标题： 磁性多层结构中的巨大八极矩 显示英文标题

标题： Giant octupole moment in magnetic multilayers

摘要： 多极矩作为有序参数，用于表征动量空间中的高阶磁效应，通过扩展磁性的概念，提供了一个描述多种磁响应的框架。 在本文中，我们介绍了一种方法，通过角度依赖的反常霍尔电流定量确定异常霍尔效应中的多极矩贡献，并明确结合了离散晶体对称性。 我们的技术独特地使能够在非周期性系统中研究八极矩贡献，特别是在界面和表面上。 通常，在具有量子阱工程的$k$点选择性的 (Ag$_{2}$Fe$_{5}$)$_{n}$多层结构中，我们通过第一性原理计算观察到传统铁磁材料中的八极矩主导的反常霍尔效应。 这些结果从根本上挑战了现有对反常霍尔效应的理论理解，表明即使传统的贡献不仅来自于偶极矩（净磁化）。 此外，我们通过两种不同的方法实现了对八极矩贡献的实际控制：界面工程和磁序重新配置，为操控高阶输运效应开辟了新的可能性。 显示英文摘要

摘要： Multipole moments serve as order parameters for characterizing higher-order magnetic effects in momentum space, providing a framework to describe diverse magnetic responses by extending the concept of magnetism. In this letter, we introduce a methodology to quantitatively determine the multipole moment contributions in anomalous Hall effect through angle-dependent anomalous Hall current, with explicit incorporation of discrete crystal symmetries. Our technique uniquely enables the investigation of octupole contribution in non-periodic systems, particularly at interfaces and surfaces. Typically, in (Ag$_{2}$Fe$_{5}$)$_{n}$ multilayers with quantum-well-engineered $k$-point selectivity, we observe an octupole-dominated anomalous Hall effect in conventional ferromagnetic materials, through first-principles calculations. These results fundamentally challenge the existing theoretical understanding of the anomalous Hall effect, showing that even the conventional contribution arises not only from the dipole moment (net magnetization). Furthermore, we establish practical control over the octupole contribution through two distinct approaches: interface engineering and magnetic ordering reconfiguration, opening new possibilities for manipulating higher-order transport effects.