Hund nodal line semimetals: The case of twisted magnetic phase in the double-exchange model

We propose a class of topological metals, which we dub \emph{Hund nodal line semimetals}, arising from the strong Coulomb interaction encoded in the Hund's coupling between itinerant electrons and localized spins. We here consider a particular twisted spin configuration, which is realized in the double exchange model which describes the manganite oxides. The resulting effective tetragonal lattice of electrons with hoppings tied to the local spin features an antiunitary \emph{non-symmorphic} symmetry that in turn, together with another non-symmorphic but unitary, glide mirror symmetry, protects crossings of a double pair of bands along a high-symmetry line on the Brillouin zone boundary. We also discuss symmetry breaking arising from various perturbations of the twisted phase. Our results may motivate further studies of other realizations of this state of matter, for instance in different spin backgrounds, properties of its drumhead surface states, as well as its stability to disorder and interactions among the itinerant electrons.