Dirac Surface States in Intrinsic Magnetic Topological Insulators ${\mathrm{EuSn}}_2{\mathrm{As}}_2$ and ${\mathrm{MnBi}}_{2n}{\mathrm{Te}}_{3n+1}$

In magnetic topological insulators (TIs), the interplay between magnetic order and nontrivial topology can induce fascinating topological quantum phenomena, such as the quantum anomalous Hall effect, chiral Majorana fermions, and axion electrodynamics. Recently, a great deal of attention has been focused on the intrinsic magnetic TIs, where disorder effects can be eliminated to a large extent, which is expected to facilitate the emergence of topological quantum phenomena. Despite intensive efforts, experimental evidence of the topological surface states (SSs) remains elusive. Here, by combining first-principles calculations and angle-resolved photoemission spectroscopy (ARPES) experiments, we reveal that ${\mathrm{EuSn}}_2{\mathrm{As}}_2$ is an antiferromagnetic TI with the observation of Dirac SSs consistent with our prediction. We also observe nearly gapless Dirac SSs in antiferromagnetic TIs ${\mathrm{MnBi}}_{2n}{\mathrm{Te}}_{3n+1}$ ($n=1$ and 2), which are absent in previous ARPES results. These results provide clear evidence for nontrivial topology of these intrinsic magnetic TIs. Furthermore, we find that the topological SSs show no observable changes across the magnetic transition within the experimental resolution, indicating that the magnetic order has a quite small effect on the topological SSs, which can be attributed to weak hybridization between the localized magnetic moments, from either $4f$ or $3d$ orbitals, and the topological electronic states. This finding provides insights for further research that the correlations between magnetism and topological states need to be strengthened to induce larger gaps in the topological SSs, which will facilitate the realization of topological quantum phenomena at higher temperatures.

Popular Summary

More than ten years ago, a new class of quantum states of matter, called topological insulators in nonmagnetic materials, was theoretically predicted and experimentally confirmed. The interiors of these materials behave as insulators, while their surfaces are electrical conductors. The introduction of magnetism into topological insulators can bring about even more novel behaviors: In 3D magnetic topological insulators, for example, the 2D surfaces can become mostly insulating while leaving 1D conductive regions on the material edges. Here, we present detailed observations of two magnetic topological insulators, one newly predicted, that provide new insight into how to control their novel behavior.

Using first-principles calculations and angle-resolved photoemission spectroscopy, we find that the ${\mathrm{EuSn}}_2{\mathrm{A}\mathrm{s}}_2$ is a magnetic topological insulator. In another widely studied family of magnetic topological insulators, our experiments also reveal topological surface behavior that had not shown up in previous investigations. Taken together, our studies indicate that the key to triggering surface insulating behavior in these materials lies with the coupling between magnetic order and electronic states.

Our results provide insights for future exploration of other, more desirable, magnetic topological insulators so that researchers can study exotic topological quantum phenomena.

Figure 1

Magnetic and topological properties of ${\mathrm{EuSn}}_2{\mathrm{As}}_2$. (a) Crystal structure of ${\mathrm{EuSn}}_2{\mathrm{As}}_2$. The green arrows represent the magnetic moments of Eu atoms, forming a doubled magnetic unit cell $c*=2c$ in the AFM phase. The blue arrow represents the half translation operator ${\ell }_{1/2}$ of the magnetic unit cell along the $c$ axis. (b) Temperature dependence of magnetic susceptibility $\chi (T)$ with magnetic field ${\mu }_{0}H=0.05\mathrm{T}$ parallel (red line) and perpendicular (blue line) to the $c$ axis. The inset shows the inverse susceptibility. (c) Field-dependent magnetization at 2 K with magnetic fields parallel (red line) or perpendicular (blue line) to the $c$ axis. (d) Bulk BZ and (001) surface BZ. $k_y$ and $k_z$ are along the $b$ and $c$ axes, respectively. (e),(f) Calculated bulk band structures of ${\mathrm{EuSn}}_2{\mathrm{As}}_2$ in the PM and $\mathrm{AFM}\text{−}b/\mathrm{AFM}\text{−}c$ phases along high-symmetry lines with spin-orbit coupling. (g) Wannier charge centers (WCC) calculated for the occupied bands with mirror eigenvalue $⟨M⟩=+i$ ($-i$) in the mirror plane $k_y=0$. (h),(i) Calculated band dispersions of the (001) SSs and projected bulk states along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ near the bulk band gap in the $\mathrm{AFM}\text{−}b$ and $\mathrm{AFM}\text{−}c$ phases. (j) Schematic diagram of the topological states of ${\mathrm{EuSn}}_2{\mathrm{As}}_2$ in three prototypical magnetic phases (PM, $\mathrm{AFM}\text{−}b$, and $\mathrm{AFM}\text{−}c$). STI, TCI, and AI are the abbreviations for strong topological insulator, topological crystalline insulator, and axion insulator, respectively.

