Coexistence of Surface Ferromagnetism and a Gapless Topological State in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$

Surface magnetism and its correlation with the electronic structure are critical to understanding the topological surface state in the intrinsic magnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. Here, using static and time resolved angle-resolved photoemission spectroscopy (ARPES), we find a significant ARPES intensity change together with a gap opening on a Rashba-like conduction band. Comparison with a model simulation strongly indicates that the surface magnetism on cleaved ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ is the same as its bulk state. The inability of surface ferromagnetism to open a gap in the topological surface state uncovers the novel complexity of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ that may be responsible for the low quantum anomalous Hall temperature of exfoliated ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$.

Figure 1

Crystal and band structure of the intrinsic magnetic TI ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. (a) The SL of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. Schematic plots of the topological surface state without (b) and with (c) effective ferromagnetic field. (d) ARPES constant energy plot taken with $\mathrm{He}\text{−}\mathrm{I}\alpha =21.2\mathrm{eV}$ at $E_F$ and $E_B=0.5\mathrm{eV}$. (e) and (f) are ARPES intensity plots measured with LCP and RCP across the $\mathrm{\Gamma }$ point, taken in the paramagnetic state at 40 K. The red arrow in (e) indicates the Dirac point at $E_B=0.3\mathrm{eV}$. The black curve shows the approximate position of the bulk conduction band. (g) shows the intensity difference between LCP and RCP. The cyan markers indicate the Rashba-like conduction band and massless Dirac cone.

Figure 2

Evidence of surface magnetic order below $T_N$. (a) and (b) are ARPES intensity plots at 5 and 40 K, respectively. These plots are obtained by adding LCP and RCP to reduce the polarization matrix elements effects. (c) and (d) are the curvature plots of (a) and (b) respectively in a narrower energy range. Cyan and orange curves act as guide to the eye indicating the Rashba-like band at 5 and 40 K. Because of the presence of the bulk state, the Rashba-like splitting derived from the curvature analysis is slightly larger than that shown in Fig. 1. A direct comparison of EDCs below (5 K) and above (40 K) $T_N$ at the $\mathrm{\Gamma }$ point is shown in (e). (f) shows the temperature-dependent intensity change of the Rashba-like band (cyan) and the TSS (orange). The integration areas are shown in (a). Purple circles are the integrated intensity of magnetic Bragg peak at $\mathit{Q}=(1,0,2.5)$ [23].

Figure 3

Intensity anomaly revealed by TRARPES. (a)–(c) TRARPES intensity plots with different time delays. The spectra were collected at 5 K. (d) shows the representative intensity difference between (a) and (b). (e) and (f) are the $k$-integrated spectra as a function of delay time taken at 40 and 5 K, respectively. (g) Integrated intensity of the Rashba-like state as a function of time delay. Cyan and orange curves represent 5 and 40 K, respectively. The dashed oval highlights the intensity increase after 4 ps.

Figure 4

(a)–(c) show simulated single-particle spectral functions for (d) nonmagnetic SL, (e) FM SL with out-of-plane spin orientation, and (f) FM SL with in-plane spin orientation, respectively.