Defect-induced magnetism in two-dimensional materials continues to attract attention due to potential applications in spintronics. Using density-functional theory (DFT) approach, we report on the magnetization in graphene containing carbon vacancy defects, i.e., nanoporous graphene. We consider single nanopores consisting of up to ten vacancies and interacting nanopores consisting in vacancy pairs, divacancy pairs and vacancy-divacancy pairs, separated at varying distances. We found that the interactions between the nanopores weaken as their separation increases such that the formation energy tends to the value for the single nanopore while the magnetic moment tends to the sum of individual magnetic moments. Introducing additional nanopore to a pre-existing nanopore may enhance graphene's magnetic moment, however, the nanopores may also interact to induce zero magnetization. The enhancement, reduction or total annihilation of the magnetic moments may be adduced to interactions between the individual nanopores resulting in the saturation of the dangling bonds and/or the realignment of the electrons responsible for the magnetization. Also, our calculated values of induced magnetic moment of different single nanopores enable us to determine an empirical model for predicting the total magnetic moment as a function of nanopore size. The model is able to produce the magnetic moment of small and large nanopore sizes which are in excellent agreement with the DFT calculated values. Finally, we found our results to be consistent with recent experimental studies on magnetic response of graphene containing vacancies introduced via a synthesis process or ion irradiation, respectively.

由于自旋电子学中的潜在应用，二维材料中的缺陷感应磁性继续受到关注。使用密度泛函理论（DFT）方法，我们报道了含碳空位缺陷的石墨烯（即纳米多孔石墨烯）中的磁化强度。我们考虑由最多十个空位组成的单个纳米孔，以及由空位对，双空位对和空位-空对对组成的相互作用纳米孔，它们以不同的距离分开。我们发现纳米孔之间的相互作用随着它们的分离增加而减弱，使得形成能趋于单个纳米孔的值，而磁矩趋于单个磁矩的总和。在现有的纳米孔中引入其他纳米孔可能会增强石墨烯的磁矩，但是，纳米孔还可相互作用以诱导零磁化。磁矩的增强，减少或完全an灭可归因于各个纳米孔之间的相互作用，从而导致悬空键饱和和/或负责磁化的电子重新排列。同样，我们计算的不同单个纳米孔的感应磁矩值使我们能够确定经验模型，以预测总磁矩随纳米孔尺寸的变化。该模型能够产生大和小纳米孔尺寸的磁矩，这些磁矩与DFT计算值非常吻合。最后，