Introduction to Single Molecular
Magnet
Nirmal Ghimire
March 16, 2010
In Class Presentation
Solid State Physics II
Instructor: Elbio Dagotto
Department of Physics and Astronomy
University of Tennessee at Knoxville
Outline




Introduction
Quantum Tunneling and Magnetic
Relaxation
Mn12ac and Fe8 as SMM
Conclusion
Introduction
External magnetic field

Arrangement of electronic spin is the root
origin of magnetism
Magnetism Retained for several days


Traditional magnetic materials: Array of
inorganic atoms composed of transitional
metal or lanthanide
Magnetized
In 1993 magnetism was observed in a new
kind of material: organic molecular cluster
containing transitional metal ions (V, Co, Fe,
Single Molecular Magnet
Ni, Mn)
(SMM)
(Gatteschi and Sessoli, Angew. Chem 2003)
Introduction
What is interesting about SMM?
Physics point of view
•
Quantum Tunneling
•
Represent the point at which classical and quantum
world meet
Application
•
Quantum Computation
Outline




Introduction
Quantum Tunneling and Magnetic
Relaxation
Mn12ac and Fe8 as SMM
Conclusion
Quantum Tunneling
Macroscopic object in one of the
two wells
• No interaction between the
states
• No tunneling
•
Quantum object in the well
• Wave function of object in one
well extends to the other
• Quantum tunneling
• Overlapping of the wave function
removes the degeneracy and gives
rise to tunnel splitting
•
Quantum Tunneling
Tunneling probability depends on:
Tunnel splitting
• Barrier height
• Smaller the ratio between the two
smaller the possibility of observing
tunneling
•
Also depends on the interaction of the particle with environment
•
Strong Coupling: Localization
• Intermediate Coupling: Incoherent Tunneling
• Weak Coupling: Coherent Tunneling
Quantum Tunneling
How to write the Hamiltonian?
•
Two equivalent wells: Unperturbed part
(Ho)
•
Wave function interaction: Perturbation
(H1)
•
Coupling between the particle and
environment: Another perturbation (H2)
•
H = Ho +H1+H2
•
These Hamiltonians depend on the
system into consideration
Magnetic Relaxation in Large Spin System
System of Interest-SMM characterized by:
Large Spin (e.g S =10)
• Negative anisotropy energy
•
HO = splitting due to crystal field + external magnetic field
The phenomenon of returning of the system
to equilibrium is known as magnetic
relaxation.
(Gatteschi and Sessoli, Angew. Chem 2003)
Magnetic Relaxation in Large Spin System
There are three ways in which magnetic relaxation
can occur:
1) Thermal relaxation
2) Thermally (phonon) assisted tunneling
3) Ground state tunneling
(J. v. Slageren )
Magnetic Relaxation in Large Spin System
In Zero Field,
in absence of
perturbation, the energy
eigenstate of the system are pure
MS states and hence tunneling is
not possible
(J. v. Slageren )
•
For tunneling, a perturbation Hamiltonian is needed.
•
Physically it can be a distortion along xy plane called transverse
anisotropy
•
A convenient form is:
Magnetic Relaxation in Large Spin System
The Hamiltonian now becomes:
+
H1 does not commute with Ho
H is admixture of
states
H1 mixes levels of S =M and S =
M±2
The degeneracy is removed due
to tunnel splitting
(J. v. Slageren )
Magnetic Relaxation in Large Spin System
In Magnetic field
Magnetic field along the easy axis removes the degeneracy in ± MS
• However, there occurs resonant tunneling under the condition:
D
Hz(n) = nD’;
D’ = g
, n =0, 1, 2,…
•
B
10
(J. v. Slageren )
-9
Magnetic Relaxation in Large Spin System
•
•
•
•
When magnetic field is
applied, the energy levels of
the spin microstates change
At certain level, these energy
levels cross
The perturbation in the form
of transverse anisotropy
couples the states and
tunneling of magnetization
occurs
Magnetization relaxation
corresponds to the steep
portion of the loops in
Hysteresis loop
(J. v. Slageren )
Outline




