⇦Chinese Physics Letters, 2021, Vol. 38, No. 10, Article code 107404 Detection of Magnetic Gap in Topological Surface States of MnBi$_{2}$Te$_{4}$ Hao-Ran Ji (季浩然)1†, Yan-Zhao Liu (刘彦昭)1†, He Wang (王贺)2, Jia-Wei Luo (骆佳伟)1, Jia-Heng Li (李佳恒)3,4, Hao Li (李昊)5,6, Yang Wu (吴扬)6,7, Yong Xu (徐勇)3,4,8, and Jian Wang (王健)1,3,9,10* Affiliations 1International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China 2Department of Physics, Capital Normal University, Beijing 100048, China 3State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China 4Frontier Science Center for Quantum Information, Beijing 100084, China 5School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China 6Tsinghua-Foxconn Nanotechnology Research Center and Department of Physics, Tsinghua University, Beijing 100084, China 7Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China 8RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan 9CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China 10Beijing Academy of Quantum Information Sciences, Beijing 100193, China Received 2 August 2021; accepted 15 September 2021; published online 29 September 2021 Supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0303302, 2018YFA0305604, and 2018YFA0307100), the National Natural Science Foundation of China (Grant Nos. 11888101, 11774008, 11704279, 11874035, and 51788104), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), the Beijing Natural Science Foundation (Grant Nos. Z180010 and 1202005), and the Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University (Grant No. KF202001).
†These authors contributed equally to this work.
*Corresponding author. Email: jianwangphysics@pku.edu.cn Citation Text: Ji H R, Liu Y Z, Wang H, Luo J W, and Li J H et al. 2021 Chin. Phys. Lett. 38 107404    Abstract Recently, intrinsic antiferromagnetic topological insulator MnBi$_{2}$Te$_{4}$ has drawn intense research interest and leads to plenty of significant progress in physics and materials science by hosting quantum anomalous Hall effect, axion insulator state, and other quantum phases. An essential ingredient to realize these quantum states is the magnetic gap in the topological surface states induced by the out-of-plane ferromagnetism on the surface of MnBi$_{2}$Te$_{4}$. However, the experimental observations of the surface gap remain controversial. Here, we report the observation of the surface gap via the point contact tunneling spectroscopy. In agreement with theoretical calculations, the gap size is around 50 meV, which vanishes as the sample becomes paramagnetic with increasing temperature. The magnetoresistance hysteresis is detected through the point contact junction on the sample surface with an out-of-plane magnetic field, substantiating the surface ferromagnetism. Furthermore, the non-zero transport spin polarization coming from the ferromagnetism is determined by the point contact Andreev reflection spectroscopy. Combining these results, the magnetism-induced gap in topological surface states of MnBi$_{2}$Te$_{4}$ is revealed. DOI:10.1088/0256-307X/38/10/107404 © 2021 Chinese Physics Society Article Text Introducing ferromagnetism (FM) to a topological insulator (TI) can break the time-reversal symmetry and generate exotic quantum phases, leading to potential applications in the fields of spintronics and quantum computing.[1–9] A traditional method to realize a magnetic TI system is doping transition metal elements into TI thin films, such as Cr-doped (Bi$_{1- x}$Sb$_{x}$)$_{2}$Te$_{3}$ thin films.[9] However, the inevitable inhomogeneity produced in the doping process impedes the realization of a perfect magnetic TI. Hence, intrinsic magnetic TI single crystal is highly desired. Recently, the high-quality MnBi$_{2}$Te$_{4}$ single crystal was successfully synthesized and verified to be such an intrinsic magnetic TI.[10–15] MnBi$_{2}$Te$_{4}$ and its family have rapidly drawn broad interest as promising platforms to investigate many long-sought topological phenomena. For example, quantum anomalous Hall effect, axion insulator state, and high-Chern-number insulator phase have been reported in MnBi$_{2}$Te$_{4}$ thin film devices.