标题： 具有各向异性交换相互作用的有效自旋模型用于半填充的自旋轨道耦合哈伯德模型 显示英文标题

标题： Effective spin model with anisotropic exchange interactions for the spin-orbit coupled Hubbard model at half-filling

摘要： 自旋-轨道耦合（SOC）在非中心对称材料中是不共格磁结构的来源。 在半导体中，它驱动Rashba自旋分裂和自旋动量锁定，而在基于过渡金属的磁绝缘体中，它诱导各向异性的自旋交换相互作用，如Dzyaloshinskii-Moriya（DM）相互作用，这驱动手性磁性和斯格明子形成。 在这里，我们通过从半填充的SOC Hubbard模型推导出一个有效自旋模型，建立了SOC与自旋交换相互作用之间的直接联系。 使用到四阶的强耦合展开，我们确定了海森堡、类似伊辛以及环交换相互作用，以及各种四体项对于现实的Hubbard参数。 这些参数限制了自旋相互作用的相对强度，提供了一种在承载复杂磁纹理的金属和绝缘相之间的自然插值。 显示英文摘要

摘要： Spin-orbit coupling (SOC) in noncentrosymmetric materials is the source of incommensurate magnetic structures. In semiconductors, it drives the Rashba spin splitting and spin momentum locking, while in magnetic insulators based on transition metals, it induces anisotropic spin exchange interactions, like Dzyaloshinskii-Moriya (DM) interaction which drive chiral magnetism and skyrmion formation. Here, we establish a direct connection between SOC and spin exchange interactions by deriving an effective spin model from the SOC Hubbard model at half-filling. Using a strong-coupling expansion up to fourth order, we identify Heisenberg, Ising-like, and ring exchange interactions, as well as a variety of four-body terms for realistic Hubbard parameters. These parameters constrain the relative strengths of spin interactions, providing a natural interpolation between metallic and insulating phases that host complex magnetic textures.