Dirac surface states in intrinsic magnetic topological insulators EuSn2As2 and MnBi2nTe3n+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. In despite of 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 have revealed that EuSn2As2 is an antiferromagnetic TI with observation of Dirac SSs consistent with our prediction. We also observe nearly gapless Dirac SSs in antiferromagnetic TIs MnBi2nTe3n+1 (n = 1 and 2), which were 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 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 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.

The quantum anomalous Hall effect has been first realized in magnetically doped (Bi,Sb)2Te3 thin films [9,10]. In the magnetically doped TIs, the magnetic impurities usually introduce strong inhomogeneity, which is believed to be one of the main reasons that the quantum anomalous Hall effect usually appears at extremely low temperatures (< 100 mK), hindering further exploration of topological quantum effects. A direct solution to avoid disorder is to seek for intrinsic magnetic TIs, which have magnetic order in the stoichiometric compositions.
In this work, we not only reveal the Dirac SSs of MnBi2Te4 and MnBi4Te7 within the large gap observed in previous ARPES studies, but also discover another intrinsic magnetic TI EuSn2As2 by combining first-principles calculations and ARPES 4 measurements. Through a systematic study of these magnetic TIs, we obtain a comprehensive picture that while the magnetic order plays an important role in timereversal-symmetry breaking, the coupling strength between the local magnetic moments and the topological electronic states is critical for the size of the opened gap in the topological SSs.
EuSn2As2 has a layered crystal structure with space group R-3m [ Fig. 1(a)]. Each trigonal Eu layer is sandwiched between two buckled honeycomb SnAs layers. Two adjacent SnAs layers are coupled by van der Waals force. This allows EuSn2As2 to be easily exfoliated into few-layer sheets like MnBi2Te4 [26,[30][31][32]41]. A previous study has revealed that EuSn2As2 undergoes a transition from a paramagnetic (PM) phase to an AF phase around 25 K [41], which is consistent with our measurements in Figs. 1(b) and 1 (c). In the AF phase, the Eu 4f magnetic moments form an A-type AF structure, i.e., ferromagnetic a-b planes coupled antiferromagnetically along the c axis. In addition, when the magnetic fields are perpendicular to the c axis, the susceptibility (T) in Fig. 1(b) shows an upturn below 10 K and the isothermal magnetization M(H) at 2 K in Fig. 1 (c) increases rapidly at low fields, indicating an in-plane ferromagnetic component probably due to canting of the magnetic moments.
We first analyzed the topological properties of EuSn2As2 in the PM phase. We  Table I. The obtained invariant Z2 = 1 indicates that EuSn2As2 is a strong TI in the PM phase.
In the band calculations of the AF phase in Fig. 1(f), we consider two metastable AF phases with the magnetic moments along the b (AF-b) and c (AF-c) axes, respectively. The Hubbard interaction U on the Eu 4f electrons was set to be 5 eV, in order to make the energy position of the Eu 4f bands consistent with the experimental results in Fig. 2(a). In the AF configuration, the pseudopotential of Eu must treat the 4f 5 states as valence states. The calculated bands of the two AF phases are almost identical.
The continuous gap throughout the BZ remains in the AF phases. In both AF phases of EuSn2As2, the time-reversal symmetry is broken and the inversion symmetry is preserved. One can compute the Z4 invariant based on the parity eigenvalues at the eight TRI points. The numbers of occupied bands of odd parity at the eight TRI points are listed in Table I. The obtained invariant Z4 = 2 indicates that EuSn2As2 is an axion insulator in the AF phase regardless of the spin orientations.
Based on the above analysis, EuSn2As2 transforms from a strong TI in the PM phase to an axion insulator in the AF phase below TN. The effects of the topological phase transition on the Dirac SSs depend on the magnetic structures, spin orientations, and sample surfaces. Here, we consider the SSs on the (001) surface in the AF-b and AF-c phases. The analysis is similar to that for EuIn2As2 [17]. In both phases, the ℓ 1/2 symmetry is broken at the (001) surface, where is the time-reversal symmetry and ℓ 1/2 is a translation operation of half of the magnetic unit cell along the c axis, as indicated in Fig. 1 line. In the AF-c phase, all vertical mirror symmetries are broken since the magnetic moments are parallel to them, leaving gapped Dirac SSs on the (001) surface. Note that the opened gap at Γ ̅ is too small (< 1 meV) to be resolved in the calculations in Fig. 1 The above analysis is illustrated in the schematic diagram in Fig. 1