[13–15] Currently, one of the research interests focuses on the experimental detection of the magnetic gap in the topological surface states of MnBi$_{2}$Te$_{4}$, which is theoretically predicted to be induced by surface FM.[16,17] So far, several angle-resolved photoemission spectroscopy (ARPES) experiments have been carried out to detect the surface gap. One ARPES work reports a surface gap even at temperatures above the antiferromagnetism (AFM) transition temperature (Néel temperature $T_{\rm N} \sim 24$ K).[10] However, some other ARPES works suggest that the topological surface states remain gapless across the $T_{\rm N}$.[18–20] Thus, the ARPES results of the gapped surface states are controversial and inconsistent with the theoretical predictions. Further evidence, especially via different experimental techniques, is strongly desired. The needle-anvil point contact spectroscopy method is a powerful tool to study the local properties of the sample surface by measuring the electrical transport through a small constriction.[21–25] Two types of point contact spectroscopy are adopted to study the sample properties: point contact tunneling spectroscopy (PCTS)[22,23] and point contact Andreev reflection spectroscopy (PCARS).[24,25] The PCTS method is carried out with a relatively large contact barrier at the tip-sample interface, in which the electron tunneling is dominant in the electrical transport across the contact. In the PCTS measurements, the obtained point contact spectra (PCS) provide the information of the electronic density of states (DOS) around the Fermi level in the sample surface.[26] The PCARS method is usually performed on the superconducting point contact formed by a superconductor and a metal. In the PCARS measurements, the transport spin polarization of the ferromagnetic sample can be measured.[25,27,28]
cpl-38-10-107404-fig1.png
Fig. 1. Transport and magnetic properties of MnBi$_{2}$Te$_{4}$ single crystal. (a) Temperature dependence of $\rho_{xx}$ measured from 200 K to 1.8 K. The kink around 24 K reveals the AFM transition. The inset shows the crystal structure of MnBi$_{2}$Te$_{4}$. Magnetic moment directions of Mn ions are denoted by red and blue arrows. (b) and (c) Behavior of $\rho_{xx}$ and $\rho_{yx}$ at different temperatures in out-of-plane magnetic field. The lower and upper critical magnetic fields are labeled by $B_{\rm c1}$ and $B_{\rm c2}$, respectively. Inset of (b) is a schematic structure of the electrical transport measurements. (d)–(e) $M$–$T$ curves of MnBi$_{2}$Te$_{4}$ measured under ZFC and FC process in a magnetic field of 0.01 T applied out-of-plane (d) and in-plane (e), respectively. (f) Magnetization versus out-of-plane magnetic field at different temperatures. Inset of (f) shows the in-plane magnetic field dependence of magnetization at 1.8 K.
In this Letter, high-quality MnBi$_{2}$Te$_{4}$ single crystals are characterized by systematic transport and magnetization measurements. The electronic and magnetic properties of MnBi$_{2}$Te$_{4}$ are consistent with the previous reports.[10,11,14] The electronic structure on the (111) surface of MnBi$_{2}$Te$_{4}$ is studied through PCTS measurements. The obtained PCS characterize an energy gap, which is around 50 meV at 2 K and disappears around $T_{\rm N} \sim 24$ K. The gap size and temperature-dependent evolution are consistent with theoretical predictions on the magnetic gap in topological surface states. The out-of-plane magnetoresistance hysteresis is obtained through point contact junctions on the sample surface, showing the surface FM in MnBi$_{2}$Te$_{4}$. The transport spin polarization of approximately 0.5 is determined by the PCARS measurements, further supporting the surface FM. The combined results suggest the experimental detection of the magnetism-induced gap in topological surface states.[16,17] MnBi$_{2}$Te$_{4}$ is a van der Waals layered material and consists of Te–Bi–Te–Mn–Te–Bi–Te septuple layers (SLs) stacking in the ABC sequence along the out-of-plane direction,[12,16] as shown in the inset of Fig. 1(a). It exhibits A-type AFM in the bulk and two-dimensional (2D) FM within each SL.