具有弱拓扑不变磁矩的二维分子磁体：化学合成目标的数学预测
2D molecular magnets with weak topological invariant magnetic moments: Mathematical prediction of targets for chemical synthesis
摘要：
应用数学中的一个开放性问题是预测化学合成的现实目标。在本文中，我们使用自旋汉密尔顿型模型来预测分子磁体（MM），其磁矩在分子随机形状变形下本质上是鲁棒的。使用概率收敛的概念，我们表明，对于所有自旋中心位于平面内，所有自旋中心的相互作用是铁磁性的，当自旋中心的数量足够大时，分子的总自旋是一个“弱拓扑不变量”。弱拓扑不变量是指分子的总自旋仅取决于分子中自旋中心的排列，并且不太可能在分子的形状变形下发生变化。我们的计算表明，只有20和50之间的自旋中心是必要的，这些电子的总自旋是一个弱拓扑不变量。对于在结构中具有少量自旋环的2D铁磁磁体，鲁棒性效果特别增强。
英文摘要：
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.
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