1. Single-Molecule Magnets: A Molecular Approach to Nanomagnetism George Christou Department of Chemistry, University of Florida Gainesville, FL 32611-7200, USA christou@chem.ufl.edu

2. Single-Molecule Magnets (SMMs) Requirements for SMMs: 1.Large ground state spin (S) 2.Negative ZFS parameter (D) Anisotropy barrier (U) = S 2 |D| Integer spin or (S 2 -1/4)|D| Half- integer spin m s = -7 m s = -1 m s = -2 m s = -3 m s = -4 m s = -5 m s = -6 m s = -8 m s = -9 m s = -10 m s = 7 m s = 1 m s = 2 m s = 3 m s = 4 m s = 5 m s = 6 m s = 8 m s = 9 m s = 10 U E m s = 0 m s =10 -10 = m s 9 -9 8 -8 7 -7 6 -6 5 -5 4 -4 3 -3 2 -2 1 0 Energy Magnetization Direction (z) The barrier to magnetization relaxation in SMMs is not due to inter-spin Interactions, as in traditional magnets, but to Ising (easy-axis) molecular anisotropy. Each molecule is a separate, nanoscale magnetic particle.

3. Molecular Advantages of SMMs over Traditional Nanoscale Magnetic Particles  truly monodisperse particles of nanoscale dimensions  crystalline, therefore contain highly ordered assemblies  well-defined ground state spin, S  truly quantum spin systems  synthesized by room temperature, solution methods  enveloped in a protective shell of organic groups (ligands)  truly soluble (rather than colloidal suspensions) in organic solvents  the organic shell (ligands) around the magnetic core can be easily modified, providing control of e.g. coupling with the environment Synthesis Properties

5. 40 mK -10 -9 -8 -7 10 9 8 7 Hysteresis Loops for an S = 10 SMM S = 10 21 energy states M S = -S, -S+1, …, S

6. Properties of the Mn 12 family  S = 10  D = -0.40 to -0.50 cm -1 (-0.58 to -0.72 K)  Magnets below 3K The Mn 12 Family of Single-Molecule Magnets (SMMs) Volume of the Mn 12 O 12 magnetic core ~ 0.1 nm 3 [Mn 12 O 12 (O 2 CR) 16 (H 2 O) 4 ] (or Mn 12 ) Mn 12 -Ac (i.e. R = CH 3 ) has axial symmetry (tetragonal space group I4(bar)), and has therefore been considered the best to study in detail. Carboxylate Substitution [Mn 12 O 12 (O 2 CMe) 16 (H 2 O) 4 ] + 16 RCO 2 H [Mn 12 O 12 (O 2 CR) 16 (H 2 O) 4 ] + 16 MeCO 2 H

7. A Mn 12 Complex with Tetragonal (Axial) Symmetry: [Mn 12 O 12 (O 2 CCH 2 Br) 16 (H 2 O) 4 ] (Mn 12 -BrAc) [Mn 12 O 12 (O 2 CMe) 16 (H 2 O) 4 ] + 16 BrCH 2 CO 2 H [Mn 12 O 12 (O 2 CCH 2 Br) 16 (H 2 O) 4 ] + 16 MeCO 2 H --- almost no symmetry-lowering contacts between [Mn 12 BrAc] and the four CH 2 Cl 2. --- in contrast to Mn 12 -Ac, where each molecule has strong H-bonding to 0,1, 2, 3 or 4 acetic acid molecules (Cornia et al., P.R.L. 2002, 89, 257201) crystallizes as [Mn 12 -BrAc]·4CH 2 Cl 2 tetragonal space group I42d

8. A New Mn 12 Complex with Tetragonal (Axial) Symmetry: [Mn 12 O 12 (O 2 CCH 2 Bu t ) 16 (MeOH) 4 ]·MeOH (Mn 12 -Bu t Ac) Mn 12 -AcMn 12 -Bu t Ac I4(bar) Muralee Murugesu --- no symmetry-lowering contacts with the solvent molecules in the crystal --- bulky R group : well separated molecules Mn 12 -Ac Mn 12 -Bu t Ac

9. Ground state tunneling Excited state tunneling Ground state tunneling Excited state tunneling The Sharpness of the Hysteresis Loops in Mn 12 -Bu t Ac allows Steps due to Excited State Tunneling to be seen Summary: Researchers have thought for over 10 years that axial Mn 12 -Ac is the best one to study, but it is not. More interesting physics is now being discovered with cleaner, truly axial Mn 12 SMMs Wernsdorfer, Murugesu and Christou, Phys. Rev. Lett., in press

