Introduction to Single Molecular Magnet

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

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 What is interesting about SMM? • Physics point of view • 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,… -9 10 (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mTobserved 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 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)

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

26. Refrences Barbara et al., J. Magn. Magn. Mater. 200 (1999), 167. 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, http://www.physics.berkeley.edu/research/hellman/NewWebPage/Magnetic Molecules.html J. Leggett et al., Rev. Mod. Phys. 59 (1987), 1. J. R. Friedman and M. P. Sarachik, Phys. Rev. Lett. 76 (1996), 3830. J. v. Slageren. Introduction to Molecular Magnetism. Retrieved March 4, 2010, from, http://obelix.physik.uni-bielefeld.de/~schnack/molmag/material/123.pdf J. Yoo et al., Inorg. Chem. 39 (2000), 3615. M. A. Novak and R. Sessoli, Quantum Tunneling of Magnetization-QMT’94(Eds: L.Gunther and B. Barbara), Kluwer Dordrecht (1995), 171. N. E. Chakov et al., Am. Chem. Soc. 44 (2005), 5304. Pulsed EPR. Retrieved March 4, 2010, from, http://www.itst.ucsb.edu/~susumu/res.htm R. Sessoli et al., nature 365 (1993), 141. C. Sangregorio et al., Phys. Rev. Lett. 78 (1997), 4645. T. Lis, Acta. Crystallogr. 36 (1980), 2042.

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