[10–12,29] The electronic and magnetic properties of MnBi$_{2}$Te$_{4}$ single crystals are characterized by systematic transport and magnetization measurements. Figures 1(a)–1(c) display the electrical transport results. The Hall bar structure was used for the measurements, as shown in the inset of Fig. 1(b). The temperature dependence of longitudinal resistivity ($\rho_{xx}$–$T$) is shown in Fig. 1(a). A distinct kink at around 24 K suggests that the Néel temperature of our sample is about 24 K, consistent with the previous reports.[12,14] Figures 1(b) and 1(c) show the longitudinal resistivity $\rho_{xx}$ and the Hall resistivity $\rho_{yx}$ as a function of the out-of-plane magnetic field at different temperatures. Below the Néel temperature, two transitions can be observed in both magnetoresistance and Hall trace curves with increasing magnetic field [Figs. 1(b) and 1(c)]. The corresponding critical fields are marked as $B_{\rm c1}$ and $B_{\rm c2}$, respectively. The lower critical field $B_{\rm c1}$ is about 3.3 T at 1.8 K. At $B_{\rm c1}$, both $\rho_{xx}$ and $\rho_{yx}$ exhibit one remarkable drop. Previous studies attribute the drop at $B_{\rm c1}$ to the occurrence of the spin-flop and the system entering a metastable canted AFM (cAFM) state.[12,14,30] As the magnetic field further increases and exceeds $B_{\rm c2}$ ($\sim $7 T), weak anomalies are detected in $\rho_{xx}$ and $\rho_{yx}$, indicating that the spins are fully polarized and the system is driven into an FM state. These two critical fields $B_{\rm c1}$ and $B_{\rm c2}$ become lower as the temperature increases and vanishes above $T_{N}$. The negative slopes of the Hall traces indicate that the charge carriers of bulk are electron-type. At the low field region below $B_{\rm c1}$, the $\rho_{yx}$ shown in Fig. 1(c) linearly decreases with increasing magnetic field. The carrier density and the mobility at 1.8 K are $1.08 \times 10^{20}$ cm$^{-3}$ and 70 cm$^{2}$/V$\cdot$s, respectively, close to the previous report.[14] The magnetization measurement results are shown in Figs. 1(d)–1(f). Figures 1(d) and 1(e) display the temperature dependence of magnetization ($M$–$T$) measured in zero-field cooling (ZFC) and field cooling (FC) process under a magnetic field of 0.01 T. Magnetic field is applied along and perpendicular to the $c$ axis, respectively. A kink around 24 K reveals the AFM transition, consistent with the transport measurement results. Curves of magnetization $M$ as a function of out-of-plane magnetic field $B$ at different temperatures are plotted in Fig. 1(f). At 1.8 K, the critical field of AFM to cAFM transition ($B_{\rm c1}$) is around 3.3 T and the kink at $B_{\rm c1}$ disappears above $T_{\rm N}$. On the contrary, only linear field dependence can be observed when the magnetic field is applied in the $ab$ plane, as shown in the inset of Fig. 1(f). The spin-flop transition in $M$–$B$ curves and anisotropic magnetization agree with the predicted A-type AFM feature.[11,12] To study the surface states and surface FM of MnBi$_{2}$Te$_{4}$, we performed point contact experiments with a standard needle-anvil configuration [inset of Fig. 2(a)]. The point contact is established between a mechanically sharpened metallic or superconducting tip and the (111) surface of MnBi$_{2}$Te$_{4}$ mounted on Attocube piezo-positioners. Differential conductance ($dI/dV$) of the PCS is obtained by standard lock-in technique in quasi-four-probe configuration. The experiments are conducted in a dilution refrigerator from Leiden. Firstly, the PCTS measurements using platinum-iridium (PtIr) tips are performed to probe the local DOS of the sample surface.[26] In our experiments, the sample is intentionally exposed to atmosphere, not only to create an oxidized barrier at the tip-sample contact interface,[23] but also to modulate the surface Fermi level of the sample.