The quantum metric and Berry curvature are two fundamental and distinct factors that describe the geometry of quantum eigenstates. Although the role of the Berry curvature in governing various condensed-matter states has been investigated extensively, the quantum metric, which has also been predicted to induce topological phenomena, has rarely been studied, particularly at ambient conditions. Here we demonstrate the room-temperature manipulation of the quantum-metric structure of electronic states through its interplay with the interfacial spin texture in a topological chiral antiferromagnet/heavy metal Mn₃Sn/Pt heterostructure, which is manifested in a time-reversal-odd second-order Hall effect. We also show the flexibility in controlling the quantum-metric structure with moderate magnetic fields. Our results open the possibility of building applicable nonlinear devices by harnessing the quantum-metric structure.

量子度量和贝里曲率是描述量子本征态几何形状的两个基本且不同的因素。尽管贝里曲率在控制各种凝聚态物质态中的作用已被广泛研究，但也被预测会引起拓扑现象的量子度量却很少被研究，特别是在环境条件下。在这里，我们通过拓扑手性反铁磁体/重金属 Mn ₃ Sn/Pt 异质结构中界面自旋纹理的相互作用，展示了电子态量子度量结构的室温操纵，这表现为时间反转奇数二阶霍尔效应。我们还展示了在中等磁场下控制量子度量结构的灵活性。我们的结果开启了利用量子度量结构构建适用的非线性器件的可能性。