Chirality in crystals arises from the exclusive presence of proper symmetry operations, such as rotations and screw axes, while improper operations like inversion, mirror planes, and rotoinversions are absent. 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 $R{\mathrm{Pt}}_2\mathrm{B}$, 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 the higher-in-energy (001) ferromagnetic configuration. We also identified Kramers-type Weyl points in the electronic structure in the $k$ paths perpendicular to the screw axis and Weyl points along the $\mathrm{\Gamma }\text{−}A$ axis. In the magnetically active chiral compound ${\mathrm{NdPt}}_2\mathrm{B}$, Zeeman splitting lifts degeneracies at the high-symmetry points; however, Weyl points persist along the screw axis due to the breaking of time-reversal $\left(\mathcal{T}\right)$ and inversion $\left(\mathcal{P}\right)$ symmetries. We also estimate the allowed anomalous Hall conductivity, finding a value of ${\sigma }_{xy}=293\mathrm{S}{\mathrm{cm}}^{-1}$, comparable to that of known kagome magnetic materials such as ${\mathrm{Mn}}_3\mathrm{PtN}$ and FeSn. Thus, our study sheds light on the intricate interplay among chirality, magnetism, and topology in rare-earth three-dimensional kagomelike materials.

Close

PrevNext

View figure in article

• Anomalous Hall effect
• Electronic structure
• First-principles calculations
• Magnetism
• Topological phases of matter