Introduction to Molecular Magnets Jason T. Haraldsen Advanced Solid State II 4/17/2007

Basic Molecular Magnets Mn 12 -acetate, S = 10 Fe 8 Br 8, S = 10 V 15, S = 1/2 [V 15 As 6 O 42 (H 2 O)]K 6 [Mn 12 O 12 (CH 3 OO) 16 (H 2 O) 4 ]. 2CH 3 COOH. 4H 2 O [(C 6 H 5 N 3 ) 6 Fe 8 (µ 3 -O) 2 (µ 2 -OH) 12 ]Br 7 (H 2 O)Br. 8H 2 O 4 Spin-3/2 8 Spin-2 8 Spin-5/2 15 Spin-1/2

Molecular Magnets: By Definition Isolated clusters containing ionic spins ranging from as few as two to up to several dozen. Molecular magnets are not limited to molecular solids. No long range order. S. Nagler et. al. Unpublished NaCuAsO 4, S = 0

Heisenberg Spin-Spin Exchange Hamiltonian Anisotropic and Zeeman terms may be added to give a more complete description of a given material. J > 0 is antiferromagnetic J < 0 is ferromagnetic

Molecular Magnets: Theory and Model Heisenberg Hamiltonian plus anisotropy and Zeeman terms

Molecular Magnets: Theory and Model Ising and XY Variations

Molecular Magnets: Dimensionality Hilbert Space For mixed valance systems For spin symmetric systems Examples of how dimensionality increases in systems Spin-1/2 Dimer Spin-1/2 Pentamer Spin-3/2 Pentamer [Mn 12 O 12 (CH 3 OO) 16 (H 2 O) 4 ]. 2CH 3 COOH. 4H 2 O

Experimental Techniques Bulk Quantities Magnetization Magnetic Susceptibility Heat Capacity Microscopic Quantities Inelastic Neutron Scattering Raman Scattering Infrared Spectroscopy

Magnetization Examines the overall magnetic moment. Steps denote magnetic spin flips in the material. J. Schnack et. al. PRB (2006)

Magnetic Susceptibility Change in magnetization over change in magnetic field. J.T. Haraldsen et. al. PRB (2005)

Heat Capacity The ability of a material to store heat as a function of temperature. The peak corresponds to either a cooperative phase transition or an anomaly. J.T. Haraldsen et. al. PRB (2005)

Effects of Dimensionality on Complexity J.T. Haraldsen et. al. PRB (2005)

Inelastic Neutron Scattering Excitation Energy Structure Factor Intensity Measures the dispersion relationship of energy transfer and momentum transfer. Tennant et. al, PRL (2005)

Infrared and Raman Spectroscopy Not usually thought of when discussion magnetic transitions. Activated when a magnetic system has an anisotropic interaction. Usually coupled to lattice excitations through the typically selections rules of dipole moment (Infrared) and polarizability (Raman). T. Room et. al. PRB (2002) - NaVO

Simplest Molecular Magnet: Spin 1/2 Dimer

The Textbook Dimer: VO(DPO 2 )0.5H 2 O Tennant et. al, PRL (2005) Spin-1/2 vanadium system. Vanadium ions are arranged structurally in a lattice. Magnetic properties show the presence of an isolated dimer.

Magnetic Susceptibility of VO(DPO 2 )0.5H 2 O J. W. Johnston et. al., J. Am. Chem. Soc. (1984)

Inelastic Neutron Scattering of VO(DPO 2 )0.5D 2 O D.A. Tennant et. al. PRL (1997)  E = J = 7.86 meV A = 4.37 Å Predicted Experiment Energy (meV) q (Å -1 )

The Textbook Dimer: VO(DPO 2 )0.5H 2 O The use of magnetic measurements on the material of VODPO 4 ½ D 2 O clarified the magnetic structure of the material. Tennant et. al, PRL (2005) V 4+

Summary Molecular magnets are magnetically isolated clusters that exhibit no long range magnetic ordering Many techniques, both bulk and microscopic, can be used to determine the magnetic structure. Magnetic structure is not always obvious from an examination of the crystal structure.