Introduction
Quantum Tunneling and Magnetic
Relaxation
Mn12ac and Fe8 as SMM
Conclusion
Mn12ac as Single Molecular Magnet
(Hellman Lab Home)
(B. Barbara et al., 1999)
Mn12ac = [Mn12O12(CH3COO)16(H2O)4].2CH3CHOO.4H20
8 Mn with s=2 (up)
4 Mn with s=3/2 (down)
Antiferromagnetic ordering: S =8×2 – 4×3/2 = 10
Mn12ac as Single Molecular Magnet
•
•
Overall antiferromagnetic coupling
is realized from temperature
dependance of mT (succesptibility
product)
19.4 emu mol-1
K(observed)
Value of mT at room
temperature is smaller than
expected for uncoupled spins
indicated antiferromagnetic
coupling
(Gatteschi and Sessoli, Angew. Chem 2003)
•
Maximumum mT observed at at
low temperature (55.6 emu mol1 K) is close to the value for
spin S = 10
31.5 emu mol-1 K (expected
for uncoupled spins)
Mn12ac as Single Molecular Magnet
•
Evidence for magnetic anisotropy
along easy axis comes from single
crystal magnetization
•
The fact that the parallel
magnetization (to the tetragonal
axis) saturates much more rapidly
than the perpendicular
magnetization indicates strong
anisotropy
(Gatteschi and Sessoli, Angew. Chem 2003)
Mn12ac as Single Molecular Magnet
•
Hysteresis loop shows unusual
stairs below blocking temperature
•
In flat portion relaxation time is
much larger than the measuring
time scale
•
In the steep portion of the loop
relaxation time is of the order of
the measuring time scale
(B. Barbara et al., 1999)
•
The loops show steps associated
with the quantum tunneling
Mn12ac as Single Molecular Magnet
•
Final proof of quantum tunneling is
associated with temperature
independence of relaxation time
•
For Mn12ac below 2K relaxation
time becomes experimentally long
and hence reliable measurement
becomes impossible
(Sessoli et al., 1993)
Fe8 as Single Molecular Magnet
(Pulsed EPR)
(Gatteschi and Sessoli, Angew. Chem 2003)
Fe8 = [Fe8O2(OH12(tacn)6Br8].(tacn = 1,4,7 –triaza-cyclonane)
6 Fe with s=5/2 (up spin)
2 Fe with s=5/2 (down spin)
Antiferromagnetic ordering: S =6×5/2 – 2×5/2 = 10
Fe8 as Single Molecular Magnet
•
Relaxation time becomes
temperature independent below
400 mK
•
This confirms the presence of pure
quantum tunneling
•
As in Mn12 ac, hysteresis shows
equidistant magnetization jumps
•
As with the relaxation time,
hysteresis becomes temperature
independent below 350 mK
(Gatteschi and Sessoli, Angew. Chem 2003)
Other Single Molecular Magnets
•
There are many other molecules showing the
behavior of SMM
•
Some are Fe4,V4, CrM6, Ni12, Mn10
•
It has been realized that size of the cluster is not
important for the behavior of SMM
•
The important factors are ground state spin S and
magnetic anisotropy
•
All the other SMM are reported to show slow
relaxation at temperature lower than Mn12ac
Outline




Introduction
Quantum Tunneling and Magnetic
Relaxation
Mn12ac and Fe8 as SMM
Conclusion
Conclusion
•
SMMs have opened an avenue for the study of
physical phenomena at the interface between
quantum and classical world
•
SMM provide signature of quantum mechanical
behavior in the macroscopic system
•
They bear the potential of application in future
quantum computers
•
Despite the various successful experimental
techniques, a neat theory is yet to be developed
Refrences
1. Barbara et al., J. Magn. Magn. Mater. 200 (1999), 167.
2. C.M. Hurd, Contemp. Phys. 23 (1982), 469.
3. Caneschi et al., J. Am. Chem. Soc. 113 (1991), 5873.
4. Caneschi et al., J. Magn. Magn. Mater. 200 (1999), 182.
5. D. Gatteschi and R. Sessoli, Angew. Chem. Int. Ed. 42 (2003), 269.
6. D. Gatteschi et al. Science 256 (1994 ), 1054.
7. E.D. Dahlberg and J. G. Zhu, Phys. Tod. 34 (1995).
8. Hellman Lab Home. Retrieved March 4, 2010, from,
http://www.physics.berkeley.edu/research/hellman/NewWebPage/Magnetic Molecules.html
9. J. Leggett et al., Rev. Mod. Phys. 59 (1987), 1.
10. J. R. Friedman and M. P. Sarachik, Phys. Rev. Lett. 76 (1996), 3830.
11. J. v. Slageren. Introduction to Molecular Magnetism. Retrieved March 4, 2010, from, http://obelix.physik.unibielefeld.de/~schnack/molmag/material/123.pdf
12. J. Yoo et al., Inorg. Chem. 39 (2000), 3615.
13. M. A. Novak and R. Sessoli, Quantum Tunneling of Magnetization-QMT’94(Eds: L.Gunther and B. Barbara), Kluwer
Dordrecht (1995), 171.
14. N. E. Chakov et al., Am. Chem. Soc. 44 (2005), 5304.
15. Pulsed EPR. Retrieved March 4, 2010, from, http://www.itst.ucsb.edu/~susumu/res.htm
16. R. Sessoli et al., nature 365 (1993), 141.
17. C. Sangregorio et al., Phys. Rev. Lett. 78 (1997), 4645.
18. T. Lis, Acta. Crystallogr. 36 (1980), 2042.
Thank You