Magnetic triple Weyl semimetals that are robust against spin-orbit coupling

Magnetic order, when coupled with band topology, gives rise to diverse magnetic topological phases. In this study, we focus on space group 173, particularly emphasizing the out-of-plane ferromagnetic order, to analyze how magnetic order and spin-orbit coupling (SOC) influence band symmetry changes. Our first-principles calculations and symmetry analysis predict that ferromagnetic ${\mathrm{La}}_{3}{\mathrm{AlCrS}}_{7}$ is an ideal candidate for the triple Weyl semimetal. In the absence of SOC, the spin-majority bands are conductive while the spin-minority bands are insulating, resulting in a fully polarized Weyl semimetal. Furthermore, within the framework of spin group theory, the triple hourglass Weyl point is stabilized by both ${C}_{6}$ screw rotation symmetry and a redefined time-reversal symmetry. Remarkably, this triple Weyl point remains robust against SOC, and the topological sextuple-helicoid surface states are clearly visible regardless of the presence of SOC. This study not only provides a promising platform for the experimental observation of triple Weyl fermions, but also opens avenues for exploring unprecedented phenomena in triple Weyl semimetals.