Chiral symmetry and magnetism in a three-dimensional kagome lattice: R Pt 2 B prototype crystals ( R = La and Nd)

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Chirality in crystals arises from the exclusive presence of proper symmetry operations, such as rotations and screw axes, while lacking improper operations like inversion, mirror planes, and roto-inversions. Crystallographic chirality is expected to be coupled with magnetic responses in magnetically active chiral compounds. Therefore, this study investigates the interplay between structural chirality and magnetic ordering in the rare-earth platinum boride family, RPt$_2$B, where R denotes lanthanide elements. Our results show that the R sites structurally form a chiral three-dimensional Kagome lattice, which can lead to magnetic frustration resolved through chiral antiferromagnetic orderings in conjunction with chiral symmetry. Symmetry analysis reveals that these chiral antiferromagnetic states are low-energy states, competing with higher-in-energy (001) ferromagnetic configuration. We also identified Kramers-type Weyl points in the electronic structure without magnetic response. In the magnetically active chiral compound NdPt$_2$B, Zeeman splitting lifts degeneracies at the high-symmetry points; however, Weyl points persist due to the breaking of time-reversal (T) and inversion (P) symmetries. We also estimate the anomalous Hall conductivity, a measurable observable of the allowed topological features finding a value of $σ_{xy} = 293$ S$\cdot$cm$^{-1}$ comparable with another Kagome magnetic materials like Mn$_3$PtN and FeSn, for example. This study elucidates the intricate interplay among chirality, magnetism, and topology in rare-earth Kagome materials.

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