Single Molecular Magnets Ge,Weihao

Introduction What is Single Molecular Magnet? Configuration: metal atom linked by oxygen, packed in ligands Described as a total single spin; size and anisotropy has great effect Why are they interesting? Theoretical: quantum behavior at mesoscopic level Application: Quantum computer: quantum interference and coherence High-density storage device Internal memory effect high integration Other applications Two kinds of these clusters Big integer spin ½ spin big molecule

Superparamagnetism Superparamagnetism Origin of superparamagnetism paramagnetism below Curie’s temperature large susceptibility superparamagnetism limit Origin of superparamagnetism magnetism: result of spin alignment thermal excitation, ferromagnetism <-> paramagnetism small scale, below Tc: thermal excitation destroys the ordering between the clusters thermal excitation cannot upset alignment within the cluster ferro~ inside & para~ outside => treated as a large spin as a whole Experiment results stepped hysteresis can be found below certain temperature. frequency dependent AC susceptibility

Quantum Tunneling Magnetization Experiment steps found in hysteresis of Mn12 cluster Model two – well model resonant tunneling thermally assisted QTM & pure QTM A commonly used form of Hamiltonian axial anisotropic term Zeeman splitting term transverse anisotropic term Experiments Model A commonly used form of Hamiltonian spins within: Heisenberg model total spin: treated as a large spin QT relaxation also. equally distributed in wells apply magnetic field -> all in 1 well field turned off -> all in 1 well tunnel back, relaxation -> relaxation time

Integer Spin SMM: Mn12 Significance Structure Hamiltonian archeological reason: first synthesized SMM & QTM first observed most widely studied Structure Mn3+, external octagon; Mn4+, internal tetrahedron. Ground state: S=10 Hamiltonian symmetry: lowest even power of transverse terms is 4 transition: probably exist low-ordered odd-powered terms

Integer Spin SMM: Fe4 Structure Hamiltonian Fe3+: centered triangle, C2 symmetry Ground state: S=5 Hamiltonian general form Advantages over Mn12 in application More efficient tunneling longer relaxation time less affected when attached to a surface stability

½ spin big molecule: V15 Structure Experimental result a center triangle between two hexagons S=1/2, no large energy barrier, large zero field splitting Experimental result hysteresis observed Rabi oscillation coherence time: ~100 μs Theoretical approaches dissipative two-level system: Landau - Zener transition exchange interaction: “spin rotation in a phonon bath” Structure Properties Theoretical approaches two-level model: relatively large zero field splitting ~80mK spin hamiltonian: hexagon cancels by anteferromagnetic coupling; only consider triangle exchange term; anisotropy term; interaction with nuclear spin; zeeman term coherence time limited by nuclear spin

Summary General introduction to single molecular magnets quantum behavior beyond the microscopic scale in these clusters Origin of the magnetism of SMM Quantum Tunneling Magnetization A result of size and anisotropy Integer spin clusters and ½ spin clusters integer: easy to interpreted by large-spin approximation ½ spin: lack of barrier, tunneling caused by spin-phonon interaction long-lived coherence

References QTM: Gatteschi,D.; Sessoli,R. “Quantum tunneling magnetization and related phenomena in Molecular Materials.” Angew. Chem.Ed. 42(3), 2003,pp.268 Mn12: Friedman,J., Sarachik,M. “Mesoscopic Measurement of Resonant Magnetization Tunneling in High-Spin Molecules.” PRL, 76(20),1996, pp.3830 Barra, A., et.al. “High-frequency EPR spectra of a molecular nanomagnet: Understanding quantum tunneling of the magnetization.” PRB. 56(13), 1997, pp.8192 Fe4: Accorsi,S., et.al. “Tuning Anisotropy Barriers in a Family of Tetraion(III) Single-Molecule Magnets with an S = 5 Ground State” JACS. 128(14), 2006, pp.4742-4755 Wernsdorfer,W., et.al. “X-ray Magnetic Circular Dichroism Picks out Single-Molecule Magnets Suitable for Nanodevices.” Adv.Mater. 21, 2009, pp.167-171 Sessoli,R., et.al. “Magnetic memory of a single-molecule quantum magnet wired to a gold surface.” Nature Mater. 8, 2009, pp.194 V15: Müller,A., et.al. “Quantum Oscillation in a molecular magnet.” Nature lett. 453, 2008 pp.203 Choirescu, et.al. “Environmental effects on big molecule with spin ½.” J.Appl.Phys.87(9) 2000 pp.5496