title: Two-dimensional molecular magnets with weak topological invariant magnetic moments: mathematical prediction of targets for chemical synthesis.
abstract: An open problem in applied mathematics is to predict interesting molecules that are realistic targets for chemical synthesis. In this paper, we use a spin Hamiltonian-type model to predict molecular magnets (MMs) 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 MMs in which all spin centres lie in-plane and all spin centre interactions are ferromagnetic, the total spin of the molecule is a 'weak topological invariant' when the number of spin centres is sufficiently large. By weak topological invariant, we mean that the total spin of the molecule depends only upon the arrangement of spin centres in the molecule, and is unlikely to change under shape deformations to the molecule. Our calculations show that only between 20 and 50 spin centres are necessary for the total spin of these MMs to be a weak topological invariant. The robustness effect is particularly enhanced for two-dimensional ferromagnetic MMs that possess a small number of spin rings in the structure.
authors.affiliation: WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan.
authors.forename: D M
authors.initials: DM
authors.lastname: Packwood
authors.affiliation: WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ; Materials Science and Engineering , Texas A&M University , College Station, TX 77843-3003, USA.
authors.forename: K T
authors.initials: KT
authors.lastname: Reaves
authors.affiliation: WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ; Department of Physics and Astronomy , University College London , Gower Street, London WC1E 6BT, UK.
authors.forename: F L
authors.initials: FL
authors.lastname: Federici
authors.affiliation: Materials Science and Engineering , Texas A&M University , College Station, TX 77843-3003, USA ; Department of Physics and Astronomy , Texas A&M University , College Station, TX 77843-4242, USA.
authors.forename: H G
authors.initials: HG
authors.lastname: Katzgraber
authors.affiliation: WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ; Materials Science and Engineering , Texas A&M University , College Station, TX 77843-3003, USA ; Department of Physics and Astronomy , Texas A&M University , College Station, TX 77843-4242, USA.
authors.forename: W
authors.initials: W
authors.lastname: Teizer
keywords: Ising model; mathematical chemistry; molecular magnets; single-molecule magnets; spin Hamiltonian; topological invariance