Large anomalous Hall effect induced by gapped nodal lines in GdZn and GdCd

The topological properties and intrinsic anomalous Hall effect of CsCl-type ferromagnets GdZn and GdCd have been studied based on first-principles electronic structure calculations. According to the calculated band structures, both GdZn and GdCd host nodal lines near the Fermi level. Once the magnetization breaks the mirror symmetries, the nodal lines are gapped. This can create a huge Berry curvature. A large anomalous Hall effect is then generated when the Fermi level resides within the opened gaps of the nodal lines. Our works indicate that GdZn and GdCd can provide a promising platform for exploring the interplay between topological property and magnetism.

Figure 1

(a) Crystal structure of the CsCl-type GdZn and GdCd. (b) Bulk Brillouin zone (BZ) and projected two-dimensional BZ of the (101) surface. The red lines indicate the high-symmetry paths in the BZ. (c) Nodal lines in the BZ without the spin-orbital coupling (SOC). The purple loops indicate the nodal rings in the ${\mathbf{k}}_{x,y,z}=\pm \pi$ planes, and the orange circles indicate the closed paths wrapping the nodal lines for the Berry phase calculation.

Figure 2

(a) Spin-resolved band structure of GdZn calculated without the SOC. The red and blue lines represent the spin-up and spin-down bands, respectively. (b) Band structure of GdZn calculated with the SOC. The magnetization sets along the [001] direction. The blue and red solid lines denote the highest valence and lowest conduction bands, respectively. (c) Density of states (DOS) and (d) partial DOS of Gd atom for ferromagnetic GdZn calculated without SOC. The upper and lower parts are the spin-up and spin-down components, respectively. The Fermi level sets to zero.

Figure 3

Band gaps of GdZn in the (a) ${\mathbf{k}}_z=\pi$ plane and (b) ${\mathbf{k}}_y=\pi$ plane with the magnetization along the [001] direction. Negative $z$ components of Berry curvatures $-{\mathrm{\Omega }}^z\left(\mathbf{k}\right)$ for GdZn in the corresponding ${\mathbf{k}}_z=\pi$ and ${\mathbf{k}}_y=\pi$ planes with the magnetization along the [001] direction at fixed energies of (c), (d) $E_f$ and (e), (f) $E_f+0.31$ eV.

Figure 4

Calculated anomalous Hall conductance with different magnetization directions along the [001] (red solid line), [110] (black solid line), and [111] (blue solid line) directions for (a) GdZn and (b) GdCd, respectively.

Figure 5

Projected band structures of the (101) surfaces along the high-symmetry lines [Fig. 1] for the Gd-terminated and Zn/Cd-terminated (101) surfaces of (a), (b) GdZn and (c), (d) GdCd, respectively. The magnetization was set along the [001] direction ($z$-axis).