Daniel M. Packwood, Kelley T. Reaves, Filippo Leonida Federici, Helmut G. Katzgraber, Winfried Teizer
An open problem for applied mathematics is to predict interesting molecules which are realistic targets for chemical synthesis. In this paper, we use a spin Hamiltonian-type model to predict single molecule magnets (SMMs) with magnetic moments that are intrinsically robust under random shape deformations to the molecule. Using the concept of convergence in probability, we show that for SMMs in which all spin centers lie in-plane and all spin center interactions are ferromagnetic, the total spin of the molecule is `weak topological invariant' when the number of spin centers is sufficiently large. By weak topological invariant, we mean that the total spin of the molecule only depends upon the arrangement of spin centers in the molecule, and is unlikely to change under shape deformations to the molecule. Our calculations show that only between 20 and 50 spin centers are necessary for the total spin of these SMMs to be a weak topological invariant. The robustness effect is particularly enhanced for 2D ferromagnetic SMMs that possess a small number of spin rings in the structure. Our results therefore give reasonable targets for synthetic chemistry, and may help identify SMMs that have intact magnetic properties upon deposition onto metal surfaces.
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http://arxiv.org/abs/1306.1273
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