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Spin Tunneling and Inversion SymmetrySpin Tunneling and Inversion Symmetry
www.physics.ucf.edu/~delbarco
ENRIQUE DEL BARCO
Department of Physics – UCF Orlando
QCPS II 2009 - Vancouver
ENRIQUE DEL BARCO, CHRISTOPHER RAMSEY (UCF)
STEPHEN HILL (NHMFL and Physics Department, FSU – Tallahassee)
SONALI J. SHAH, CHRISTOPHER C. BEEDLE AND DAVID N. HENDRICKSON(Chemistry Department, UCSD – La Jolla-San Diego)
PHILIP C.E. STAMP AND IGOR TUPITSYN(PITP-Physics, UBC, Vancouver)
Nature Physics 4, 277-281 (2008)
Spin Tunneling and Inversion SymmetrySpin Tunneling and Inversion Symmetry
THE MOLECULETHE MOLECULE
[Mn12(Adea)8(CH3COO)14]·7CH3CN
Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).
2
2
22
2
2 5/2
5/2
5/2
5/2
5/2
5/2
SS=7=7
MAGNETIZATION - QTMMAGNETIZATION - QTM
-0.6 -0.3 0.0 0.3 0.6-1.0
-0.5
0.0
0.5
1.0 = 0.2 T/min
T = 0.90 KT = 0.80 KT = 0.70 KT = 0.65 KT = 0.60 KT = 0.50 KT = 0.41 KT = 0.27 K
M/M
s
H (T)
Tc ~0.3K
TB ~0.9K
S = 7D = 0.4K
T = 0.9K
S = 7, D = 0.4 K
50m
wheel axis
HL
mS = +7
+6
+5
+4
-7
-6
+3
+2
+1
BR gDkH /
MAGNETIZATION - QTMMAGNETIZATION - QTM
exc.
k =
0
0.00 0.29 0.580
5
10
15
exc.
k =
2k =
1(S
)
dM/d
H (
a.u.
)
H (T)
k =
1(A
)
S = 7, D = 0.4 K
0.00 0.29 0.58-25
-20
-15
-10
En
erg
y (K
)
H (T)
Ms =7
Ms =6
Ms =5
zzBz HSgDS 2 H
0.00 0.29 0.580
5
10
15
dM/d
H (
a.u.
)
H (T)0.00 0.29 0.58
0
5
10
15
dM/d
H (
a.u.
)
H (T)
?
HL
HT
[Mn12(Adea)8(CH3COO)14]·7CH3CN
Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).
2
2
22
2
2 5/2
5/2
5/2
5/2
5/2
5/2
SS=7=7
THE MOLECULETHE MOLECULE
THE MOLECULETHE MOLECULE
[Mn12(Adea)8(CH3COO)14]·7CH3CN
d*
d*
d
dd
dd
dd
dd
d
davg~3.17Å
d*~3.49Å
J ~2-5 cm-1
J* <<J Fo
gu
et-
Alb
iol,
D.
et
al.,
An
ge
w.
Ch
em
. In
t. E
dn
44
, 8
97
–9
01
(2
00
5)
Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).
THE MOLECULETHE MOLECULE
d*
d*
Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).
7/27/2
7/27/2
[Mn12(Adea)8(CH3COO)14]·7CH3CN
EXCHANGE-COUPLED SPINSEXCHANGE-COUPLED SPINS
QUANTUM TUNNELING BTW. STATES OF DIFFERENT SPIN LENGHQUANTUM TUNNELING BTW. STATES OF DIFFERENT SPIN LENGH
2121 SJSHHH
HS i gSSESDH Byixizii ˆ2,
2,2/7
2,2/7 2/7iS )2(~865.02/7 DKD )2(~156.02/7 EKE KJJ z 39.0
yyxxzzz SSSSJSSJ 212121
QUANTUM INTERFERENCEQUANTUM INTERFERENCEHARD
2,
2,2/7 yixi SSE
BERRY PHASE INTERFERENCE OF TWO COUPLED TUNNELING SPINSBERRY PHASE INTERFERENCE OF TWO COUPLED TUNNELING SPINS
HL
HT
NEW TOPOLOGICAL EFFECTNEW TOPOLOGICAL EFFECT
Quantum Tunneling Spin
Fe8: Wernsdorfer & Sessoli, Science (1999)Mn12: del Barco et al., PRL (2003)
Mn12 -tBuAc: da Silva Neto et al., (2008)
EXPERIMENT
THEORYLoss et al., PRL (1992)
Von Delft et al., PRL (1992)Garg, EPL (1993)
Coupled Tunneling Spins
SINGLE SPINClassical spin precession
i.e. Wagh et al., PRL (1998)
Pancharatnam (1956)(light interference)
Berry (1984)(quantal systems)
Aharanov and Anandan (1987)(generalization Hilbert space)
.
