Symmetry-Protected Weyl Nodal Loops in a Triangular Altermagnet

Abstract

Weyl semimetals and altermagnets represent two distinct classes of quantum materials exhibiting nontrivial topological and magnetic order, respectively. Here we report the realization of a Weyl nodal-loop altermagnet in Cr${}_7$Se${}_8$, combining neutron diffraction and first-principles calculations. The hexagonal system hosts a coplanar $120^{\circ }$ compensated magnetic order on a triangular lattice, which breaks inversion-time-reversal and translation-time-reversal symmetries simultaneously while preserving a crystalline mirror plane. The resulting electronic structure features linearly dispersing nodal loops close to the Fermi level ($E_F$) confined to the mirror-invariant $k_z=0$ plane. Along high-symmetry directions, the crossings near $E_F$ form Dirac-like fourfold degeneracies in the absence of spin-orbit coupling; at generic momenta, these crossings split into twofold and form continuous Weyl-like nodal loops protected by mirror symmetry. The momentum-dependent spin polarization exhibits an $f$-wave-like pattern characteristic of odd-parity altermagnets.