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Magnetic Molecules - A tutorial (“up to speed” in 40 minutes!)

Magnetic Molecules - A tutorial (“up to speed” in 40 minutes!). Marshall Luban (luban@ameslab.gov) Ames Laboratory (U.S. Dept. of Energy) & Department of Physics and Astronomy, Iowa State University, Ames, Iowa, 50011, USA. ISCOM Conference. Key West, Florida, USA Sept 14 , 2005.

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Magnetic Molecules - A tutorial (“up to speed” in 40 minutes!)

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  1. Magnetic Molecules - A tutorial (“up to speed” in 40 minutes!) Marshall Luban (luban@ameslab.gov) Ames Laboratory (U.S. Dept. of Energy) & Department of Physics and Astronomy, Iowa State University, Ames, Iowa, 50011, USA ISCOM Conference Key West, Florida, USA Sept 14 , 2005

  2. Outline • Introduction • What are “magnetic molecules”? • Examples • Character, tools, and requirements for progress • Issues and motivation • Energy spectrum • “Frustration” • equilibrium characteristics • competing phases and metamagnetic transitions • Quantum vs classical behavior (intrinsic spin, temperature) • Magnetization relaxation for pulsed magnetic fields • Exotic emerging systems • Summary • Outlook • Acknowledgments

  3. What are magnetic molecules? • Primary focus - “single” magnetic molecules: • Crystalline samples • Intra-molecular: • N embedded paramagnetic ions (“spins”, s = 1/2,..., 5/2, …) • Apart from “warts”… Heisenberg exchange, spins i,j: • Inter-molecular: Negligible magnetic interactions • Macroscopic number of identical, uncoupled molecules • Scores of very diverse compounds available… • Some examples…

  4. “Ferric Wheel” {Fe10} :[Fe(OCH3)2 (O2CCH2Cl)]10 Fe3+ ions, spins 5/2; Hilbert space: D = 610= 6.05 × 107

  5. {Cr12Ni3}, an S-shaped molecule S.L. Heath et al. Angew. Chem. Int. Ed. 43, 6132 (2004) D = 412×33 = 4.53×108

  6. The giant Keplerate {Mo72Fe30} [Mo72Fe30O252(Mo2O7H2O)2 (Mo2O8H2(H2O)) (CH3COO)12(H2O)91]•150H2O  {Mo72Fe30 }•150H2O Achim Müller’s creation! (U. Bielefeld) Mol. Wt. 18,700 g/mol (approx.)

  7. The giant Keplerate {Mo72Fe30} • 30 paramagnetic Fe3+ ions (spins s = 5/2) on the vertices of an icosidodecahedron • Hilbert space dimension: 630 ≈ NA/3 ChemPhysChem, 2, 517-521 (2001)

  8. Character of the field • Highly interdisciplinary! • Exotic chemical synthesis • Experimental methods • Low-field susceptibility vs T • Magnetization vs H (pulsed, static, 60 Tesla) • Inelastic neutron scattering • Resonance methods (ESR, NMR, …) • Optical studies • Theoretical methods • Analytical methods • Matrix diagonalization methods, • Classical spin dynamics simulations • Quantum Monte Carlo methods • Modern statistical mechanics

  9. Necessary requirements for progress… • Strong, highly-interactive team • “suppliers”- incredibly creative synthetic chemists • experimentalists • theorists • Establish team effort (multi-institutional, multi-national) • Broad spectrum of expertise, with few gaps • Sophisticated, expensive instrumentation and facilities • Great patience

  10. Some of my collaborators… • Chemical Synthesis • L. Cronin (U. Glasgow) • *P. Kögerler (Ames Lab) • A. Müller (U. Bielefeld) • R.E.P. Winpenny (U. Manchester) • Experiment • F. Borsa (NMR, Ames Lab & U. Pavia) • Y. Ajiro (Pulsed fields, U. Kyoto) • V. Garlea, C. Stassis, D. Vaknin, J. Zarestky (Neutrons; Ames Lab) • *J. Musfeldt (Optics, U. Tennessee) • S. Nagler (Neutrons, Oak Ridge) • H. Nojiri (Pulsed fields, ESR, U. Tohoku) • R. Prozorov (Static fields-mK, Ames Lab) • B-J. Suh (NMR, Seoul) • *J. van Slageren (ESR, U. Stuttgart) • Theory • K. Bärwinkel, H-J. Schmidt, *J. Schnack, (U. Osnabrück) • C. Schröder (U. Applied Sci. - Bielefeld; Ames Lab) • L. Engelhardt & I. Rousochatzakis (PhD students, Ames Lab)

  11. Outline • Introduction • What are “magnetic molecules”? • Examples • Character, tools, and requirements for progress • Issues and motivation • Energy spectrum • “Frustration” • equilibrium characteristics • competing phases and metamagnetic transitions • Quantum vs classical behavior (intrinsic spin, T) • Magnetization relaxation for pulsed magnetic fields • Exotic emerging systems • Summary • Outlook • Acknowledgments

  12. Tool Box for Quantum Spin Systems • Analytical methods: • Only very small or specialized systems: (dimer, trimer, tetrahedron,…pantahedron; square, octahedron) • Matrix methods: • Full set, D < 106; Lanczos method for a small subset • Energy eigenvalues • Partition function derivatives • Magnetization vs field • Susceptibility vs temperature • Specific heat vs temperature • Time-dep. correlation funcs. (but…zillions of matrix elements!!!) • Quantum Monte Carlo: (Partition function derivatives) • Non-frustrated - all T • Frustrated -

