1. Magnetization Hysteresis in Triangular Ring -Quantum and Classical cases
Hiroyuki Nojiri, Department of Physics, Okayama University
Introduction
Hysteresis in
regular triangle V15
distorted triangle V3
Mn3 and other
Summary

2. Collaborators Okayama University T. Taniguchi, K . Aikawa
Kyushu University Y. Ajiro
Laboratory de Magnetisme Loise Néel, B. Barbara
University of Bielefeld A. Müeller
Tokyo Institute of Technology T. Yamase, E. Ishikawa
Acknowledgement S. Miyashita

3. Molecular magnets Ensemble of Independent molecules
Study of 1-molecule property by bulk measurement
Study of Quantum Dynamics
Discrete energy spectrum
Coherence, phase of wave function
Control of Hamiltonian　
Magnetic field with time structure
Decoupling from thermal bath
S=75
S=10
S=3/2
1023
1015
104
101
SQUID
Molecule
Atom

4. Quantum Dynamics of SpinH
Quantum Dynamics of Spin
Thermal assisted tunneling
Non-Adiabatic process
Cross relaxation
Tunneling
Thermal process
Adiabatic(=equilibrium) process

5. Low spin molecular magnet
Rectangular, Four spin ring
S=0, 1, 2, equally spaced steps
with no hysteresis
What about triangle?
(1)Effect of frustration
(2)Double degeneracy of
the ground state
(3)Mixing and symmetry
V12 S=2

6. Quantum? hysteresis in V15 for Hidden double degeneracy
K6[V15As6O42(H2O)] • 8H2O
Fifteen S=1/2 spins
Hexagon sites
　AF Interaction ~800 K
Singlet state
Triangular site
　AF interaction
S=1/2 ground state
　 S=3/2 Excited state
　 D=3.7 K
Y. Ajiro et al.

7. Hysteresis at zero field
Magnetization in S=1/2 system
Tunneling gap ~0.1 K
Kramers doublet
Time reversal symmetry
Hidden Double Degeneracy
Two-sets of doubles separated by
Dzyaloshinskii Moriya interaction
S. Miyashita and N. Nagaosa
Prog. Theor. Phys. 106(2001)533
S=1/2ー3/2 level crossing?
Chiorescu et al. PRL 84(2000)3454

8. Magnetization process at low temperature
In steady field
Jump to 3 mB at level crossing
In pulsed field
Hysteresis and half jump
T=0.5 K 　
M (μb）
up sweep
down sweep
I. Chiorescu et al.
J.Magn.Magn.Mater.221(2000)103.

9. Half jump at level crossing
Up sweep DS=1/2
S=1/2 to S=1 Half jump
Down sweep DS=1
S=3/2 to S=1/2 Full jump
Saturate in a certain time

10. Quenching of thermal effect
Comparison of width of dM/dH
Width is narrower in pulsed fields
Quench of thermal fluctuations
Observation of pure quantum
phenomenon

11. Double degeneracy and quantum hysteresis
Transition only from the blue level
Thermalize of the red level in 1 ms
Reach saturation
Populate only in the blue level
Thermalize
S=3/2 D
S=1/2
DM interaction causes
asymmetric splitting
S. Miyashita and K. Saito at LT23, 2002

12. Relaxation time among different levels
t1/2: Relaxation in Kramers doublets
t3/2:Relaxation between 1/2 and 3/2 Dt2> t1/2>Dt1
Fast
Slow

13. Distorted triangle V3-Sb, Bi
K11H[(VO)3(SbW9O33)2]･27H2O.
Slightly Distorted
triangle :V :O
A spin triangle consists of three S=1/2 spins

14. Magnetization process of V3-Bi
V3-Bi powder
　 T=0.5 K
Double peak
Hc=4 T
Hc=5T　
down
M(μB）
dM/dH(arb.units) up
down up
B (T)
B (T)

15. Magnetization at finite temperature
Population
P1(red) ＞P2(blue)
P1+P2＝１
1μB E
S=3/2
Hc1
Hc2 H
5.5 K
Red+Blue M
1.1 K
2μb
S=1/2
1μB
Hc1
Hc2 H
Hc1
Hc2 H

16. Summary Hysteresis in triangles,caused by mixing structure
Suppress of Thermal fluctuation
Magnetization is sensitive to double degeneracy
Adiabatic transition
Large spin system with Fragile ground state
Anisotropy of MH with single crystal of V3
D M interaction vs HF coupling
Non adiabatic regime in ultra-fast sweeping fields
Quantum Oscillation