.
.
INTERACTING SPINSClassical coupled-spins precession
Sjoqvist, PRA (2000)
THEORY
(??)
Mn12 wheel: Ramsey et al., Nature Physics (2008)
EXPERIMENT
SYMMETRY RULESSYMMETRY RULES
ANTI-SYMMETRIC TERM NEEDED
Dzyaloshinskii–Moriya interaction
21 SSDHDM
2121 SJSHHH
NOT ALLOWED ON A DIMER MODEL with
INVERSION SYMMETRY
SYMMETRY RULESSYMMETRY RULES
7/27/2
7/27/2
Wernsdorfer, PRB (2008)a - Dimer model identically used in a Mn6 wheel (CI) b - DM interaction used to explain results
Wernsdorfer, PRL (2008)a - Dimer model used in an “identical” Mn12 wheelb – DM interaction used to explain results
Rejected by NP: See our response in arXiv:0806.1922
Wernsdorfer, arXiv:0804.1246v1,v2,v3a - Dimer model not valid
SYMMETRY RULESSYMMETRY RULES
7/27/2
7/27/2
Wernsdorfer, PRB (2008)a - Dimer model identically used in a Mn6 wheel (CI) b - DM interaction used to explain results
Wernsdorfer, PRL (2008)a - Dimer model used in an “identical” Mn12 wheelb – DM interaction used to explain results
Rejected by NP: See our response in arXiv:0806.1922
Wernsdorfer, arXiv:0804.1246v1,v2,v3a - Dimer model not valid
Wernsdorfer-justification:1)Disorder2)Local DM interactions are not forbidden
del Barco et al., PRL (2009)1)Disorder2)Local DM interactions are not forbidden
SYMMETRY RULESSYMMETRY RULES
2
2
2
2
2
25/25/2
5/2
5/25/2
5/2 d1center of inversion
middle point
7/2
7/2
middle point
center of inversionD = 0
SYMMETRY RULESSYMMETRY RULES
7/2
7/2
middle point
center of inversion
D 0 parallel to z-axis (Ramsey, Nature Physics)D 0 tilted (Wernsdorfer, PRL)
1221 HHHΗ
HgSSSEDSH iBiyixizi
ˆ222
The Hamiltonian of the coupled half-wheels:
Each half-wheel:
Exchange coupling:
2112 SJSΗ S
AS ΗΗΗ 121212
Symmetric exchange:
Antisymmetric exchange (DM interaction):
2112 SSDΗ A
SYMMETRY RULESSYMMETRY RULES
2
2
2
2
2
25/25/2
5/2
5/25/2
5/2 d1center of inversion
middle point
D
*
*
D
x
y
z
SYMMETRY RULESSYMMETRY RULES
2
2
2
2
2
25/25/2
5/2
5/25/2
5/2 d1center of inversion
middle point
D
x
y
z
D
x
y
z
SYMMETRY RULESSYMMETRY RULES
H
H
Center of Inversion
SYMMETRY RULESSYMMETRY RULES
2
2
2
2
2
25/25/2
5/2
5/25/2
5/2 d1center of inversion
middle point
D
x
y
z
D
x
y
z
2
2
3/2
3/2center of inversion
middle point
(d’<d ,J’>>J)
(d ,J)D
x
y
z
D
x
y
zD’’
’
x
y
z
D’’
’
x
y
z
SYMMETRY RULESSYMMETRY RULES
)(, jijiij
ii HHΗ
The Hamiltonian of 4 coupled quarter-wheels:
HgSSSEDSH iBiyixizi
ˆ222
Each quarter-wheel:
Exchange coupling:Aij
Sijij ΗΗΗ
Antisymmetric exchange (DM interaction):
jiijAij SSDΗ
jiijSij SSJΗ
Symmetric exchange:
wJJJ 3412 )(4123 ws JJJJ Center of inversion symmetry imposes:
*
*
k = 1(A) is degenerate
2
2
3/2
3/2center of inversion
middle point
(d’<d ,J’>>J)
(d ,J)D
x
y
z
D
x
y
zD’’
’
x
y
z
D’’
’
x
y
z
0.0 0.1 0.2 0.3 0.4
10-8
10-7
10-6
10-5
12
= 0o
34
= 1o
34
= 5o
34
= 10o
34
= 30o
34
= 90o
34
= 120o
34
= 150o
34
= 170o
34
= 180o
k=1(
A) (
K)
HT (T)
SYMMETRY RULESSYMMETRY RULES
