论文标题
多旋转手性磁相互作用的多片段方法：应用于一维Rashba电子气体
Multiple-scattering approach for multi-spin chiral magnetic interactions: Application to the one- and two-dimensional Rashba electron gas
论文作者
论文摘要
最近已经揭幕了手性质的各种多旋转磁交流（MEI）。由于它们对扭曲自旋纹理的实现的潜在影响，它们对旋转或量子计算的影响非常有前途。在这里，我根据可在基于绿色函数的方法中实现的多种形式主义的基础上解决了多旋MEI的远程行为。我考虑了一（1D）和二维（2D）RashBA模型中所述的自旋轨道耦合（SOC）的影响，从中提取了四旋和六旋相互作用的分析形式，并将其与双线性各向同性，各向异性，各向异性，dzyaloshinskii-Moriya互动（DMI）进行了比较。与两个站点$ i $和$ j $之间的DMI类似，有一个垂直于连接这两个站点的债券的四旋手性手性向量。分析并量化了MEI及其作为原子间距离功能的衰减的振荡行为，并针对表征AU表面的Rashba表面状态进行了量化。跳动效应和SOC强度的相互作用产生了一个广泛的参数空间，其中手性MEI比各向同性更突出。 $ n $磁矩衰减的plaquette的多旋交互作用，例如$ \ {q_f^{n-d} R^{\left[1+\frac{N}{2}(d-1)\right]}N\}^{-1}$ for equidistant atoms, where $d$ is the dimension of the mediating electrons, $q_F$ the Fermi wave vector, $L$ the perimeter of the plaquette while $P$ is the product of interatomic distances.这恢复了双线性MEI的行为，$ \ {q_f^{2-d} r^{d} \} \}^{ - 1} $，并表明增加plaquette的外围会削弱MEI。更重要的是，与与2D MEI相关的线性依赖性相比，与距离依赖的1D MEI有关的幂律对plaquette中的原子数不敏感。
Various multi-spin magnetic exchange interactions (MEI) of chiral nature have been recently unveiled. Owing to their potential impact on the realisation of twisted spin-textures, their implication in spintronics or quantum computing is very promising. Here, I address the long-range behavior of multi-spin MEI on the basis of a multiple-scattering formalism implementable in Green functions based methods. I consider the impact of spin-orbit coupling (SOC) as described in the one- (1D) and two-dimensional (2D) Rashba model, from which the analytical forms of the four- and six-spin interactions are extracted and compared to the bilinear isotropic, anisotropic and Dzyaloshinskii-Moriya interactions (DMI). Similarly to the DMI between two sites $i$ and $j$, there is a four-spin chiral vector perpendicular to the bond connecting the two sites. The oscillatory behavior of the MEI and their decay as function of interatomic distances are analysed and quantified for the Rashba surfaces states characterizing Au surfaces. The interplay of beating effects and strength of SOC gives rise to a wide parameter space where chiral MEI are more prominent than the isotropic ones. The multi-spin interactions for a plaquette of $N$ magnetic moments decay like $\{q_F^{N-d} P^{\frac{1}{2}(d-1)}L\}^{-1}$ simplifying to $\{q_F^{N-d} R^{\left[1+\frac{N}{2}(d-1)\right]}N\}^{-1}$ for equidistant atoms, where $d$ is the dimension of the mediating electrons, $q_F$ the Fermi wave vector, $L$ the perimeter of the plaquette while $P$ is the product of interatomic distances. This recovers the behavior of the bilinear MEI, $\{q_F^{2-d} R^{d}\}^{-1}$, and shows that increasing the perimeter of the plaquette weakens the MEI. More important, the power-law pertaining to the distance-dependent 1D MEI is insensitive to the number of atoms in the plaquette in contrast to the linear dependence associated with the 2D MEI.