(j).
We then investigated the electronic structures on the (001) surface of EuSn2As2 with ARPES measurements. The electronic structures measured at different photon energies (hν) in Fig. 2(b) have no obvious changes. We use the data collected with hν = 29 eV to illustrate the electronic structures near EF in the PM phase in Figs. 2(c)-2(e).
The data reveal that all near-EF bands lie around the BZ center Γ ̅ . Two hole-like bands (labelled as  and ) form two circular FSs centered at Γ ̅ . In addition, one can see a 6 small feature at EF at Γ ̅ (labelled as ), which should be the bottom of an electron-like band, and an "M"-shaped band below EF (labelled as ). The experimental data are consistent with the calculated valence bands in Fig. 2(f) except for a rigid band shift of ~ 0.18 eV. This suggests that the EuSn2As2 samples are hole doped, which is similar to the case of EuSn2P2 [24].
For the hole-doped samples, conventional ARPES measurements cannot obtain the information in the band gap. Instead, we used time-resolved ARPES (tr-ARPES) with the pump-probe method to measure the unoccupied electronic states above EF. In   Fig. 4(k) and their second-derivative spectra in Fig.   4(l).
Note that the gap exists in both PM and AF phases of MnBi2Te4 (TN = 24 K). In 8 Fig. 4(l), the second-derivative spectra of the EDCs at Γ ̅ determines that the gap is 12 meV at 40 K and 13.5 meV at 8 K. This difference is within the energy resolution (E = 4.5 meV) in the experiments, indicating that the AF order has quite small effect on the Dirac SSs. This is in contrast to the theoretical calculations that have proposed that the Dirac SSs open an energy gap of tens of meV when MnBi2Te4 undergoes an AF transition into the AF-c phase [19][20][21]23,40]. The AF-c phase in MnBi2Te4 has been confirmed by neutron diffraction experiments [35].
In MnBi2Te4, the magnetic moments derive from the Mn 3d states, and the We also revealed the existence of Dirac SSs within the large gap previously observed in MnBi4Te7 [28,29], as shown in Figs. 5. In the single crystal X-ray diffraction data in Fig. 5(a), all the peaks can be indexed by the (00l) reflections of MnBi4Te7 with c = 23.811(2) Å, which is consistent with the previous results [36]. The magnetic susceptibility (T) in Fig. 5(b) with H//c shows a cusp at 12.6 K, which is an indication of an AF transition consistent with the previous studies [28,29,43].  We have observed the Dirac SSs across the bulk band gap of EuSn2As2 and MnBi2nTe3n+1 (n = 1 and 2), demonstrating their nontrivial topology. The Dirac SSs have almost no change when the long-range AF order develops in these materials, which can be attributed to weak coupling between the local magnetic moments and the topological electronic states. It is highly desirable to find the intrinsic magnetic TIs in that the topological electronic states are heavily involved in the magnetic order, which may be critical to realize topological quantum phenomena at higher temperatures.
Note added: We become aware of similar studies in Ref. [44][45][46] and the updated version of Ref. [26] showing the Dirac SSs in MnBi2Te4 when finalizing our paper and during the review process.

Sample synthesis
Single crystals of EuSn2As2 were grown by the Sn flux method at the Institute of Physics, Chinese Academy of Sciences. The high-purity Eu (rod), Sn (shot), and As (lump) were put into corundum crucibles and sealed into quartz tubes with a ratio of

Synchrotron and laser angle-resolved photoemission spectroscopy
Synchrotron ARPES measurements on EuSn2As2 were performed at the 11 "CASSIOPEE" beamline, SOLEIL, France, with a Scienta R4000 analyzer, and the "dreamline" beamline at the Shanghai Synchrotron Radiation Facility (SSRF) with a Scienta DA30 analyzer. Synchrotron ARPES measurements on MnBi2Te4 were performed at the 03U beamline at the Shanghai Synchrotron Radiation Facility (SSRF) and at the 13U beamline at the National Synchrotron Radiation Laboratory at Hefei with a Scienta DA30 analyzer. High-resolution ARPES measurements on MnBi2Te4 and MnBi4Te7 were performed using the 7-eV laser ARPES at the Institute of Solid Physics, University of Tokyo with a Scienta R4000 analyzer.

Time-resolved angle-resolved photoemission spectroscopy
The tr-ARPES experiments were performed at Shanghai Jiao Tong University. In tr-ARPES measurements, infrared photon pulses with wavelength centered at 700 nm (1.77 eV) and pulse length of 30 fs were used to excite the sample, and the nonequilibrium states were probed by ultraviolet pulses at 205 nm (6.05 eV).
Photoelectrons were collected by a Scienta DA30L-8000R analyzer. The overall time resolution and energy resolution are 130 fs and 19 meV, respectively [47]. Sample was cleaved at a pressure better than 3×10 -11 torr at 4 K.