Coexistence of fully spin-polarized Weyl nodal loop, nodal surface, and Dirac point in a family of quasi-one-dimensional half-metals

Abstract

Recent investigation has connected topology with magnetization, which has been attracting great research interest. Here, based on symmetry analysis and first-principle calculations, we reveal rich band crossings in ferromagnetic quasi-one-dimensional compounds ${XYZ}_{3}$ ($X=\mathrm{Cs},\mathrm{Rb}$, $Y=\mathrm{Cr},\mathrm{Cu}$, $Z=\mathrm{Cl},\mathrm{I}$). We show that these materials host hourglass Weyl loops, nodal surfaces, and Dirac points in the absence of spin-orbital coupling. Notably, these topological phases only occur in a single spin channel, leading to fully spin-polarized phases. Based on symmetry analysis, we present that the hourglass-like Weyl loop is enforced by nonsymmorphic symmetries, which give rise to drumhead surface states. Particularly, the Weyl loop can persist when a magnetic direction is normal to the plane where it lies on. Additionally, we also find the nodal surfaces protected by the combination of screw rotation and time reversal symmetry. Besides, there exists a Dirac point enabled by nonsymmorphic symmetry and time reversal symmetry. Notably, this Dirac point shows a linear dispersion in one direction and quadratic dispersion in the normal plane, showing two Fermi arcs in its surface energy spectrum. By tuning the direction of magnetization, the Dirac point can be reduced to a pair of Weyl points. Our work suggests a concrete platform for exploring the fascinating physics associated with nonsymmorphic band crossings in quasi-one-dimensional ferromagnetic systems.