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Materials containing multiple topological characteristics become more exoticwhen combined with noncentrosymmetric crystal structures and unusual magneticphases such as the compensated half-metal state, which is gapped in one spindirection and conducting in the other. First principles calculations revealthese multiple topological features in the compensated half-metal Cr$_2$CoAlhaving neither time-reversal nor inversion symmetries. In the absence of(minor) spin-orbit coupling (SOC), there are (1) a total of twelve pairs ofmagnetic Weyl points, (2) three distinct sets of triple nodal points near theFermi level that are (3) interconnected with six symmetry related nodal lines.This combination gives rise to fully spin polarized nexus fermions, in a systemwith broken time-reversal symmetry but negligible macroscopic magnetic field.The observed high Curie temperature of 750 K and calculated SOC hybridizationmixing of several meV should make these nexus fermions readily measurable.Unlike topological features discussed for other Heuslers which emphasize theirstrong ferromagnetism, this compensated half-metal is impervious to typicalmagnetic fields, thus providing a complementary set of experimental phenomena.Making use of the soft calculated magnetic state, large magnetic fields can beused to rotate the direction of magnetism, during which certain topologicalfeatures will evolve. Our results suggest that these features may be common ininverse-Heusler systems, particularly the isostructural and isovalent Ga and Inanalogs.

Noncentrosymmetric compensated half-metal hosting pure spin Weyl nodes, triple nodal points, nodal loops, and nexus fermions