[figure: 9.7 cm]

Spin correlations in antiferromagnetic ferric wheels Fe_{6} and Fe_{10}

Sylwia Bucikiewicz, Wojciech Florek

Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

There are several mesoscopic clusters composed of transition-metal ions (Mn, Ni, Co etc.) bridged by oxo-groups. Antiferromagnetic ferric wheels Fe_{n}, n = 6, 10, 18, are profound examples of such molecules, when compensation of single-ion spins is complete, so the total spin S = 0. On the other hand these aggregates can be very well described as finite spin systems with dihedral symmetry group (D_{n}) and Hisenberg-like interactions between the nearest neighbours. The two first rings (Fe_{6} and Fe_{10}) are investigated with application of group-theoretical and combinatorial methods followed by exact determination of states with given S and the total magnetization M = 0. The largest ferric wheel (Fe_{18}) is a subject of the so-called ‘combinatorial explosion’ (there are more than 10^{14} basic spin configurations) and left out in the present stage of calculations. It seems that we can perform some calculations for Fe_{14} ring (about 8 · 10^{10} basic states), but synthesis of such a molecule has not been reported yet. Having determined eigenstates of a given Heisenberg Hamiltionan (for states with M = 0 and labelled by one-dimensional irreps of the symmetry group) we are able to investigate their properties such as spin correlations ω_{r}^{z}, for 1 ≤ r ≤ n/2. It occurs that ω_{1}^{z} is very well approximated by linear function aE + b, where E is energy per spin, but the coefficients a, b depend on the total spin S: a(S) is a linear function αS + β with α, β > 0, whereas b(S) is best fitted by the parabolic function −γS^{2} + δS − ε with γ, δ, ε > 0.

[figure: 13.4 cm]

Subject category :

6. Theory of Magnetism

Presentation mode : poster

Corresponding author : Wojciech Florek

Address for correspondence : Institute of Physics, Adam Mickiewicz University Umultowska 85, 61-614 Poznań, Poland

Email address : florek@spin.amu.edu.pl