Dirac fermions in the antiferromagnetic spintronics material CuMnAs

Dirac semimetals (DSMs) are the focus of study as new candidates for topological superconductivity and spintronics. Although the Dirac points are not necessarily associated with crystalline symmetries, the experimentally realized robust DSMs such as $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$ have fourfold-degenerate Dirac points at generic wave vectors on high symmetry line enabled by a fourfold crystalline symmetry. The magnetic counterpart of these robust DSMs remains unknown. On the other hand, the theoretically proposed magnetic DSMs in potential antiferromagnetic (AFM) spintronics materials where both time-reversal $\left(\mathcal{T}\right)$ and inversion $\left(\mathcal{P}\right)$ symmetry are broken but their combination $\mathcal{P}\mathcal{T}$ is preserved have Dirac points on the boundary of the Brillouin zone protected by a low-order twofold crystalline symmetry. Here, combined with first-principles calculations and symmetry analysis, we find the Dirac fermion at generic wave vector on high symmetry line with associated nontrivial surface states in $\mathcal{P}\mathcal{T}$-symmetric tetragonal CuMnAs, which is the prototype AFM spintronics material observed in experiments. Furthermore, we reveal the hidden spin textures in this $\mathcal{P}\mathcal{T}$-symmetric magnetic system, demonstrating interesting vortex-like spin textures. Our study opens the way for designing robust magnetic DSMs that can serve as an ideal platform to study the interplay of magnetism, Dirac fermions, and spin-orbit interactions, and could stimulate a series of research in the field of topological antiferromagnetic spintronics.

Figure 1

(a) Crystallographic and magnetic structures of the tetragonal CuMnAs. (b) The Brillouin zone of CuMnAs. (c) The electronic structures of the tetragonal CuMnAs along the high-symmetry lines with SOC within GGA+U frame ([001] magnetization). The two red dashed lines represent the valence band (highest occupied band) and conduction band (lowest unoccupied band), while the blue solid lines are the other bands far away from the $E_{\mathrm{F}}$. The symbol “DC” means Dirac cone.

Figure 2

(a) Enlarged band structure near the Dirac cone point with [001] magnetization. The overlap of the red solid line and the blue dashed line represents twofold degeneracy, of which the crossing leads to a Dirac cone. (b)–(d) Schematic diagrams that elucidate the symmetry protection mechanism. The colors represent different eigenvalues of the key symmetries, which are $R_{100}$ (or $R_{110}$) in (b) and $S_{4z}$ in (c) and (d). The twofold-degenerate bands are separately plotted for the visibility of the band colors.

Figure 3

(a) The Brillouin zone of CuMnAs and its projection to the (010) surface, and the location of the Dirac points are marked along the $Z\text{−}\mathrm{\Gamma }\text{−}{Z}^{\prime }$ path. (b) The surface states connected with two Dirac points.

Figure 4

(a) and (b) represent the schematic diagram of $k_x\text{−}{k}_y$ and $k_x\text{−}{k}_z$ at the vicinity of the Dirac point (DP). (c) and (e) represent the results of the $k_x\text{−}{k}_y$ plane, and (d) and (f) represent the results of the $k_x\text{−}{k}_z$ plane. The 3D projected local spin polarization at the Dirac cones is represented by green (in the $\alpha$ sector) and purple (in the $\beta$ sector) arrows for Mn and As atoms, respectively. (g) The orbital-resolved band structures of the Dirac cone with [001] magnetization. The different colored dots represent the contributions from the corresponding atomic orbital of the Mn and As atoms, respectively. The $E_{\mathrm{F}}$ is set to zero.

Figure 5

(a), (c) Projected local spin polarization is represented by green (in the $\alpha$ sector) and brown (in the $\beta$ sector) arrows at the region of the shadow boxes in Fig. 1. (b), (d) 2D diagram of the spin textures of CB-M and VB-X bands at the same regions, respectively. The arrows indicate the in-plane spin direction and the color scheme indicates the out-of-plane ($k_z$) spin component. The scaling of the in-plane arrow is shown in the boxes.