Electronic structure of the antiferromagnetic topological insulator candidate GdBiPt

We studied the electronic structures of antiferromagnetic (AFM) GdBiPt with propagating vectors $\overrightarrow{Q_1}=(0,0,\pi$) (A-type) and $\overrightarrow{Q_2}=(\pi ,\pi ,\pi$) (G-type) by performing first-principles calculation based on density-functional theory with modified Becke and Johnson local-density approximation potentials plus Hubbard U (MBJLDA+U). With the total energy calculation, the G-type AFM spin-ordered state is relatively more stable than the A-type AFM spin-ordered state, although the difference in total energy is minute. Our band-structure calculation predicts that the A-type AFM state is topologically nontrivial due to a single $s$-character band inversion at the $\mathrm{\Gamma }$ point, which is similar to the band inversions in half-Heusler topological insulator candidates and bulk HgTe semiconductors, while the G-type AFM state is topologically trivial due to the absence of $s/p$ band inversion. With a realistic tight-binding model calculation with 20 bands coupled to an AFM Zeeman field, GdBiPt with A-type AFM spin order presents a metallic surface state on the terminations with AFM aligned Gd ions, and this surface state is independent of the strength of the AFM Zeeman field, i.e., this surface state will be preserved in a nonmagnetic case. Upon terminating the ferromagnetic spin-aligned Gd ions, the surface state is dependent on the strength of the Zeeman field, and the metallic surface can recover when the Zeeman field approaches zero.

Figure 1

The crystal structure of the cubic GdBiPt unit cell with the $F-43m$ space group. (a) The magnetic unit cell of AFM GdBiPt with propagating vector $\overrightarrow{Q_1}=(0,0,\pi$) (A-type) and lowered space group $P-42m$ resulting from the inequivalent Gd atoms with different spin direction, and (b) the magnetic unit cell of AFM GdBiPt with propagating vector $\overrightarrow{Q_2}=(\pi ,\pi ,\pi$) (G-type) and lowered space group $R3m$ resulting from splitting the magnetic Gd atoms in a hexagonal representation (c) and a rhombohedral representation (d).

Figure 2

Band-structure magnetic GdBiPt with A-type AFM spin order (a) and G-type AFM spin order (b) calculated by MBJLDA+U. The weight of $s$ orbitals and $p$ orbitals from Bi and Pt atoms and $5d$ orbitals from Gd is represented by red, blue, and green, respectively.

Figure 3

Surface state on the [101] surface with AFM aligned Gd ions and Zeeman field strength $B=2.0$ eV.

Figure 4

Surface state on the [001] surface with FM aligned Gd ions and Zeeman field strength $B=2.0$ eV.

Figure 5

Surface state on the [001] surface with FM aligned Gd ions and Zeeman field strength $B=0.0$ eV.