2D molecular magnets with weak topological invariant magnetic moments: Mathematical prediction of targets for chemical synthesis

TL;DR

This paper predicts 2D molecular magnets with robust magnetic moments that are stable under shape deformations, using a mathematical model to identify targets suitable for chemical synthesis.

Contribution

It introduces a mathematical framework showing that certain 2D ferromagnetic molecular magnets have a total spin as a weak topological invariant, depending only on the arrangement of spin centers.

Findings

Total spin becomes a weak topological invariant with 20-50 spin centers.

Robustness is enhanced in 2D ferromagnetic MMs with few spin rings.

Total spin stability persists under random shape deformations.

Abstract

An open problem in 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 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 centers lie in-plane and all spin center interactions are ferromagnetic, the total spin of the molecule is a `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 MMs to be a weak topological invariant. The robustness effect is particularly enhanced for 2D ferromagnetic MMs that possess a small number of spin rings in the structure.