10. Spin Injection into Mn 12 One - electron additions to Mn 12 in bulk Mn 12 + I - [Mn 12 ] - + ½ I 2 Mn 12 + 2 I - [Mn 12 ] 2- + I 2 RE 1 (V) a E 2 (V) b CHCl 2 0.910.61 C 6 H 3 (NO 2 ) 2 -2,40.740.45 C6F5C6F5 0.640.46 CH 2 Cl0.600.30 CH 2 CH 3 0.02-0.50 CH 2 Cl 2 solution vs. ferrocene Potential (V) -0.40.00.40.81.21.6 50  A 0.86 0.56 0.24 - 0.03 0.95 0.64 0.34 0.91 0.61 0.29 10  A Current CyclicVoltammetry Differential Pulse Voltammetry Electrochemistry Redox Potentials

11.  added electrons localized on two Mn  S does not change significantly  |D| decreases with added electrons  barrier decreases with added electrons Effect of Electron Addition to Mn 12 [Mn 12 ] 2- S-D / cm -1 U eff / K Mn 12 100.4 - 0.560 - 65 [Mn 12 ]-19/20.3 - 0.440 - 50 [Mn 12 ] 2- 100.2 - 0.325 - 40 Also: Quantum Phase Interference and Spin-Parity in Mn 12 Single-Molecule Magnets Phys. Rev. Lett. 2005, 95, 037203

12. [Mn 12 ] 2- Mn 12 [Mn 12 ] - R = C 6 F 5 19 F NMR in solution

13. Mn 4 SMMs with S = 9/2 Mn III X Mn IV O Mn III O O  3Mn 3+, Mn 4+  C 3v virtual core symmetry  Mn 3+ Jahn-Teller axial elongations  Core ligands (X): Cl -, Br -, F -, NO 3 -, N 3, NCO -, OH -, MeO -, Me 3 SiO -, etc Advantages  Variation in core X group, for given organic groups  Variation in organic groups, for a given Mn 4 O 3 X core.  Soluble and crystalline  Mn 4 O 3 X core volume ~ 0.01 nm 3

14. Properties of Mn 4 SMMs magnetization orientation energy  S = 9 / 2  D = – 0.65 to – 0.75 K  U = ΔE = (S 2 - 1 / 4 )|D| = 20 D E XOSiMe 3 J 34 (cm -1 )-34.35 J 33 (cm -1 )+13.41 g1.97 S9/2 1 st ex. state264 cm -1 S = 9/2

15. Mn 4 SMMs with S = 9/2 (2S i + 1) energy states S = 9/2 : 10 energy states M S = -S, -S+1, …, S H i = – D Ŝ iz 2 + H i trans + g μ B μ 0 Ŝ i H D = Xgµ B /k B (X is the step separation)

16. [Mn 4 Pr] 2 Hexagonal R3(bar) (S 6 symmetry) Distances C…Cl 3.71 Å C-H…Cl 2.67 Å Cl…Cl 3.86 Å Angle C-H…Cl 161.71° Supramolecular Dimers of Mn 4 SMMs: Exchange-biased Quantum Tunnelling of Magnetization Pr group

17. Quantum Tunnelling in an [Mn 4 ] 2 dimer of SMMs using [Mn 4 Pr] 2 ·MeCN (NA3) Wernsdorfer, Christou, et al. Nature 2002, 416, 406 D = - 0.50 cm -1 = - 0.72 K J intra = - 0.07 cm -1 = - 0.1 K

18. R= CH 3 (Ac) R’= H R= CH 2 CH 3 (Pr) R’= H R= CH 2 CH 3 (Pr) R’= H R= CH 2 CH 3 (Pr) R’= D Space GroupR3bar Temp(°C)118130173 Solvent in the crystal NA2 MeCN NA3 MeCN NA11 hexane NA3-D MeCN (Å) Cl ··· Cl3.739(13)3.858(12)3.712(10)3.844(7) (Å) Cl ··· C3.6003.7063.6643.721 (°) C-H··· Cl158.15158.00151.94157.36 (Å) Mn III ···Mn III 7.6307.788 7.622 7.750 Derivatives of [Mn 4 O 3 Cl 4 (O 2 CR) 3 (py-p-R´) 3 ] 2 Dimers Nuria Aliaga-Alcalde Nature Science

19. -0.5 0 0.5 1 -0.500.51 0.140 T/s 0.070 T/s 0.035 T/s 0.017 T/s 0.008 T/s M/M s µ 0 H (T) NA11 0.04 K -0.5 0 0.5 1 -1.2-0.8-0.400.40.81.2 0.140 T/s 0.070 T/s 0.035 T/s 0.017 T/s 0.008 T/s 0.004 T/s M/M s µ 0 H (T) 0.04 K NA3 -0.5 0 0.5 1 -0.500.51 0.035 T/s 0.017 T/s 0.008 T/s 0.004 T/s M/M s µ 0 H (T) 0.04 K NA2 Variation of Exchange-bias and Fine-structure in [Mn 4 ] 2 SMM Dimers [Mn 4 Ac] 2 · MeCN[Mn 4 Pr] 2 · MeCN (Nature) [Mn 4 Pr] 2 · hexane (Science) Two effects: 1) Variation in exchange-bias (J intra ) 2) Variation in fine structure (J inter ) The properties of [Mn 4 ] 2 are very sensitive to the ligands and the solvent in the crystal

