标题： 与RKKY机制中的磁四极相互作用相关的受挫自旋三聚体系统Gd$_{3}$Ru$_{4}$Al$_{12}$（具有呼吸Kagome结构）的磁各向异性和Skyrmion晶格 显示英文标题

标题： Magnetic Anisotropies and Skyrmion Lattice Related to Magnetic Quadrupole Interactions of the RKKY Mechanism in Frustrated Spin-Trimer System Gd$_{3}$Ru$_{4}$Al$_{12}$ with a Breathing Kagome Structure

摘要： 讨论了钆基化合物 Gd$_{3}$Ru$_{4}$Al$_{12}$中磁四极矩（MQ）相互作用的起源，该化合物被公认为是一种受挫自旋系统，并且是一种具有中心对称晶体结构的斯格明子基质材料。从偶极子合成鲁德曼-基特尔-卡斯瓦-约瑟夫（RKKY）相互作用的角度推导出铁磁（FM）三聚体之间的 MQ 相互作用，这些三聚体具有不完美的铁磁方向性。提出了一种同时包含 MQ 相互作用和偶极子相互作用的哈密顿量，并基于此哈密顿量讨论了磁各向异性、磁相变以及 MQ 相互作用对稳定斯格明子晶格（SkL）的贡献。由三聚体携带的 MQ 自由度有助于稳定在有限温度下出现的 SkL。 显示英文摘要

摘要： The origin of the magnetic quadrupole (MQ) interactions in Gd$_{3}$Ru$_{4}$Al$_{12}$ which is known as a frustrated spin system and as a host material of skyrmion with a sentrosymmetric crystal structure are discussed. The MQ interactions between ferromagnetic (FM) spin trimers with imperfect FM directivity are deduced from synthesis of dipole Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. The Hamiltonian which includes both the MQ interactions and dipole interactions is proposed, and magnetic anisotropies, magnetic phase transitions and contribution of the MQ interactions to stabilize the skyrmion lattice (SkL) are discussed based on this Hamiltonian. Degrees of MQ freedom carried by the trimers contribute to stabilizing SkL which appears at finite temperatures.