3 $d$ -5 $d$锯齿链中的Dzyaloshinski-Moriya相互作用和手性磁性：紧束缚模型和从头计算
Dzyaloshinskii-Moriya interaction and chiral magnetism in 3$d$-5$d$ zig-zag chains: Tight-binding model and ab initio calculations
摘要：
采用基于密度泛函理论的第一性原理计算，研究了平面3 $d$ -5 $d$双原子金属链（3 $d$：Fe，Co; 5 $d$：Ir，Pt，Au）中的手征磁序.我们发现，反对称交换相互作用，通常称为Dzyaloshinskiii-Moriya相互作用（Dzyaloshinskiii-Moriya interaction，简称Dzyaloshinskii-Moriya interaction），对磁结构的能量学有显著贡献。采用全势线性缀加平面波方法，对均匀自旋螺旋进行了自洽计算，在一级微扰理论的基础上，考虑了自旋-轨道相互作用（SOI）的影响，计算了自旋螺旋的量子效率.为了深入了解我们的从头计算的结果，我们开发了一个最小的紧束缚模型的三个原子和4轨道，包含所有的基本特征：自旋倾斜之间的磁性$3d$原子，自旋轨道相互作用在$5d$原子，和结构反转的不对称性由三角形几何便利。我们发现，自旋倾斜可以导致自旋-轨道活性本征态，由于在$5d$原子的自旋-轨道相互作用的能量分裂。结果表明，杂化的符号和强度、磁性和非磁性位置的$d$ -轨道之间的成键或反键性质、不同自旋投影的占据态和未占据态之间的带宽和能量差决定了杂化的符号和强度.在三聚体模型中观察到的关键特征也可以在第一原理结果中找到。
英文摘要：
We investigate the chiral magnetic order in free-standing planar 3$d$-5$d$ bi-atomic metallic chains (3$d$: Fe, Co; 5$d$: Ir, Pt, Au) using first-principles calculations based on density functional theory. We found that the antisymmetric exchange interaction, commonly known as Dzyaloshinskii-Moriya interaction (DMI), contributes significantly to the energetics of the magnetic structure. We used the full-potential linearized augmented plane wave method and performed self-consistent calculations of homogeneous spin spirals, calculating the DMI by treating the effect of spin-orbit interaction (SOI) in the basis of the spin-spiral states in first-order perturbation theory. To gain insight into the DMI results of our ab initio calculations, we develop a minimal tight-binding model of three atoms and 4 orbitals that contains all essential features: the spin-canting between the magnetic $3d$ atoms, the spin-orbit interaction at the $5d$ atoms, and the structure inversion asymmetry facilitated by the triangular geometry. We found that spin-canting can lead to spin-orbit active eigenstates that split in energy due to the spin-orbit interaction at the $5d$ atom. We show that, the sign and strength of the hybridization, the bonding or antibonding character between $d$-orbitals of the magnetic and non-magnetic sites, the bandwidth and the energy difference between states occupied and unoccupied states of different spin projection determine the sign and strength of the DMI. The key features observed in the trimer model are also found in the first-principles results.
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