Magnetic Kagome Lattice—Topology and Frustration

Recently, there has been a surge of interest in topological quantum materials exhibiting nontrivial topological states, marking a dynamic frontier in condensed matter physics. [1]. Within the realm of topological quantum materials, those featuring a kagome lattice have recently garnered significant attention. This lattice not only gives rise to geometrically frustrated magnetism but also hosts a nontrivial topological electronic structure, showcasing Dirac points, van Hove singularities, and flat bands. The unique structure of the kagome lattice, coupled with multiple spin, charge, and orbit degrees of freedom, creates a fertile ground for exploring the interplay between frustrated magnetism, nontrivial topology, and correlation effects. This interplay results in a multitude of quantum states, offering a platform for investigating emergent electronic orders and their correlations. These materials can be broadly categorized into magnetic [2] and non-magnetic kagome materials such as CsV₃Sb₅. Magnetic kagome materials, such as Mn₃Sn [3], Co₃Sn₂S₂[4], RET₆X₆ [5] FeGe etc. primarily involve 3d transition metal-based (T=Ti, V, Cr, Mn, Fe, Co, Ni, Cu) kagome systems. The interplay between magnetism and the topological band structure significantly influences the electronic response, leading, for example, to the enhancement of the Berry curvature and the emergence of a large intrinsic anomalous Hall and Nernst effect due to the presence of massive Dirac or Weyl fermions. Additionally, the frustrated structure of kagome materials allows them to host topologically protected skyrmion lattices or noncoplanar spin textures, resulting in a topological Hall effect arising from real-space Berry phases.