10-7
10-6
10-5
10-4
med
ium
yk = 0
k = 1(A)
(K
)
x~30o
hard
k = 1(S)
-0.4 0.0 0.4 0.8
10-7
10-6
(K
)
HT (T)
12 = 0o
12 = 30o
12 = 60o
12 = 90o
SYMMETRY RULESSYMMETRY RULES
In a centro-symmetric molecule
local DM-interactions MUST BE related by inversion symmetry and
DO NOT BREAK THE DEGENERACY BETWEEN LEVELS OF OPPOSITIVE PARITY
independently of how complex the Hamiltonian is
because PARITY (good quantum number) MUST BE CONSERVED
SYMMETRY RULESSYMMETRY RULES
DM-interactions are important in S = 1/2 systems
ONLY SOURCE OF DEGENERACY BREAKING
but never mix states of opposite parity in a system with inversion symmetry
(Kagome lattice – weak ferromagnetism)
when inversion symmetry is not present
BOTH SYMMETRIC and ANTISYMMETRIC INTERACTIONSCAN BREAK DEGENERACIES
E. del Barco, S. Hill and D. N. Hendrickson, Phys. Rev. Lett. in press (2009)E. del Barco et al., In preparation
2
2
2
2
2
25/25/2
5/2
5/25/2
5/2 d1center of inversion
middle point
D
x
y
z
D
x
y
z
Dipolar fields? (Philip?)Dipolar fields? (Philip?)
CONCLUSIONSCONCLUSIONSQuantum superposition of states with different spin length in a SMMQuantum superposition of states with different spin length in a SMM
New topological effect: Quantum phase interference of two coupled tunneling spinsNew topological effect: Quantum phase interference of two coupled tunneling spins
Local DM interactions in a centro-symmetric SMM do not break the degeneracy Local DM interactions in a centro-symmetric SMM do not break the degeneracy between states of opposite paritybetween states of opposite parity
Del Barco LabDel Barco Lab
Low temperature nanomagnetismLow temperature nanomagnetismSingle-molecule magnetsFM thin films and nanowiresNanoparticles
Low temperature nanotransportLow temperature nanotransportMolecular spintronicsMolecular spintronicsSingle-electron transistorsSingle-electron transistorsLow-dimensional systems Low-dimensional systems i.e. graphene, nanowires, i.e. graphene, nanowires, nanoparticles, molecules,…nanoparticles, molecules,…
Physics collaborationsPhysics collaborationsStephen Hill (NHMFL-FSU)
Masa Ishigami, Robert Peale, Lee Chow (UCF)Agustin Camon, Fernando Luis (UZ-Spain)
Javier Tejada (UB-Spain)Oliver Waldmann (U.Freiburg-Germany)
Andrew Kent (NYU)XiXiang Zhang (KAUST)
Eduardo Mucciolo, Michael Leuenberger (UCF)Philip Stamp, Igor Tupitsyn (UBC-Canada)
Chemistry collaborationsChemistry collaborationsDavid Hendrickson (UCSD)
George Christou (UF)Eugenio Coronado (UV-Spain)
Florenzio Hernandez (UCF)Joel Miller (UU)
[Mn12(Adea)8(CH3COO)14].7CH3CN
0.00 0.29 0.580
5
10
15
dM
/dH
(a
.u.)
H (T)
S = 7/2 + 7/2
[Mn12(Edea)8(CH3CH2COO)14]
S = 7
[Mn12(Edea)8(CH3COO)2(CH3CH2COO)12]
S = 7
d*
d*
d
dd*
d*d*
d*
d
dd
d
d*/davg = 1.100d*/davg = 1.093 d*/davg = 1.091< >
SISTER MOLECULESSISTER MOLECULES
J*/Javg J*/Javg J*/Javg>> <<
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