20. Quantum Superpositions in Exchange-coupled [Mn 4 ] 2 Dimers -- with [Mn 4 Pr] 2 · hexane (NA11) Hill, Edwards, Aliaga-Alcalde, Christou, Science 2003, 302, 1015 J z J x, J y J z J x, J y

21. Hysteresis evidence for inter-dimer exchange interactions (↓ ↓ ↓) (↑ ↓ ↓) (↑ ↑ ↓) (↑ ↑ ↑) View down S 6 axes ↓ ↓↓ ↓ R. Tiron, W. Wernsdorfer, N. Aliaga-Alcalde, and G. Christou, Phys. Rev. B 2003, 68, 140407(R)

22. A New Generation of Mn Clusters: A Mn 84 Torus Tasiopoulos et al. Angew. Chem. Int. Ed. 2004, 43, 2117 [Mn 12 O 12 (O 2 CR) 16 (H 2 O) 4 ] + MnO 4 - in MeOH/MeCO 2 H The structure consists of six Mn 14 units i.e. [Mn 14 ] 6

23. Side-view Front-view

24. 10 -5 10 -3 10 10 1 3 5 7 9 05 15 20 DC AC (s)  1/T (1/K) U eff = 18 K τ 0 = 5.7 x 10 -9 s  M ′T vs T  M ′′T vs T S = 6

25. Mn 4 Mn 30 Mn 12 110100 1000 N Quantum worldClassical world Mn 84 Comparison of Sizes and Néel Vectors Molecular (bottom-up) approach Classical (top-down) approach 3 nm Co nanoparticle A meeting of the two worlds of nanomagnetism Tasiopoulos et al. Angew. Chem. Int. Ed. 2004, 43, 2117

26. 1.4 nm A Mn 70 Torus EtOH yields a smaller torus of five units i.e. [Mn 14 ] 5 3.7 nm Alina Vinslava Anastasios Tasiopoulos

27. ~ 3.7 nm ~ 1.2 nm ~ 1.4 nm 10 -5 10 -3 10 10 1 3 5 7 9 05 1520 DC  (s) 1/T (1/K) U eff = 23 K τ 0 = 1.7 x 10 -10 s Compare Mn 84 : U eff = 18 K, τ 0 = 5.7 x 10 -9 s

28. A Mn 25 SMM with a Record S = 51/2 Spin for a Molecular Species Murugesu et al., JACS, 2004, 126, 4766 A B C S = 51/2, D = - 0.022 cm -1 green, Mn IV ; purple, Mn III ; yellow, Mn II ; red, O; blue, N S = 15/2 + 0 + 21/2 + 0 + 15/2 = 51/2 A B C B A A B C MnCl 2 + pdmH 2 + N 3 - + base → [Mn 25 O 18 (OH) 2 (N 3 ) 12 (pdm) 6 (pdmH) 6 ] 2+ pdmH 2 Mn IV, 18 Mn III, 6 Mn II

29. Summary and Conclusions Mn 12 and many other SMMs can be easily modified in various ways; this is one of the major advantages of molecular nanomagnetism Two more Mn 12 SMMs, Mn 12 BrAc and Mn 12 Bu t Ac, with tetragonal (axial) symmetry have been studied, and they exhibit data of far superior quality than Mn 12 Ac “All tetragonal Mn 12 complexes have axial symmetry, but some are more axial than others”(with apologies to George Orwell, Animal Farm) The techniques of molecular and supramolecular chemistry can be used to modify the quantum properties of SMMs Giant SMMs represent a meeting of the two worlds of nanoscale magnetism, the traditional (‘top-down’) and molecular (‘bottom-up’) approaches

30. Dr. Tasos Tasiopoulos (Mn 84, Mn 12 ) Dr. Muralee Murugesu (Mn 25 ) Dr. Philippa King (Mn 12, Mn 18 ) Nuria Aliaga (Mn 4, [Mn 4 ] 2 ) Nicole Chakov (Mn 12 ) Alina Vinslava (Mn 84, Mn 70 ) Khalil Abboud (U. of Florida, X-ray) Naresh Dalal (Florida State Univ) Stephen Hill (U. of Florida, Physics) Ted O’Brien (IUPUI) Wolfgang Wernsdorfer (Grenoble) $$ NSF and NSF/NIRT $$ Acknowledgements

32. [Mn 12 Ac][Mn 12 Bu t Ac] S10 D (K)-0.72-0.73 U eff (K) 6468 DC Reduced Magnetization fit S = 10 D = - 0.51 cm -1 = - 0.73 K AC Susceptibility Magnetic Properties of [Mn 12 O 12 (O 2 CCH 2 Bu t ) 16 (MeOH) 4 ] (Mn 12 Bu t Ac) Arrhenius Plot U eff = 67.8 K τ 0 = 5.58 x 10 -8 s Muralee Murugesu

33. Landau-Zener Tunnelling (1932) Tunnelling probability at an avoided level crossing