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

TL;DR

This work addresses the emergence and symmetry protection of Dirac nodal features in the collinear antiferromagnet Mn$_{5}$Si$_{3}$ in its AF2 phase. By combining symmetry analysis with first-principles calculations, it identifies an eight-fold degenerate Dirac nodal line near the Fermi level in the absence of spin–orbit coupling, protected by a pure-spin symmetry and lattice/magnetic-space-group symmetries; including SOC, this line splits into two four-fold DNLs. The study further shows that SOC-induced band splitting near the DNL enhances the intrinsic spin Hall conductivity, with anisotropic SHC tensor components consistent with the symmetry constraints, and argues that AHE is symmetry-forbidden in this phase. Overall, Mn$_{5}$Si$_{3}$ emerges as a promising, silicon-compatible material for spintronics, enabling efficient spin-current generation and detection in an AFM setting.

Abstract

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 Néel 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.

Figures (3)

• Figure 1: (a) Magnetic structure of the AF2 phase of Mn$_{5}$Si$_{3}$. The brown, purple, and red circles represent the inequivalent positions of Mn1, Mn21, and Mn22 atoms, respectively. The arrows indicate the direction of the magnetic moments of the Mn22 atoms. (b) Spin charge density ($\rho_{\uparrow} - \rho_{\downarrow}$) projected along the [010] direction of Mn$_{5}$Si$_{3}$. (c) Density of states (DOS) of Mn$_{5}$Si$_{3}$ in the AF2 phase without SOC.
• Figure 2: (a) Band structure of Mn$_{5}$Si$_{3}$ in the AFM2 phase without SOC. (b) 3D view of the eight-fold degenerate DNL along the U-R path (green line) in the $k_{z} = \pi$ plane without SOC. (c) First Brillouin zone (BZ) with the representation of the DNL (red lines) and the eight-fold degenerate band (green line) without SOC. (d) Band structure of Mn$_{5}$Si$_{3}$ in the AFM2 phase with SOC. (e) 3D view of the DNLs (red lines) along the Z-U and U-R path in the $k_{z} = \pi$ plane with SOC. (f) First Brillouin zone with the representation of the DNLs (red line) along the Z-U and U-R path with SOC. Band degeneracy is indicated in parentheses.
• Figure 3: (a) Band structure of Mn$_{5}$Si$_{3}$ in the AF2 phase with spin-orbit coupling. The color scale represents the logarithm of the $k$-resolved spin Berry curvature, $\log \Omega^y_{xz}$, along the Brillouin zone. The SBC intensity is highest at the DNL along the U-R path. This results in a significant signal of the spin Hall conductivity where the DNL is located in energy. (b) The components $\sigma^y_{xz}$ and $\sigma^y_{zx}$ are plotted as a function of energy, with zero energy aligned to the Fermi level.