1. Single Molecular Magnets
Ge,Weihao

2. Introduction What is Single Molecular Magnet?
Configuration: metal atom linked by oxygen, packed in ligands
Described as a total single spin; size and anisotropy has great effect
Why are they interesting?
Theoretical: quantum behavior at mesoscopic level
Application:
Quantum computer:
quantum interference and coherence
High-density storage device
Internal memory effect
high integration
Other applications
Two kinds of these clusters
Big integer spin
½ spin big molecule

3. Superparamagnetism Superparamagnetism Origin of superparamagnetism
paramagnetism below Curie’s temperature
large susceptibility
superparamagnetism limit
Origin of superparamagnetism
magnetism: result of spin alignment
thermal excitation, ferromagnetism <-> paramagnetism
small scale, below Tc:
thermal excitation destroys the ordering between the clusters
thermal excitation cannot upset alignment within the cluster
ferro~ inside & para~ outside => treated as a large spin as a whole
Experiment results
stepped hysteresis can be found below certain temperature.
frequency dependent AC susceptibility

4. Quantum Tunneling Magnetization
Experiment
steps found in hysteresis of Mn12 cluster
Model
two – well model
resonant tunneling
thermally assisted QTM & pure QTM
A commonly used form of Hamiltonian
axial anisotropic term
Zeeman splitting term
transverse anisotropic term
Experiments
Model
A commonly used form of Hamiltonian
spins within: Heisenberg model
total spin: treated as a large spin
QT relaxation also.
equally distributed in wells
apply magnetic field -> all in 1 well
field turned off -> all in 1 well
tunnel back, relaxation -> relaxation time

5. Integer Spin SMM: Mn12 Significance Structure Hamiltonian
archeological reason: first synthesized SMM & QTM first observed
most widely studied
Structure
Mn3+, external octagon; Mn4+, internal tetrahedron.
Ground state: S=10
Hamiltonian
symmetry:
lowest even power of transverse terms is 4
transition:
probably exist low-ordered odd-powered terms

6. Integer Spin SMM: Fe4 Structure Hamiltonian
Fe3+: centered triangle, C2 symmetry
Ground state: S=5
Hamiltonian
general form
Advantages over Mn12 in application
More efficient tunneling
longer relaxation time
less affected when attached to a surface
stability

7. ½ spin big molecule: V15 Structure Experimental result
a center triangle between two hexagons
S=1/2, no large energy barrier, large zero field splitting
Experimental result
hysteresis observed
Rabi oscillation
coherence time: ~100 μs
Theoretical approaches
dissipative two-level system:
Landau - Zener transition
exchange interaction:
“spin rotation in a phonon bath”
Structure
Properties
Theoretical approaches
two-level model: relatively large zero field splitting ~80mK
spin hamiltonian: hexagon cancels by anteferromagnetic coupling; only consider triangle
exchange term; anisotropy term; interaction with nuclear spin; zeeman term coherence time limited by nuclear spin

8. Summary General introduction to single molecular magnets
quantum behavior beyond the microscopic scale in these clusters
Origin of the magnetism of SMM
Quantum Tunneling Magnetization
A result of size and anisotropy
Integer spin clusters and ½ spin clusters
integer:
easy to interpreted by large-spin approximation
½ spin:
lack of barrier, tunneling caused by spin-phonon interaction
long-lived coherence

9. References
QTM:
Gatteschi,D.; Sessoli,R. “Quantum tunneling magnetization and related phenomena in Molecular Materials.” Angew. Chem.Ed. 42(3), 2003,pp.268
Mn12:
Friedman,J., Sarachik,M. “Mesoscopic Measurement of Resonant Magnetization Tunneling in High-Spin Molecules.” PRL, 76(20),1996, pp.3830
Barra, A., et.al. “High-frequency EPR spectra of a molecular nanomagnet: Understanding quantum tunneling of the magnetization.” PRB. 56(13), 1997, pp.8192
Fe4:
Accorsi,S., et.al. “Tuning Anisotropy Barriers in a Family of Tetraion(III) Single-Molecule Magnets with an S = 5 Ground State” JACS. 128(14), 2006, pp
Wernsdorfer,W., et.al. “X-ray Magnetic Circular Dichroism Picks out Single-Molecule Magnets Suitable for Nanodevices.” Adv.Mater. 21, 2009, pp
Sessoli,R., et.al. “Magnetic memory of a single-molecule quantum magnet wired to a gold surface.” Nature Mater. 8, 2009, pp.194
V15:
Müller,A., et.al. “Quantum Oscillation in a molecular magnet.” Nature lett. 453, 2008 pp.203
Choirescu, et.al. “Environmental effects on big molecule with spin ½.” J.Appl.Phys.87(9) 2000 pp.5496