Xu Wei, Che J G
Department of Physics and Collaborative Innovation Center of Advanced Microstructures, Surface Physics Laboratory (National Key Laboratory), Key Laboratory of Computational Physical Sciences (MOE), Fudan University, Shanghai 200433, People's Republic of China.
J Phys Condens Matter. 2019 Mar 6;31(9):095801. doi: 10.1088/1361-648X/aaf7f4. Epub 2018 Dec 11.
Based on first principles calculations, we reveal that the origin of ferromagnetism caused by [Formula: see text] electrons in graphene with vacancies can be traced to electrons partially filling [Formula: see text]-antibonding and [Formula: see text]-nonbonding states, which are induced by the vacancies and appear near the Fermi level. Because the spatial wavefunctions of both states are composed of atomic orbitals in an antisymmetric configuration, their spin wavefunctions should be symmetric according to the electron exchange antisymmetric principle, leading to electrons partially filling these states in spin polarization. Since this [Formula: see text] state originates not from interactions between the atoms but from the unpaired [Formula: see text] orbitals due to the removal of [Formula: see text] orbitals on the minority sublattice, the [Formula: see text] state is constrained, distributed on the atoms of the majority sublattice, and decays gradually from the vacancy as ∼[Formula: see text]. According to these characteristics, we concluded that the [Formula: see text] state plays a critical role in magnetic ordering in graphene with vacancies. If the vacancy concentration in graphene is large enough to cause the decay-length regions to overlap, constraining the [Formula: see text] orbital components as little as possible on the minority sublattice atoms in the overlap regions results in the vacancy-induced [Formula: see text] states being coherent. The coherent process in the overlap region leads to the wavefunctions in all the involved regions antisymmetrized, consequently causing ferromagnetism according to the electron exchange antisymmetric principle. This unusual mechanism concerned with the origin of [Formula: see text]-electron magnetism and magnetic ordering has never before been reported and is distinctly different from conventional mechanisms. Consequently, we can explain how such a weak magnetization with such a high critical temperature can be experimentally observed in proton-irradiated graphene.
基于第一性原理计算，我们发现具有空位的石墨烯中由[公式：见原文]电子引起的铁磁性起源可追溯到部分填充由空位诱导且出现在费米能级附近的[公式：见原文]-反键态和[公式：见原文]-非键态的电子。由于这两个态的空间波函数由反对称构型的原子轨道组成，根据电子交换反对称原理，它们的自旋波函数应该是对称的，导致电子在自旋极化中部分填充这些态。由于这种[公式：见原文]态并非源于原子间的相互作用，而是由于少数子晶格上[公式：见原文]轨道的去除导致未配对的[公式：见原文]轨道，所以[公式：见原文]态受到约束，分布在多数子晶格的原子上，并从空位逐渐衰减，衰减规律为 ∼[公式：见原文]。根据这些特性，我们得出结论，[公式：见原文]态在具有空位的石墨烯的磁有序中起着关键作用。如果石墨烯中的空位浓度足够大，导致衰减长度区域重叠，那么在重叠区域中尽量减少少数子晶格原子上的[公式：见原文]轨道成分的约束，会使空位诱导的[公式：见原文]态变得相干。重叠区域中的相干过程导致所有涉及区域的波函数反对称化，进而根据电子交换反对称原理产生铁磁性。这种与[公式：见原文]电子磁性起源和磁有序相关的异常机制此前从未被报道过，且与传统机制明显不同。因此，我们可以解释在质子辐照的石墨烯中如何能够通过实验观察到如此高临界温度下的微弱磁化现象。
