Berry curvature multipoles appearing in topological quantum materials have recently attracted much attention. Their presence can manifest in novel phenomena, such as nonlinear anomalous Hall effects (NLAHE). The notion of Berry curvature multipoles extends our understanding of Berry curvature effects on the material properties. Hence, research on this subject is of fundamental importance and may also enable future applications in energy harvesting and high-frequency technology. It was shown that a Berry curvature dipole can give rise to a second-order NLAHE in materials of low crystalline symmetry. Here, we demonstrate a fundamentally new mechanism for Berry curvature multipoles in antiferromagnets that are supported by the underlying magnetic symmetries. Carrying out electric transport measurements on the kagome antiferromagnet FeSn, we observe a third-order NLAHE, which appears as a transverse voltage response at the third harmonic frequency when a longitudinal ac drive is applied. Interestingly, this NLAHE is strongest at and above room temperature. We combine these measurements with a scaling law analysis, a symmetry analysis, model calculations, first-principle calculations, and magnetic Monte Carlo simulations to show that the observed NLAHE is induced by a Berry curvature quadrupole appearing in the spin-canted state of FeSn. At a practical level, our study establishes NLAHE as a sensitive probe of antiferromagnetic phase transitions in other materials—such as moiré superlattices, two-dimensional van der Waal magnets, and quantum spin liquid candidates, which remain poorly understood to date. More broadly, Berry curvature multipole effects are predicted to exist for 90 magnetic point groups. Hence, our work opens a new research area to study a variety of topological magnetic materials through nonlinear measurement protocols.

中文翻译：

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反铁磁体中贝里曲率四极杆的实验证据


拓扑量子材料中出现的贝里曲率多极子最近引起了人们的广泛关注。它们的存在可以体现在新颖的现象中，例如非线性反常霍尔效应（NLAHE）。贝里曲率多极子的概念扩展了我们对贝里曲率对材料特性影响的理解。因此，对该主题的研究具有根本重要性，也可能使未来在能量收集和高频技术中的应用成为可能。结果表明，贝里曲率偶极子可以在低晶体对称性材料中产生二阶 NLAHE。在这里，我们展示了反铁磁体中贝里曲率多极子的全新机制，该机制由基础磁对称性支持。在 Kagome 反铁磁体 FeSn 上进行电输运测量时，我们观察到三阶 NLAHE，当应用纵向交流驱动时，它表现为三次谐波频率的横向电压响应。有趣的是，这种 NLAHE 在室温及以上温度下最强。我们将这些测量结果与标度律分析、对称性分析、模型计算、第一性原理计算和磁性蒙特卡罗模拟结合起来，表明观察到的 NLAHE 是由 FeSn 自旋倾斜态中出现的贝里曲率四极杆引起的。在实践层面上，我们的研究将 NLAHE 确立为其他材料中反铁磁相变的敏感探针，例如莫尔超晶格、二维范德华磁体和量子自旋液体候选材料，迄今为止人们对这些材料的了解还很少。更广泛地说，贝里曲率多极效应预计存在于 90 个磁点组中。 因此，我们的工作开辟了一个新的研究领域，通过非线性测量协议研究各种拓扑磁性材料。