在原型磁性系统中寻找手征多位相互作用
Prospecting chiral multi-site interactions in prototypical magnetic systems
摘要：
原子自旋模型在解决磁性材料的性质方面取得了巨大的成功，其基础是识别相关的潜在磁相互作用。磁skyrmions和其他非共线磁结构领域的巨大发展很大程度上是由于我们对手性Dzyaloshinskiii-Moriya相互作用的理解。最近，各种工作提出了新类型的手性相互作用，看似不同的形式，但大的图片仍然缺失。在这里，我们提出了一个系统的建设，广义自旋模型包含各向同性和手性多网站的相互作用。这些都是出于一个微观模型，结合当地的自旋矩和自旋轨道相互作用，并建立其对称性。我们表明，手性相互作用产生的自旋-轨道相互作用和多站点的相互作用不一定要遵循Moriya的规则，不像Dzyaloshinskiiii-Moriya和手性双二次相互作用。由于反转对称性，手性多位点相互作用不会消失，并且符合广义的Moriya规则：如果由相互作用连接的所有位点位于同一镜像平面，则手性相互作用矢量必须垂直于该平面。然后，我们说明我们的理论考虑与密度泛函理论计算的原型磁系统。这些是在Re（0001）、Pt（111）和Au（111）表面上由Cr、Mn、Fe和Co吸附原子构建的三角形三聚体，适用于$C_\mathrm{3v}$对称性，以及在Pt（001）上具有$C_\mathrm{4v}$对称性的Cr和Fe方形四聚体。在比较不同磁结构的能量时，多位相互作用的幅度很大，不能忽略。最后，我们根据我们的研究结果讨论了最近的文献，并澄清了几个不清楚或混淆的点。
英文摘要：
Atomistic spin models have found enormous success in addressing the properties of magnetic materials, grounded on the identification of the relevant underlying magnetic interactions. The huge development in the field of magnetic skyrmions and other noncollinear magnetic structures is largely due to our understanding of the chiral Dzyaloshinskii-Moriya interaction. Recently, various works have proposed new types of chiral interactions, with seemingly different forms, but the big picture is still missing. Here, we present a systematic construction of a generalized spin model containing isotropic and chiral multi-site interactions. These are motivated by a microscopic model that incorporates local spin moments and the spin-orbit interaction, and their symmetry properties are established. We show that the chiral interactions arise solely from the spin-orbit interaction and that the multi-site interactions do not have to follow Moriya's rules, unlike the Dzyaloshinskii-Moriya and chiral biquadratic interactions. The chiral multi-site interactions do not vanish due to inversion symmetry, and comply with a generalized Moriya rule: If all sites connected by the interaction lie in the same mirror plane, the chiral interaction vector must be perpendicular to this plane. We then illustrate our theoretical considerations with density functional theory calculations for prototypical magnetic systems. These are triangular trimers built out of Cr, Mn, Fe and Co adatoms on the Re(0001), Pt(111) and Au(111) surfaces, for which $C_\mathrm{3v}$ symmetry applies, and Cr and Fe square tetramers on Pt(001) with $C_\mathrm{4v}$ symmetry. The multi-site interactions are substantial in magnitude and cannot be neglected when comparing the energy of different magnetic structures. Finally, we discuss the recent literature in light of our findings, and clarify several unclear or confusing points.
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