Eightfold Degenerate Dirac Nodal Line in Collinear Antiferromagnet Mn$_5$Si$_3$

We study the electronic, magnetic, and spin transport properties of the orthorhombic Mn$_{5}$Si$_{3}$ compound in the $AF2$ phase using symmetry analysis and ab-initio calculations. Our ground state energy calculations align with experimental observations, demonstrating that the collinear antiferromagnetic (AFM) order, with N\'{e}el vector in the [010] direction, is the most stable magnetic configuration both with and without spin-orbit coupling (SOC) in a bulk lattice geometry. We identified an unconventional eight-fold degenerate Dirac nodal line (DNL) close to the Fermi level, characterized by negligible SOC. This DNL is robustly protected by a unique combination of a pure-spin symmetry and a lattice symmetry together with magnetic space group symmetries. Upon introducing SOC, this degeneracy is reduced to two four-fold DNLs, being protected by the combination of time-reversal, partial translation and nonsymmorphic symmetries within the magnetic space group. We predict also a large intrinsic spin Hall conductivity (SHC) which correlates with the presence of SOC-induced splitting of these eight-fold degenerate DNLs near the Fermi level. These intriguing characteristics position collinear antiferromagnet Mn$_{5}$Si$_{3}$ as a compelling candidate for spintronic applications, particularly in the generation and detection of spin currents, while remaining compatible with modern silicon technology.