Alternating Antisymmetric Interaction in Nanoscale Iron Ring

1
Alternating Antisymmetric Interaction in
Nanoscale Iron Ring
Workshop on the Quantum Dynamics of Molecular
Magnets
4th December 2002

• Hiroki Nakano ????
• Himeji-Institute of Technology

Seiji Miyashita ???? University of Tokyo
2
Nanoscale Iron Clusters Fen
n6 n10

• d electrons in Fe3

S5/2
L0
n18 n12
3
Experimental Magnetization Process
Fe6 (Chaneschi, et al Chem.Eur.J.2(1996)1379)
J28.7K
T1.5 K
Fe10 (Taft, et al.Am.Chem.Soc.116(1994)823)
J13.8K
T0.6 K
4
Pure Heisenberg chain including finite spins
Finite temperature
T0
Equivalent peaks with equivalent intervals
5
Experimental peaks in dM/dH

• Fe6 Fe10

Width or Height
What is the origin of the transition?
Quantum transition due to lattice structure
6
Thermal effects in experiments of Fe12
(Ajiro, Narumi et al.private communications)
T1.3K
Satellite peaks appear.
T0.09K
Satellite peaks disappear.
What is the origin of the asymmetry?
7
Hamiltonian
Heisenberg-type interaction
Zeeman term
Anisotropy term
Single-ion anisotropy
Dipole-Dipole interaction
Antisymmetric interaction
8
Lattice structure of Fe10
Local symmetry of each neighboring pair
?
Alternating branches of bonds in neighboring pairs
? Details will be discussed later.
9
Lattice structure of Fe12
Deviation from the regular polygon
Fe-Fe-Fe angle 117.3136.3
Neighboring spins
D
10
Calculation method
The number of states is large.
S5/2 66 46656
610 60466176 6122 109 cf.
S1/2 2664, 2101024, 2124096
The method can treat dynamical behavior.
Dynamical simulation using an effective basis
Numerical solution of quantum master equation
by Runge-Kutta method
11
Calculations capturing thermal effects
bosons ? phonons
Quantum master equation
12
Effective basis
Lanczos diagonalization
We use instead of .
S1
16 states from 46656
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Result of dM/dH for Fe10
D/J0.005, kBT/J0.043
dM/dH
Contribution of is small.
The origin is the antisymmetric interaction.
Increasing field
Satellite peaks appear due to magnetic Foehn
effect.
14
Mechanism of magnetic Foehn effect
Two kinds of speed characterizing behaviors of
system
Quantum transition is nonadiabatic.
Energy
Relaxation is dominant. The system is isothermal.
Probability of higher state
v
v2
Fast
Slow
v1
Region of magnetic Foehn effect
Spin temperature
15
Magnetic Foehn effect in M(H) and dM/dH
Probability of higher state
Magnetization
dM/dH
? A satellite peak appear.
16
Experiments of Fe12 dM/dH
(Ajiro, Narumi, et al.private communications)
Second peak is the highest.
T1.3K
Satellite peaks appear.
T0.09K
Satellite peaks disappear.
17
Results of Fe12
J/kB36K, D/kB1.7K
2000, l0.09
T1.3K
dM/dh
h
T0.09K
h
Main peaks and satellite peaks agree well with
experiments.
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Consideration of lattice structure
Symmetry of Fe10
Inversion symmetry
C2 symmetry
Inversion center
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Symmetry of Fe10
Mirror symmetry
C5 symmetry
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A set of D vectors from static regular structure
ltyMHDMyM1gt0
The DM interaction of the above D vectors is not
the origin of the peaks in dM/dH.
21
Oscillation of methyl groups
Structure is measured at Tst226 K.
Each ellipsoid shows 50 possibility.
Oblong thermal ellipsoids with the longer
radius a
Elastic constant of an elastic energy of a methyl
group is briefly estimated as K 0.672
kBTst/a2.
22
Coupled oscillation of the collective mode
HmethylS n110 -(h2/2m0)(?/ ?xn)2
Kxn2/2P(xn-xn-1)2/2
Fourier transformation mode of wave number0
H0 -(h2/2m0)(?/ ?q0)2 Kq02/2
Zero-point motion due to the quantum fluctuation
even at low temperatures
-xZPM xZPM 50 possibility from the
zero-point motion xZPM 0.13 Å
qZPM 11 degrees
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Schematic motion of the oscillation
Due to the above oscillation, the symmetries of
C5 and mirror survive while the symmetries of
inversion and C2 are broken .
Alternating DM interaction is allowed.
It makes the characteristic heights of peaks in
dM/dH.
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Case of Fe6
Experiment
Theoretical result
dM/dH
Lattice fluctuation has not been specified in
Fe6.
Fe6 may include other origins for quantum mixing.
25
Fe(salen)Cl2
(Shapira, et al. PRB59(1999)1046)
Dimer molecule of S5/2 spins
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Summary
Magnetization processes of nanoscale ring cluster
of irons are studied.

• Main peaks originate from the lattice structure
• DM interaction in Fe10
• DM interaction dipole-dipole interaction in
  Fe12
• Thermal effect from the lattice
• ? Magnetic Foehn effect
• ? Asymmetry of the peaks

Quantum fluctuation of lattice Zero-point motion

• References

HN and S. Miyashita JPSJ 70 (2001) 2151 HN and
S. Miyashita J.Phys.Chem.Solids 63 (2002)
1521 HN and S. Miyashita JPSJ 71 (2002) 2580