Post on 28-Dec-2015
transcript
Internal Degrees of Freedomand 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: 1
SMMs and Giant Spin ApproximationGSA 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 PatternsInternal Degrees of Freedom
OUTLINE
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SMMs and the GSA MODEL
8MnIII(S=2) = 16
-4MnIV(S=3/2) = 6~ S = 10
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SMMs and the GSA MODEL
~ S = 10
up
downx
y
z
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SMMs and the GSA MODEL
~ S = 10
up
downx
y
zM
ag
neti
c fi
eld
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SMMs and the GSA MODEL
~ S = 10
up
downx
y
zon
-res
ona
nce
QT on (fast relaxation)
QT off (non relaxation)
off-
reso
nanc
eon
-res
ona
nce
2,5 3,0 3,5 4,0 4,5 5,0-1,0
-0,5
0,0
0,5
1,0
M/M
s
Hlong
(T)
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SMMs and the GSA MODEL
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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)
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MULTI-SPIN DESCRIPTION LOW NUCLEARITY SMMs
Connection between Dmol and dion
Higher-order molecular anisotropyConsequences 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).
Ni4 (S = 4)Mn6 (S = 4,12)Mn3 (S = 2,6)
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MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM
[Mn4(Bet)4(mdea)4(Hmdea) 2] (BPh4)4
K. J. Heroux et al., unpublished.
S = 9 (at low-T)
MnII (S = 5/2)
MnIII (S = 2)
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MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM
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MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM
( )
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test: k=1?
MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM
( )13
MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM
TIME REVERSAL INVARIANCE OF THE SPIN-ORBIT INTERACTION
HSgLSH B
SL
LS
H HS
=ODD
=ODD
=ODD
=EVEN
=EVEN
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MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM
Second order anisotropy (symmetries):
a) 3 mutually orthogonal two-fold rotation axesb) 3 mutually orthogonal mirror planesc) 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 REVERSALTRI GUARANTEES THE TWO PATTERNS TO BE MIRROR IMAGES
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MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM
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i
i
i
i
d
e
e
d
00
00
00�
gggg zzyyxx
JJJJ zzyyxx
MULTI-SPIN DESCRIPTION
iii ,,Euler angles:
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MULTI-SPIN DESCRIPTION
(z - easy axis)
(x - hard axis)
CENTRAL ION (2)
EXTERNAL IONS (1,3)
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SOME RELAXATION ISSUES
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SOME RELAXATION ISSUES
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SOME RELAXATION ISSUES
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SOME RELAXATION ISSUES
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ACKNOWLEDGEMENTS
STUDENTS:
Hajrah M. Quddusi and Simran Singh (UCF)Junjie Liu (FSU)
Katie Heroux and Chris Beedle (UCSD)