  13. ABC’s of a Heisenberg energy spectrum • 6 spins s = 3/2, D = 4096 • Accessible to experiment (neutrons, M vs H, ESR)

  14. An antiferromagnetically coupled tetrahedron of s = 1 spin centers (e.g. {Ni4Mo12}) with J = –5 K:

  15. HC 2HC 3HC 4HC

  16. 4HC 3HC HC 2HC For T = 0 K – only the ground state is populated:

  17. Quantum Monte Carlo…The tool of choice… {Cr12Ni3}, D = 4.53x108, L. Engelhardt (2005)

  18. The Tool Box of Classical Spin Dynamics C. Schröder (Bielefeld, Ames) What can be calculated? • Classical ground state properties • Thermal properties • Susceptibility vs T • Magnetization vs H • Specific heat vs T • Equilibrium time-dependent spin correlation functions • NMR relaxation times 1/T1 • Neutron scattering cross sections • Effects of time-dependent fields (e.g. pulsed fields) Accuracy of classical treatment of quantum spins?…

  19. Icosidodecahedron - a 3-colorable graph M. Axenovich & M. Luban, Phys. Rev. B. 63, 100407(R), (2001)  Frustrated Spin Ordering!

  20. Determination of Static Thermal Properties A. Müller, M. Luban, C. Schröder, R. Modler, P. Kögerler, M. Axenovich, J. Schnack, P. Canfield, S. Bud’ko, N. Harrison “Classical and Quantum Magnetism in Giant Keplerate-type Magnetic Molecules“ ChemPhysChem, Vol. 2, pp. 517-521, (2001) T [K]

  21. Icosidodecahedron: a 3-colorable graph -> “umbrella” phase Classical, 0 K R. Modler, 0.46 K (J =1.57 K, g = 1.974, s = 5/2)

  22. Surprise for T > 0 K, at 1/3 saturation field

  23. dM/dB in 3-colorable classical systems

  24. Competing phases in 3-colorable systems • See C. Schröder et al., Phys. Rev. Lett. 94, 017205 (2005)

  25. Quantum rotational band model for {Mo72Fe30} J. Schnack, M. Luban, & R. Modler, Europhys. Lett. 56, 863 (2001)

  26. Energy 1 2 1: 0.68 meV 2: 0.70 meV 3: 27 µeV 3 The target for neutron scattering… {Mo72Fe30}

  27. V. Garlea et al. (2005) {Mo72Fe30} - Inelastic neutron scattering (zero magnetic field) Experiment Theory* * Simplified version of rotational band model- Single non-zero matrix element |Sf - Si| = 0, 1 and |Mf - Mi| = 0, 1

  28. Competing phases & metamagnetic transition in the antiferromagnetic Heisenberg icosahedron

  29. Metastability, Antiferro Icosahedron C. Schröder et al, Phys Rev Lett., 94, 207203 (2005) Isotropic, nearest-neighbor Heisenberg exchange only!

  30. Magnetization relaxation in pulsed magnetic fields I. Rousochatzakis et al. Phys. Rev. Lett. 94, 147204 (2005) {V6}: Two very weakly coupled spin triangles ~ 58 K

  31. “Dynamical hysteresis” loops… T = 1.7 K B t (ms)

  32. Increased temperature → shorter relaxation time T = 4.2 K t (ms)

  33. Adiabatic Landau-Zener-Stückelberg transitionsand dynamical hysteresis T = 1.7 K

  34. Outline • Introduction • What are “magnetic molecules”? • Examples • Character, tools, and requirements for progress • Issues and motivation • Energy spectrum • “Frustration” • equilibrium characteristics • competing phases and metamagnetic transitions • Quantum vs classical behavior (intrinsic spin, temperature) • Magnetization relaxation for pulsed magnetic fields • Exotic emerging systems • Summary • Outlook • Acknowledgments

  35. Dodecahedron - A strategy (P. Kögerler et al) Modifying the inner surface of a {Mo132}-type Keplerate allows coordination of up to 20 transition metal ions defining the vertices of a dodecahedron {Mo132M20}, 2.9 nm diameter

  36. {Mo72V30}, spin 1/2 (quantum) version of {Mo72Fe30} First steps… A. Müller, et al., Angew. Chem. 44, 3857 (2005) B. Botar, P. Kögerler, C. Hill, Chem. Commun. 3138 (2005) Warped icosidodecahedron- Inversion symmetry only Refined version under construction, P. Kögerler & B. Botar

  37. Ferrimagnetic Fe-V Keplerates {Mo80Fe7V15} P. Kögerler et al. Chem. Commun. (submitted)

  38. Ferrimagnetic Fe-V Keplerates {Mo80Fe11V11}

  39. Summary, Outlook, Acknowledgements • Summary • Magnetic molecules, as zero-dimensional objects, exhibit new and exciting phenomena • Strong inter-disciplinary, collaborative effort • Numerous powerful experimental and theoretical tools exist • Outlook • Many new and exotic systems are emerging • Controlled design of nanomagnetic systems • Pre-adolescent stage: Exciting adventures ahead • Acknowledgements • Especially my many wise collaborators… • U.S. Department of Energy • Organizers of ISCOM  Thank you!

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