Introduction to Single Molecular Magnet

Nirmal Ghimire

March 16, 2010

In Class PresentationSolid State Physics II

Instructor: Elbio DagottoDepartment of Physics and AstronomyUniversity of Tennessee at Knoxville

Introduction Quantum Tunneling and Magnetic

Relaxation Mn12ac and Fe8 as SMM Conclusion

OutlineOutline

IntroductionIntroduction

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)

(Gatteschi and Sessoli, Angew. Chem 2003)

External magnetic field

Magnetized

Magnetism Retained for several days

Single Molecular Magnet (SMM)

IntroductionIntroduction

Physics point of view

• Quantum Tunneling

• Represent the point at which classical and quantum world meet

What is interesting about SMM?

Application

• Quantum Computation

Introduction Quantum Tunneling and Magnetic

Relaxation Mn12ac and Fe8 as SMM Conclusion

OutlineOutline

Quantum TunnelingQuantum 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 TunnelingQuantum 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 TunnelingQuantum 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 Magnetic Relaxation in Large Spin SystemSystem System of Interest-SMM

characterized by:• Large Spin (e.g S =10)• Negative anisotropy energy

HO = splitting due to crystal field + external magnetic field

(Gatteschi and Sessoli, Angew. Chem 2003)

The phenomenon of returning of the system to equilibrium is known as magnetic relaxation.

Magnetic Relaxation in Large Spin Magnetic Relaxation in Large Spin SystemSystem

There are three ways in which magnetic relaxation can occur:

1)Thermal relaxation2)Thermally (phonon) assisted tunneling3)Ground state tunneling

(J. v. Slageren )

Magnetic Relaxation in Large Spin Magnetic Relaxation in Large Spin SystemSystem

• For tunneling, a perturbation Hamiltonian is needed.

• Physically it can be a distortion along xy plane called transverse anisotropy

• A convenient form is:

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 )

Magnetic Relaxation in Large Spin Magnetic Relaxation in Large Spin SystemSystem

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 Magnetic Relaxation in Large Spin SystemSystem

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,…

Bg

D

(J. v. Slageren )

10 -9

Magnetic Relaxation in Large Spin Magnetic Relaxation in Large Spin SystemSystem

• 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 )

Introduction Quantum Tunneling and

Magnetic Relaxation Mn12ac and Fe8 as SMM Conclusion

OutlineOutline

MnMn112ac as Single Molecular Magnet2ac 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

MnMn112ac as Single Molecular Magnet2ac 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

(Gatteschi and Sessoli, Angew. Chem 2003)

19.4 emu mol-1 K(observed)

31.5 emu mol-1 K (expected for uncoupled spins)

MnMn112ac as Single Molecular Magnet2ac 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)

MnMn112ac as Single Molecular Magnet2ac 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)

Mn12ac as Single Molecular MagnetMn12ac 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 MagnetFe8 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 MagnetFe8 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 MagnetsOther 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

Introduction Quantum Tunneling and

Magnetic Relaxation Mn12ac and Fe8 as SMM Conclusion

OutlineOutline

ConclusionConclusion

• 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

RefrencesRefrences

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.uni-

bielefeld.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