[14,18] The $dI/dV$ spectra of PCTS measurements exhibit a common feature: the linear conductance structure (LCS) in a bias voltage range over tens of millivolts, which is a signature of the tunneling type point contact.[31–36] Typical PCS at different temperatures are shown in Fig. 2(a), where the $dI/dV$ value exhibits a linear increase with applied bias voltage, leading to the LCS in the spectra. This kind of LCS in the spectra has been reported in previous tunneling junctions and PCTS experiments with an oxidized or anodized surface.[34–36] The LCS in the $dI/dV$ spectra is normally ascribed to the inelastic tunneling effect at the contact interface.[31–35] As seen from the two $dI/dV$ curves in Fig. 2(a), at 6 K, there is a sharp minimum structure around zero bias voltage, which is smoothed out as the temperature increases to 24 K. This thermal smearing effect is consistent with the inelastic tunneling scenario, which can be characterized by the full width at half maximum (FWHM) of the second derivative of differential conductance $d^{2}G/dV^{2}$, where $G$ denotes the $dI/dV$.[31] As shown in Fig. 2(b), the FWHMs of $d^{2}G/dV^{2}$ of the spectra at different temperatures exhibit a monotonic and linear increase with a slope of $6.1k_{\scriptscriptstyle {\rm B}}T$ ($k_{\scriptscriptstyle {\rm B}}$ is the Boltzmann constant). This temperature-dependent behavior is in agreement with the theoretical calculations.[31] Thus, the LCS in the measured PCS indicates that the corresponding point contacts are in the tunneling limit and meet the PCTS conditions. More discussions on the PCTS measurements can be found in the Supplementary Materials. Since the LCS is the inelastic tunneling feature originating from the tunneling barrier,[31–36] it does not affect the intrinsic PCTS features from the sample.[32]
cpl-38-10-107404-fig2.png
Fig. 2. The PCTS measurements on MnBi$_{2}$Te$_{4}$ single crystal with a PtIr tip. (a) A typical type of normalized $dI/dV$ spectra obtained at 6 K and 24 K that show a large V-shaped LCS. Solid lines are guiding lines for the LCS. The zero-bias contact resistance at 6 K is 1354 $\Omega$. Inset in (a) is a schematic of the point contact configuration. (b) The FWHMs of the $d^{2}G/dV^{2}$ of the spectra and the best linear fit. The dotted line in the inset of (b) is the $d^{2}G/dV^{2}$ around zero bias of the spectrum at 6 K in (a). The red solid line is the best Gauss fitting curve that gives the FWHM value of the $d^{2}G/dV^{2}$. (c) Normalized $dI/dV$ spectra at selected temperatures from another point contact state. The zero-bias contact resistance at 2 K is 699 $\Omega$. Two vertical dashed lines indicate the detected dip feature that deviates from the background. Solid lines are guiding lines for the LCS. The spectra are shifted for clarity. Inset in (c) is the whole set of normalized and shifted spectra of (c). Two vertical dashed lines indicate the detected gap. (d) Normalized $dI/dV$ spectra after removal of the background from (c). Two vertical dashed lines indicate the detected dip feature. The spectra are shifted for clarity.
In addition to the LCS, spectral features implying a gapped electronic structure are also observed on multiple point contact states. One typical set of PCS is shown in the inset of Fig. 2(c). The spectra at selected temperatures are shown in Fig. 2(c) for clarity. All the spectra exhibit the distinct LCS, indicating that the point contact is in the tunneling limit. The main difference in Fig. 2(c), compared with the PCS in Fig. 2(a), is that a zero bias conductance dip feature emerges at relatively low temperature and vanishes at high temperature. For the PCS at 2 K and 3 K shown in Fig. 2(c), it can be clearly distinguished that a sharp dip structure emerges within several tens of millivolts, deviating from the LCS. Here, the spectrum at 24 K is taken as a background and subtracted from this set of PCTS result, since the dip structure completely disappears at 24 K and no clear difference can be found when temperature increases from 22 K to 24 K. The subtracted curves are shown in Fig. 2(d) where the dip structure gets more distinct. The characteristic energy around 50 meV can be determined by the two kinks in the PCS. With increasing temperature, the dip structure gradually smears out and disappears above 22 K. The conductance dip in the $dI/dV$ spectra with such temperature dependence is generally taken as a sign of an energy gap.