1. Alternating Antisymmetric Interaction in Nanoscale Iron Ring
Workshop on the Quantum Dynamics of Molecular Magnets
4th December 2002
Alternating　Antisymmetric　Interaction in Nanoscale Iron Ring
Hiroki Nakano 中野博生
Himeji-Institute of Technology
　Seiji Miyashita 宮下精二
University of Tokyo

2. Nanoscale Iron Clusters Fen
n= n=10
d electrons in Fe3+
S=5/2
L=0
[NaFe6(OCH3)12 (dmb)6] : monoclinic 単斜晶系 a \ne b \ne c, alpha=gamma=90degree \ne beta
[NaFe6(OCH3)12 (pmdbm)6]+ : trigonal 　菱面体晶系 a=b=c, alpha=beta=gamma \le 120degree or \ne 90degree
Fe : monoclinic
Fe : monoclinic
Fe : trigonal
n= n=12

3. Experimental Magnetization Process
Fe6 (Chaneschi, et al: Chem.Eur.J.2(1996)1379) J=28.7K
T=1.5 K
Fe10 (Taft, et al.:Am.Chem.Soc.116(1994)823) J=13.8K
T=0.6 K

4. Pure Heisenberg chain including finite spins
Finite temperature
T=0
Equivalent peaks with equivalent intervals

5. Experimental peaks in dM/dH
Fe 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)
T=1.3K
Satellite peaks
appear.
T=0.09K
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: 117.3～136.3°
Neighboring spins D

10. Calculation method Dynamical simulation using an effective basis
The number of states is large.
S=5/2 : 66=
610=
612～2 × 109
cf. S=1/2 : 26=64, 210=1024, 212=4096
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 . S=1
16 states from 46656

13. Result of dM/dH for Fe10 The origin is the antisymmetric interaction.
D/J=0.005, kBT/J=0.043
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
Slow v1 v2
Fast
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.
T=1.3K
Satellite
peaks appear.
T=0.09K
Satellite
peaks
disappear.

17. Results of Fe12 J/kB=36K, D/kB=1.7K =2000, l=0.09 T=1.3K dM/dh h
Main peaks and satellite peaks agree well with experiments.

18. Consideration of lattice structure
Symmetry of Fe10
Inversion symmetry
C2 symmetry
Inversion center

19. Symmetry of Fe10
C5 symmetry
Mirror symmetry

20. A set of D vectors from static regular structure
<yM|HDM|yM+1>=0
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 Tst=226 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 ～ kBTst/a2.

22. Coupled oscillation of the collective mode
Hmethyl=S ｎ=110 [-(h2/2m0)(∂/ ∂xｎ)2 +Kxｎ2/2+P(xｎ-xｎ-1)2/2]
Fourier transformation & mode of wave number=0
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

23. 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.

24. Case of Fe6 Lattice fluctuation has not been specified in 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)Cl]2 Dimer molecule of S=5/2 spins
(Shapira, et al.: PRB59(1999)1046)
Dimer molecule
of S=5/2 spins

26. Summary References Quantum fluctuation of lattice Zero-point motion
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