First-principles theoretical analysis of magnetically tunable topological semimetallic states in antiferromagnetic DyPdBi

A number of compounds in the family of rare-earth half-Heusler alloys have been predicted to be topologically nontrivial semimetals, classified as Weyl, triple-point, and Dirac semimetals based on the multiplicity of degeneracy of the nodal points or crossing of linearly dispersed electronic bands. Here, we present a first-principles theoretical characterization of the electronic topology of the antiferromagnetic half-Heusler alloy DyPdBi. In the antiferromagnetic state preserving ${C}_{3v}$ symmetry of the crystal, DyPdBi is a triple-point semimetal hosting four triply degenerate nodes along the threefold symmetry axis of the Brillouin zone. In contrast, the antiferromagnetic state of DyPdBi with local magnetic moments on Dy rotated to a direction perpendicular to the ${C}_{3}$ axis breaks the threefold rotational symmetry, and hosts four Weyl nodes in its Brillouin zone. Our calculations of the Berry curvature of their electronic states clearly show that the triple-point fermions of DyPdBi exhibit a signature peak in the anomalous Hall conductivity, while the Weyl fermions do not contribute to anomalous Hall conductivity. As these two topologically distinct magnetic states are separated by a small energy difference of $\ensuremath{\approx}$15 meV, we expect them to be switchable with a magnetic field or spin torque and distinguishable experimentally from anomalous Hall conductance.