[37–39] In our experiment, the gap completely disappears at 24 K, corresponding to the Néel temperature of our MnBi$_{2}$Te$_{4}$ sample (see Fig. 1). Thus, the occurrence of the gap structure is likely connected to the magnetism of MnBi$_{2}$Te$_{4}$. Also, the characteristic energy scale of 50 meV is consistent with the theoretical predictions of the magnetic gap in the topological surface states on the (111) surface of MnBi$_{2}$Te$_{4}$.[16] Given the characteristics of the observed gap and its consistencies with theoretical calculations, the gap structure in PCTS curves can be interpreted as the magnetism-induced gap in the topological surface states. The gap features are also detected in different point contact states with similar critical temperatures (from 20 to 24 K) and energy sizes (from 30 to 50 meV), which can be found in the Supplemental Materials. However, the gap structure is absent in some other point contact states. This phenomenon can be attributed to some possible mechanisms, including the large energy difference between the Fermi level and the location of the surface gap, the imperfect magnetic order on the surface,[18,20] etc. The small chance of the detection of the gap indicates that only small parts of the sample surface host the gapped surface states. Such an assumption may explain the gapless surface states results observed in previous ARPES works, considering that ARPES results are the spatially averaged signals collected in the light spot. In our point contact measurements, sharp tips with needle sizes smaller than a few micrometers are used, which makes it possible to detect the surface gap in some small areas of the sample surface. The magnetic origin of the gap is implied by its occurrence around $T_{\rm N}$. According to the theoretical prediction,[16] the spins ferromagnetically couple in each SL, and an out-of-plane FM emerges on the surface of MnBi$_{2}$Te$_{4}$ below $T_{\rm N}$. The surface FM, once exists, may be detected through surface sensitive techniques, such as point contact measurements. Figure 3 shows the magnetoresistance of the point contacts on the (111) surface of MnBi$_{2}$Te$_{4}$ using an Nb tip. The magnetoresistance (MR) is defined by $\mathrm{ MR=}\frac{R(B)-R(B=0)}{R(B=0)}\times 100\%$, and $R$ denotes the differential resistance in point contact measurements at zero bias voltage. The hysteretic behavior with two sharp dips at $B_{\bot} \sim \pm 0.7$ T is observed by sweeping the out-of-plane magnetic field [Fig. 3(a)]. In contrast, no hysteresis is observed by sweeping the in-plane magnetic field [Fig. 3(b)]. The obtained MR hysteresis substantiates the FM on the MnBi$_{2}$Te$_{4}$ surface, which orients along the $c$-axis, supporting the magnetic origin of the gap on the (111) surface of MnBi$_{2}$Te$_{4}$.
cpl-38-10-107404-fig3.png
Fig. 3. Magnetoresistance of MnBi$_{2}$Te$_{4}$ single crystal obtained by point contact measurement using an Nb tip at 2 K and zero-bias voltage with (a) an out-of-plane magnetic field and (b) an in-plane magnetic field. The zero-bias point contact resistance at $B=0$ is 820 $\Omega$.
cpl-38-10-107404-fig4.png
Fig. 4. The PCARS measurement on MnBi$_{2}$Te$_{4}$ single crystal with a superconducting Nb tip. (a) Normalized $dI/dV$ spectra at selected temperatures. The zero-bias contact resistance at 4 K is 294 $\Omega$. The spectra are symmetrized for the convenience of fitting. The solid lines are the theoretical spin-polarized BTK fitting. The curves are shifted for clarity. (b) The squares are the $\varDelta$ values obtained from the spin-polarized BTK fitting. The solid line is the BCS fitting curve, giving a BCS ratio of 2$\varDelta /k_{\scriptscriptstyle {\rm B}}T_{\rm c}=4.04$. Inset in (b) shows the fitted spin-polarization parameter $P$ and broadening parameter $\varGamma$ at different temperatures.
