The $s=1/2$ Antiferromagnetic Heisenberg Model on Fullerene-Type Symmetry Clusters

Abstract

The $s_i=1/2$ nearest neighbor antiferromagnetic Heisenberg model is considered for spins sitting on the vertices of clusters with the connectivity of fullerene molecules and a number of sites $n$ ranging from 24 to 32. Using the permutational and spin inversion symmetries of the Hamiltonian the low energy spectrum is calculated for all the irreducible representations of the symmetry group of each cluster. Frustration and connectivity result in non-trivial low energy properties, with the lowest excited states being singlets except for $n=28$. Same hexagon and same pentagon correlations are the most effective in the minimization of the energy, with the $n=32-D_{3h}$ symmetry cluster having an unusually strong singlet intra-pentagon correlation. The magnetization in a field shows no discontinuities unlike the icosahedral $I_h$ fullerene clusters, but only plateaux with the most pronounced for $n=28$. The spatial symmetry as well as the connectivity of the clusters appear to be important for the determination of their magnetic properties.

Extended to include low energy spectra, correlation functions and magnetization data of clusters up to 32 sites

References in corpus (4)

• Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
• The Antiferromagnetic Heisenberg Model on Clusters with Icosahedral Symmetry
• Strong Correlation Effects in the Fullerene C20
• Quantum Theory of Molecular Magnetism

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• Ground-state magnetic properties of spin ladder-shaped quantum nanomagnet: Exact diagonalization study
• Origin of the classical magnetization discontinuities of the dodecahedron