[figure: 9.7 cm]

Néel probability in antiferromagnetic ferric wheels Fe_{6} and Fe_{10}

Wojciech Florek, Sylwia Bucikiewicz

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

Antiferromagnetic ferric wheels Fe_{n}, n = 6, 10, 18, are profound examples of molecules consisting of transition-metal ions bridged by oxo-groups with complete compensation of single-ion spins, 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 Hisenberglike 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. 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 the probability of finding a system in the classical antiferromagnetic ground-state, hence in the Néel state. The global Néel probability is also taken into account, i.e. we analyze all states with maximal sublattice magnetization (15/2 i 25/2 for n = 6, 10, respectively) and the total magnetization M = 0. The Néel probability (not global) shows exponential decreasing with respect to the energy per spin E for all values of the total spin S, so it can be written as ln p_{N} = −(αE + β), α, β > 0. Both coefficients depend exponentially on S, but their sum is constant (in good approximation).

[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