Figure 2

Electronic structures below $E_F$ of ${\mathrm{EuSn}}_2{\mathrm{As}}_2$. (a) Core-level photoemission spectrum showing the characteristic peaks of As $3d$, Sn $4d$, and Eu $4f$ orbitals. (b) Curvature intensity map of the ARPES data at $E_F$ along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ taken in a range of $h\nu$ from 18 to 35 eV. (c) ARPES intensity map at $E_F$ around $\overline{\mathrm{\Gamma }}$. (d) ARPES intensity map along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$. (e) Curvature intensity map of the data in (d). (f) Calculated band dispersions of the (001) SSs and projected bulk states along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$. The ARPES data in (c) and (d) are collected at $h\nu =29\mathrm{eV}$. All ARPES data in this figure are collected at 50 K.

Figure 3

Dirac SSs above $E_F$ on the (001) surface of ${\mathrm{EuSn}}_2{\mathrm{As}}_2$. (a) Snapshots of the tr-ARPES intensity along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ taken with the pump-probe method at different delay times. (b),(c) Curvature intensity maps of the pump-probe data at the delay time 0.2 ps taken at 40 and 4 K. (d) Combination of the data in Figs. 3 and 2. (e) Stack of curvature intensity maps of the pump-probe data at different constant energies. The energy of the Dirac point ($E_D$) is set to zero.

Figure 4

Dirac SSs on the (001) surface of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. (a),(c) ARPES intensity maps along the cut through $\overline{\mathrm{\Gamma }}$ taken at $h\nu =13.8\mathrm{eV}$ at 50 and 10 K. (b),(d) Intensity maps of the second derivative with respect to the energy of the data near the bulk band gap in (a) and (c). DP is the abbreviation for Dirac point. (e) Resonant valence band spectra of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ taken at the Mn $3p\text{−}3d$ absorption edge. On- and off-resonance spectra are obtained at $h\nu =51$ and 47 eV, respectively. (f) Three-dimensional plot of the ARPES data around $\overline{\mathrm{\Gamma }}$ taken with the 7-eV laser. (g),(h) ARPES intensity maps (left) and their second derivative with respect to the energy (right) along the cut through $\overline{\mathrm{\Gamma }}$ taken with the 7-eV laser at 40 and 15 K. The red and blue arrows indicate splitting of the conduction and valance bands, respectively, below $T_N$. (i),(j) Enlarged ARPES intensity maps near the Dirac point in (g) and (h). (k) EDCs at $\overline{\mathrm{\Gamma }}$ at 40 and 15 K. (l) Second derivative of the EDCs in (k).

Figure 5

Dirac SSs on the (001) surface of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$. (a) X-ray diffraction pattern on the (001) surface of a ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ single crystal. (b) Temperature dependence of magnetic susceptibility $\chi (T)$ at magnetic field ${\mu }_{0}H=0.01\mathrm{T}$ parallel and perpendicular to the $c$ axis under zero-field cooling (ZFC) and field cooling (FC). (c) Field-dependent magnetization $M(H)$ at 2 K with magnetic fields parallel (red line) and perpendicular (blue line) to the $c$ axis. (d) Three-dimensional intensity plot of the ARPES data around $\overline{\mathrm{\Gamma }}$ measured with the 7-eV laser. (e),(f) ARPES intensity maps (left) and their second derivative with respect to the energy (right) along the cut through $\overline{\mathrm{\Gamma }}$ measured with the 7-eV laser at 40 and 8 K. The red and blue arrows indicate splitting of the conduction and valance bands, respectively, across $T_N$. (g),(h) Enlarged ARPES intensity maps near the Dirac point in (e) and (f). (i) EDCs at $\overline{\mathrm{\Gamma }}$ measured at 40 and 8 K. (j) Second derivative of the EDCs in (i).