Magnetic Anisotropy of Two Cyclic Hexanuclear Fe(III) Clusters Entrapping Alkaline Ions O. Waldmann,* ,† J. Schu 1 lein, † R. Koch, † P. Mu 1 ller, † I. Bernt, ‡ R. W. Saalfrank, ‡ H. P. Andres, § H. U. Gu 1 del, § and P. Allenspach | Physikalisches Institut III, Universita ¨t Erlangen-Nu ¨rnberg, D-91058 Erlangen, Germany, Institut fu ¨r Organische Chemie, Universita ¨t Erlangen-Nu ¨rnberg, D-91058 Erlangen, Germany, Departement fu ¨r Chemie und Biochemie, Universita ¨t Bern, CH-3000 Bern 9, Switzerland, and Laboratorium fu ¨r Neutronenstreuung, ETHZ & PSI Villigen, CH-5232 Villigen PSI, Switzerland ReceiVed June 4, 1999 The magnetic anisotropy of the two cyclic hexanuclear Fe(III) clusters [Li⊂Fe 6 L 6 ]Cl‚6CHCl 3 and [Na⊂Fe 6 L 6 ]- Cl‚6CHCl 3 ,L ) N(CH 2 CH 2 O) 3 , was investigated. Based on a spin Hamiltonian formalism, the magnetic anisotropy was calculated exactly to first order, i.e., in the strong exchange limit, using Bloch’s perturbational approach and irreducible tensor operator techniques. Experimentally, the magnetic anisotropy was investigated by magnetic susceptibility and high-field torque magnetometry of single crystals as well as inelastic neutron scattering. It is demonstrated that torque magnetometry provides a valuable tool for the study of magnetic anisotropy in spin cluster complexes. The experimental data could be accurately reproduced by the calculations, and the different methods yield consistent values for the coupling constants and zero-field-splitting parameters. Both the anisotropy and the exchange interaction parameter are found to increase with increasing Fe-O-Fe angle. 1. Introduction Dinuclear complexes of magnetic transition and rare earth metal ions have been used extensively for a detailed study of the nature of exchange interactions. 1,2 They serve as molecular model systems for magnets with extended interactions. Mag- netostructural correlations have been established in related series of complexes, 3,4 and in some cases the orbital exchange pathways have been identified. 5 In contrast to systems with extended interactions, the effective Hamiltonians describing the magnetic coupling of dinuclear complexes can be solved exactly. In recent years a new class of high-nuclearity spin clusters (HNSC) has become the focus of very intensive research activity, both by chemists and physicists. At first, this was driven by synthetic chemists coming up with species exhibiting an enormous variety of structures. 6-8 Transition metal and rare earth metal ions as well as organic radicals were used as building blocks for polynuclear species. More recently, it was found that some of these spin clusters exhibit very unusual physical properties. Mn 12 O 12 (O 2 CCH 3 ) 16 (H 2 O) 4 and [Fe 8 O 2 (OH) 12 - (tacn) 6 ] 8+ with cluster ground states S ) 10 and S ) 8, respectively, have become prototypes of this specific class of spin clusters. 9,10 At very low temperatures they exhibit quantum tunneling as well as magnetic hysteresis effects. 11,12 The synthetic and magnetic properties of several ferric wheels with the number of Fe(III) ions ranging from 6 to 18 have been reported. 7,13-20 They represent ideal model systems for quantum spin chains which are relevant for the calculation of thermo- dynamic properties of one-dimensional magnetic materials. Recently we reported the new hexanuclear wheels [Li⊂Fe 6 L 6 ]- Cl‚6CHCl 3 (1) and [Na⊂Fe 6 L 6 ]Cl‚6CHCl 3 (2), L ) N(CH 2 - CH 2 O) 3 . 18 The alkali ion is situated at the center of the hexagonal wheel and stabilizes the complex. The perchlorate salts of the same complexes, [Li⊂Fe 6 L 6 ]ClO 4 ‚2MeOH (3) and [Na⊂Fe 6 L 6 ]ClO 4 ‚2MeOH (4), as well as the alkali free [Fe 6 L 6 ]‚ 6MeOH (5) cluster were synthesized using a different strategy. Their magnetic properties were reported in ref 20. In the present paper we report a detailed study of the magnetic properties of the Fe 6 clusters 1 and 2. Besides magnetic susceptibility measurements we applied torque magnetometry † Physikalisches Institut III, Universita ¨t Erlangen-Nu ¨rnberg. ‡ Institut fu ¨r Organische Chemie, Universita ¨t Erlangen-Nu ¨rnberg. § Universita ¨t Bern. | ETHZ & PSI Villigen. (1) Kahn, O. W. Molecular Magnetism; VCH Publishers: New York, 1993. (2) Willet, R. D.; Gatteschi, D.; Kahn, O. Magneto-Structural Correlations in Exchange Coupled Systems; NATO ASI Series; D. Reidel Publishing Company: Dordrecht, Holland, 1985. (3) Hatfield, W. E. In ref 2, p 555. (4) Weihe, H.; Gu ¨del, H.-U. J. Am. Chem. Soc. 1997, 119, 6539. (5) McCarthy, P. 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