Inelastic neutron scattering on an Mn10 supertetrahedron: assessment of exchange coupling constants, ferromagnetic spin waves and an analogy to the Hückel method.

The synthesis, crystal structure and magnetic characterisation by magnetisation and inelastic neutron scattering (INS) of a mixed-valent Mn(10) supertetrahedral aggregate [Mn(III)(6)Mn(II)(4)(µ(4)-O)(4)(µ(3)-N(3))(3)(µ(3)-Br)(Hmpt)(6)(Br)]Br(0.7)(N(3))(0.3)·2MeOH·3MeCN (1) (H(3)mpt=3-methylpentan-1,3,5-triol) is reported. The magnetic core of the molecule can be described as an octahedron of six S=2 Mn(III) ions with four faces, each capped by a S=5/2 Mn(II) ion such as to form the supertetrahedron. Unlike most related complexes, the molecular symmetry is slightly reduced from approximately T(d) to C(3). The magnetic data reveal a total spin of S=22 in the ground state due to ferromagnetic exchange couplings within the molecule. The combined INS and magnetic data permits the accurate determination of the exchange coupling constants. Two types are found. The couplings between the Mn(III) ions in the inner octahedron are characterised by J(a)=18.4(3) K, whereas the couplings between the apical Mn(II) ions to the neighbouring Mn(III) ions are given by J(b)=7.3(2) K. The significantly larger coupling strength J(a) as compared to J(b), and the near-T(d) symmetry have profound consequences on the energy spectrum, which are discussed and carefully analysed. In particular, the observed INS spectra can consistently be reproduced by a simplified model in which the inner octahedron is replaced by one large spin of length S(0)=12. This model provides intuitive insight into the structure of the magnetic spectrum. Additionally, the magnetic excitations at low temperature are analysed within the frame of ferromagnetic linear spin-wave theory, which permits an analytical calculation of the energy levels. For ferromagnetic clusters, a close analogy to the Hückel method of electronic structure calculation can be drawn, which allows one to grasp the results of the spin-wave theory or the magnetic excitation spectrum, respectively, in a chemical language.