To further demonstrate the surface FM of MnBi$_{2}$Te$_{4}$, we carried out the PCARS measurements by pressing superconducting niobium (Nb) tips on the (111) surface of MnBi$_{2}$Te$_{4}$ to form a superconducting point contact.[25,27,28] In a ferromagnet, the conduction electrons are spin-polarized, resulting in a difference in spin population near the Fermi level. If a point contact is formed between a ferromagnetic sample and a conventional superconductor, the Andreev reflection process would be limited by the spin minority electrons around the Fermi level in the process of forming spin-singlet cooper pairs. The current through the contact can be viewed as two parts, namely the un-polarized current that obeys the conventional BTK theory and the fully polarized current that is entirely a quasiparticle current. Therefore, the resultant spin polarization coming from the ferromagnetic sample surface can be quantitatively studied by fitting the $dI/dV$ curve with the BTK model incorporating spin-polarization.[25,27,28] Here, the PCARS measurement is conducted below 10 K, well below the Néel temperature of MnBi$_{2}$Te$_{4}$ of 24 K. As shown in Fig. 4(a), the symmetrized spectra of the PCARS measurement show a clear double-peak structure that fades away as temperature gradually reaches 9 K, which is close to the superconducting transition temperature of Nb ($T_{\rm c}=9.26$ K).[40] The double-peak structure and its temperature-dependent behaviors are in accord with the features of superconducting PCS in the ballistic regime.[21,25] The superconductivity conductance enhancement in the detected PCS is less than 10% and the $dI/dV$ minimum around zero bias reaches a value that is close to the value of the normal state. These kinds of spectra are possibly due to two mechanisms: one is a relatively large interface barrier strength (parameter $Z$ in the modified BTK model) with proper broadening effects (parameter $\varGamma$) and the other is the spin-polarization (parameter $P$ in the spin-polarized BTK model) existing in the sample surface. Under the former condition, the PCS can be fitted with the BTK model without spin-polarization. However, in our work, three unreasonable fitting results make this condition improper: (i) the parameter $Z$ cannot be fixed in the fitting process; (ii) the BCS fitting gives a $T_{\rm c}$ of 9.9 K, which is larger than the $T_{\rm c}$ of Nb; (iii) the parameter $\varGamma$ is too large to stabilize a superconducting phase. The BTK fitting results without spin-polarization and the detailed discussions can be found in the Supplemental Materials. Under the latter condition, the modified BTK model incorporating spin-polarization is applied. The fitting curves of the experimental data are shown in Fig. 4(a). The fitting result gives a temperature-independent $Z=0.04$ and the $\varGamma$ values that are far smaller than the $\varDelta$ values. According to the fitting results, the superconducting gap vs temperature behavior agrees with the BCS characteristic [Fig. 4(b)] and the BCS fitting values of $\varDelta=1.61$ meV ($T=0$ K) and $T_{\rm c}=9.26$ K are consistent with the properties of Nb ($\varDelta=1.53$ meV, $T_{\rm c}=9.26$ K).[40] The spin-polarization is around 50% and changes little with increasing temperature, as shown in the inset of Fig. 4(b). Thus, the spin-polarized BTK model can well explain the PCARS results, and the spin-polarization from the out-of-plane electron transport supports the surface FM of MnBi$_{2}$Te$_{4}$. In summary, we have investigated the surface states of MnBi$_{2}$Te$_{4}$ by point contact measurements. A surface gap of MnBi$_{2}$Te$_{4}$ emerging just below the Néel temperature is detected via PCTS measurements. The gap exhibits a characteristic energy scale of $\sim $50 meV, and gradually smears with increasing temperature and eventually disappears around 24 K. These properties are consistent with the theoretical prediction of the magnetism-induced gap in the topological surface states in MnBi$_{2}$Te$_{4}$. Furthermore, the out-of-plane MR hysteresis is observed through the point contacts on the surface of MnBi$_{2}$Te$_{4}$, substantiating the surface FM. Additionally, the out-of-plane transport spin polarization on the surface is determined through the PCARS measurement, which further demonstrates the surface FM of MnBi$_{2}$Te$_{4}$. Our research clarifies an essential property of the magnetic TI MnBi$_{2}$Te$_{4}$: the magnetism-induced gap in the topological surface states, which is the foundation for understanding many novel topological phenomena and quantum phenomena in this material, such as topological magneto-electric or magneto-optic effects. We thank Yanan Li and Jun Ge for helpful discussions. 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