMs Mn3 (S = 2,6) Mn6 (S = 4,12) Ni4 (S = 4) Connection between Dmol and dion 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).
MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM MnIII (S = 2) MnII (S = 5/2) S = 9 (at low-T) [Mn4(Bet)4(mdea)4(Hmdea)2] (BPh4)4 K. J. Heroux et al., unpublished.
MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM
MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM test: k=1? ( )
MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM ( )
MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM TIME REVERSAL INVARIANCE OF THE SPIN-ORBIT INTERACTION =ODD =EVEN =ODD =EVEN =ODD
MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM Second order anisotropy (symmetries): 3 mutually orthogonal two-fold rotation axes 3 mutually orthogonal mirror planes Inversion center (b) Guarantees invariance w.r.t. reversal of HT IMPOSES SYMMETRIC BPI PATTERNS WHETHER HL=0 or HL0 xy-mirror symmetry must be broken TO ALLOW ASYMMETRIC BPI PATTERNS W.R.T. HT REVERSAL TRI GUARANTEES THE TWO PATTERNS TO BE MIRROR IMAGES
MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM
MULTI-SPIN DESCRIPTION Euler angles:
MULTI-SPIN DESCRIPTION CENTRAL ION (2) (z - easy axis) (x - hard axis) EXTERNAL IONS (1,3)
ACKNOWLEDGEMENTS STUDENTS: Hajrah M. Quddusi and Simran Singh (UCF) Junjie Liu (FSU) Katie Heroux and Chris Beedle (UCSD)