1. 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

2. Outline Introduction Quantum Tunneling and Magnetic Relaxation
Mn12ac and Fe8 as SMM
Conclusion

3. Introduction
External magnetic field
Arrangement of electronic spin is the root origin of magnetism
Traditional magnetic materials: Array of inorganic atoms composed of transitional metal or lanthanide
In 1993 magnetism was observed in a new kind of material: organic molecular cluster containing transitional metal ions (V, Co, Fe, Ni, Mn)
Magnetism Retained for several days
Magnetized
Single Molecular Magnet (SMM)
(Gatteschi and Sessoli, Angew. Chem 2003)

4. Introduction Physics point of view What is interesting about SMM?
Quantum Tunneling
Represent the point at which classical and quantum world meet
Application
Quantum Computation

5. Outline Introduction Quantum Tunneling and Magnetic Relaxation
Mn12ac and Fe8 as SMM
Conclusion

6. 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

7. 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

8. 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

9. 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)

10. Magnetic Relaxation in Large Spin System
There are three ways in which magnetic relaxation can occur:
Thermal relaxation
Thermally (phonon) assisted tunneling
Ground state tunneling
(J. v. Slageren )

11. 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:

12. 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 )

13. 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:
Hz(n) = nD’; D’ = , n =0, 1, 2,… 10 -9
(J. v. Slageren )

14. 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 )

15. Outline Introduction Quantum Tunneling and Magnetic Relaxation
Mn12ac and Fe8 as SMM
Conclusion

16. 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

17. Mn12ac as Single Molecular Magnet
Overall antiferromagnetic coupling is realized from temperature dependance of mT (succesptibility product)
Value of mT at room temperature is smaller than expected for uncoupled spins indicated antiferromagnetic coupling
Maximumum mT observed at at low temperature (55.6 emu mol- 1 K) is close to the value for spin S = 10
19.4 emu mol-1 K(observed)
(Gatteschi and Sessoli, Angew. Chem 2003)
31.5 emu mol-1 K (expected for uncoupled spins)

18. 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)

19. 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
The loops show steps associated with the quantum tunneling
(B. Barbara et al., 1999)

20. 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)

21. Fe8 as Single Molecular Magnet
(Gatteschi and Sessoli, Angew. Chem 2003)
(Pulsed EPR)
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

22. Fe8 as Single Molecular Magnet
Relaxation time becomes temperature independent below 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)

23. 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

24. Outline Introduction Quantum Tunneling and Magnetic Relaxation
Mn12ac and Fe8 as SMM
Conclusion

25. 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

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C.M. Hurd, Contemp. Phys. 23 (1982), 469.
Caneschi et al., J. Am. Chem. Soc. 113 (1991), 5873.
Caneschi et al., J. Magn. Magn. Mater. 200 (1999), 182.
D. Gatteschi and R. Sessoli, Angew. Chem. Int. Ed. 42 (2003), 269.
D. Gatteschi et al. Science 256 (1994 ), 1054.
E.D. Dahlberg and J. G. Zhu, Phys. Tod. 34 (1995).
Hellman Lab Home. Retrieved March 4, 2010, from, Molecules.html
J. Leggett et al., Rev. Mod. Phys. 59 (1987), 1.
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J. v. Slageren. Introduction to Molecular Magnetism. Retrieved March 4, 2010, from,
J. Yoo et al., Inorg. Chem. 39 (2000), 3615.
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27. Thank You