TY - JOUR

T1 - Two-dimensional molecular magnets with weak topological invariant magnetic moments

T2 - Mathematical prediction of targets for chemical synthesis

AU - Packwood, D. M.

AU - Reaves, K. T.

AU - Federici, F. L.

AU - Katzgraber, H. G.

AU - Teizer, W.

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2013/12/8

Y1 - 2013/12/8

N2 - 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.

AB - 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.

KW - Ising model

KW - Mathematical chemistry

KW - Molecular magnets

KW - Single-molecule magnets

KW - Spin Hamiltonian

KW - Topological invariance

UR - http://www.scopus.com/inward/record.url?scp=84888184332&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888184332&partnerID=8YFLogxK

U2 - 10.1098/rspa.2013.0373

DO - 10.1098/rspa.2013.0373

M3 - Article

AN - SCOPUS:84888184332

VL - 469

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8444

IS - 2160

M1 - 20130373

ER -