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Symmetry IssuesSymmetry Issues
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)
Nature Physics 4, 277-281 (2008)
QUANTUM TUNNELING BTW. STATES OF DIFFERENT SPIN LENGHQUANTUM TUNNELING BTW. STATES OF DIFFERENT SPIN LENGH
yyxxzzz SSSSJSSJHHH 21212121
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
SYMMETRY RULES and DMSYMMETRY RULES and DM
SYMMETRY RULES and DMSYMMETRY RULES and DM
ANTI-SYMMETRIC TERM NEEDED
a) Hyperfine interaction / state mixing
AJJ
A
2
2
~
b) Dzyaloshinskii–Moriya interaction
xyyxDM SSSSJH 2121sin
JJ z cosJJ
o037.0
yyxxzzz SSSSJSSJHHH 21212121
NOT ALLOWED ON A DIMER MODELDUE TO INVERSION SYMMETRY
c) Tilts of easy axes?
SYMMETRY RULES and DMSYMMETRY RULES and DM
7/27/2
7/27/2
Wernsdorfer, arXiv:0804.1246v1a - Experiment invalidb - Dimer model not validc - DM interaction not possible
Wernsdorfer, PRB (2008)a - Dimer model identically used in a Mn6 wheel (CI) b - DM interaction used to explain results
Wernsdorfer, PRL (2008) (accepted)a - Dimer model used in an “identical” Mn12 wheelb – DM interaction used to explain results
, v2perhaps invalid
, v3
clearly existingRejected by NP: See our response in arXiv:0806.1922
SYMMETRY RULES and DMSYMMETRY RULES and DM
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
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
7/2
7/2
middle point
center of inversionD = 0
SYMMETRY RULES and DMSYMMETRY RULES and DM
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:
21212112 2
1SSSSJSSJΗ xyzzz
S
AS ΗΗΗ 121212
Symmetric exchange:
Antisymmetric exchange (DM interaction):
2112 SSDΗ A
2
2
2
2
2
25/25/2
5/2
5/25/2
5/2 d1center of inversion
D
middle point
D
*
*
x
y
z
SYMMETRY RULES and DMSYMMETRY RULES and DM
2
2
3/2
3/2center of inversion
middle point
x
y
z
D
D
*
*
(d’<d ,J’>>J)
(d ,J)
SYMMETRY RULES and DMSYMMETRY RULES and DM
2
2
3/2
3/2center of inversion
middle point
x
y
z
D
D
*
*
(d’<d ,Js>>Jw)
(d ,Jw)413423124321 HHHHHHHHΗ
The Hamiltonian of 4 coupled quater-wheels:
HgSSSEDSH iBiyixizi
ˆ222
Each quarter-wheel:
Exchange coupling:Aij
Sijij ΗΗΗ
Antisymmetric exchange (DM interaction):
jiijAij SSDΗ
)sin(3412 wJDD
04123 DD
jijixyijjzizzij
Sij SSSSJSSJΗ
2
1
Symmetric exchange:
wJJJ 3412 )(4123 ws JJJJ
Center of inversion symmetry imposes:
180*
180*
hard x-axis
x
y
D
~30o
QUESTION 1
NEW TOPOLOGICAL EFFECTNEW TOPOLOGICAL EFFECT
Quantum Tunneling Spin
Fe8: Wernsdorfer & Sessoli, Science (1999)Mn12: del Barco et al., PRL (2003)
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 (1954)(quantal systems)
Aharanov and Anandan (1987)(generalization Hilbert space)
.
.
.
INTERACTING SPINSClassical coupled-spins precession
Sjoqvist, PRA (2000)
THEORY
(none yet?)
Mn12 wheel: Ramsey et al., Nature Physics (2008)
EXPERIMENT
QUESTION 2