夹心团簇V_n（C_6H_6）_{n+1}磁耦合的理论分析
Theoretical analysis of magnetic coupling in sandwich clusters V_n(C_6H_6)_{n+1}
摘要：
用第一性原理计算和模型分析研究了夹心团簇$_n$（$_6$ $_6$）$_{n+1}$的铁磁性稳定性机制.发现V与苯（Bz）之间的三种键中的每一种都起着不同的作用。V 3d $_{z^2}$轨道沿分子轴延伸，与Bz的HOMO-1轨道弱杂化形成$σ$ -键。它是非常局域化和单占据的，这有助于1 $μ_B$的磁矩，但几乎没有相邻的V磁矩的磁耦合。面内d $_{x^2-y^2}$、d $_{xy}$轨道与Bz的LUMO杂化并构成$δ$ -键。虽然$δ$态对总磁矩没有净贡献，但这种杂化是中等的，对磁耦合至关重要。Bz的d $_{xz}$、d $_{yz}$和HOMO形成一个很强的$π$ -键来保持分子结构，但由于它们的能级远离费米能级，所以它们的磁性是不活跃的。基于第一性原理计算结果，我们指出铁磁稳定性与Kanamori和Terakura [J. Kanamori和K.寺仓，物理学会，日本70，1433（2001）]。然而，边缘Bz在簇中的存在引入了重要的修改。构造了一个简单的模型来解释物理图像的本质。
英文摘要：
The mechanism of ferromagnetism stability in sandwich clusters V$_n$(C$_6$H$_6$)$_{n+1}$ has been studied by first-principles calculation and model analysis. It is found that each of the three types of bonds between V and benzene (Bz) plays different roles. V 3d$_{z^2}$ orbital, extending along the molecular axis, is weakly hybridized with Bz's HOMO-1 orbital to form the $σ$-bond. It is quite localized and singly occupied, which contributes 1$μ_B$ to the magnetic moment but little to the magnetic coupling of neighboring V magnetic moments. The in-plane d$_{x^2-y^2}$, d$_{xy}$ orbitals are hybridized with the LUMO of Bz and constitute the $δ$-bond. This hybridization is medium and crucial to the magnetic coupling though the $δ$ states have no net contribution to the total magnetic moment. d$_{xz}$, d$_{yz}$ and HOMO of Bz form a quite strong $π$-bond to hold the molecular structure but they are inactive in magnetism because their energy levels are far away from the Fermi level. Based on the results of first-principles calculation, we point out that the ferromagnetism stability is closely related with the mechanism proposed by Kanamori and Terakura [J. Kanamori and K. Terakura, J. Phys. Soc. Jpn. 70, 1433 (2001)]. However, the presence of edge Bz's in the cluster introduces an important modification. A simple model is constructed to explain the essence of the physical picture.
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