Heesch Nodal Lines in Inadmissible Achiral Antiferromagnets
Recently, a new class of Weyl semimetals in antiferromagnets named Heesch Weyl semimetals was discovered, which have inadmissible chiral magnetic point group symmetries (inadmissible magnetic point groups are incompatible with ferromagnetic order) and distinctive surface Fermi arcs. In Heesch Weyl semimetals, the Weyl points are pinned at high symmetry momenta with two-dimensional irreducible corepresentations in the Brillouin zone. As the Weyl points are pinned, the Weyl points with opposite topological charges cannot emerge or be brought together for creation and annihilation as in conventional Weyl semimetals. In this work, we show that when mirror or rotoinversion symmetries are restored so that the point group becomes achiral, long doubly degenerate lines connecting Weyl points with opposite topological charges emerge. We call these lines the Heesch nodal lines (HNLs) and their host materials the Heesch nodal line antiferromagnets. HNLs result in a large number of two-dimensional massless Dirac cones for planes intercepting the HNLs in the Brillouin zone. Moreover, a large subset of the HNL antiferromagnets has the special property that the lowest nonvanishing order of the nonlinear anomalous Hall effect starts with the third order. First-principles calculations on representative collinear and noncollinear antiferromagnets, such as MnTe, CrSb, and Mn$_3$GaN, confirm our predictions on the presence of HNLs. When the inadmissible symmetry is broken by strain, the double degeneracy of the HNLs is lifted and the associated massless Dirac cones are gapped out, providing a route to realizing sizable anomalous Hall effects in antiferromagnetic crystals. We conclude that all inadmissible antiferromagnets without parity-time symmetry are topological. They are either Heesch Weyl antiferromagnets or Heesch nodal line antiferromagnets.