Optical study of magnetic topological insulator MnBi4Te7

Zhi-Yu Liao(廖知裕), Bing Shen(沈冰), Xiang-Gang Qiu(邱祥冈),4,†, and Bing Xu(许兵),‡

1Beijing National Laboratory for Condensed Matter Physics,Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China

2School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

3State Key Laboratory of Optoelectronic Materials and Technologies,School of Physics,Sun Yat-Sen University,Guangzhou 510275,China

4Songshan Lake Materials Laboratory,Dongguan 523808,China

Keywords: infrared spectroscopy,magnetic topological insulator,Drude model,band reconstruction

1.Introduction

Finding various new electronic states and unusual quantum phases has been an important subject in condensed matter physics.Since the nontrivial dissipationless edge state was observed in topological insulators (TIs), significant research efforts have been devoted to introducing magnetism into TIs to form magnetic TIs over the past few years.With the interplay between magnetism and nontrivial band topologies,magnetic TIs can be an ideal materials playground for realization of various peculiar quantum states,such as the quantum anomalous Hall (QAH) state[1–4]and axion insulator.[5–9]In 2013, the QAH effect was realized for the first time in Cr-doped topological(Bi,Sb)2Te3film at about 100 mK.[3]Such a low working temperature is due to the inhomogeneous distribution of magnetic dopants.However,stoichiometric topological materials with intrinsic magnetic order can avoid this problem and may be promising systems to find QAH effect at higher temperature.

Recently, the van der Waals layer compound MnBi2Te4with antiferromagnetic (AFM) order belowTN= 24 K has been proposed to be an intrinsic AFM TI.[10–15]Its rhombohedral crystal structure can be viewed as a stacking of septuple layers along thecaxis.Of which one septuple layer contains a magnetic Mn–Te layer inserted into a quintuple layer of topological insulator Bi2Te3.Magnetotransport experiments on few-layer flakes of MnBi2Te4have revealed signatures of QAH state and axion insulator phase.[16–18]Furthermore, angle-resolved photoemission spectroscopy(ARPES)studies on bulk crystals have observed topological gapless Dirac cone surface states,[19–23]although some research groups have reported gapped Dirac cone surface states.[12,24–26]MnBi2Te4can also constitute the progenitor of a modular(Bi2Te3)n(MnBi2Te4)series compounds,where the interlayer antiferromagnetic exchange coupling can be weakened by increasing the separation of the magnetic septuple layers with nonmagnetic quintuple layers along thecaxis.This offers a new approach to manipulating the band topology.In the case of MnBi4Te7withn=1,it exhibits an A-type antiferromagnetic structure, similar to MnBi2Te4, with in-plane ferromagnetic arrangement coupled antiferromagnetically along thec-axis belowTN= 13 K, as revealed by single-crystal neutron diffraction measurement.[27,28]ARPES studies have provided strong evidences of topological surface states on both surface terminations of Bi2Te3and MnBi2Te4.[13,22,29–36]A gap induced by hybridization effect was identified on the Bi2Te3-termination,while a gapless Dirac-cone band structure was observed on the MnBi2Te4-termination.This suggests different surface magnetic orders on the two terminations and calls for further detailed studies.[34]Meanwhile,the influence of bulk magnetic order on the low-energy excitations is still not fully understood.

In this study, we investigate the bulk electronic properties of MnBi4Te7both above and belowTNusing infrared spectroscopy.Our optical results reveal the presence of two Drude peaks in the low-frequency optical conductivity with a free-carrier response of multiple bands.The interband transitions start above 2000 cm−1and the spectral weight analysis supports the transfer of spectral weight from the interband transitions to the Drude response with decreasing temperature.Furthermore,belowTN,we observe anomalies in the low-frequency optical conductivity,which serve as signatures of a band reconstruction induced by the antiferromagnetic order.

2.Experiment

High-quality single crystals of MnBi4Te7were synthesized by a flux method.[19]We measured theab-plane frequency-dependent reflectivityR(ω) of MnBi4Te7with fresh surface at a near-normal angle of incidence, using a Bruker 80v Fourier transform infrared (FTIR) spectrometer.Anin situgold evaporation technique[37]was used for obtaining the absolute reflectivity of the sample.Data from 30 cm−1to 12000 cm−1were collected at varying temperatures with a commercial ARS-Helitran cryostat.We obtained the real part of the optical conductivityσ1(ω) through a Kramers–Kronig analysis ofR(ω).A Hagen–Rubens relationR(ω)=was applied for low-frequency extrapolation.On the high-frequency side, we used the room-temperature data from 4000 cm−1to 50000 cm−1via a commercial ellipsometer(Woollam VASE).Meanwhile, the high-frequency extrapolation was anchored by the ellipsometry data,where we assumed a constant reflectivity up to 110000 cm−1(13.6 eV),followed by a free-electron(ω−4)response.

3.Results and discussion

The temperature (T) dependence of in-plane resistivityρ(T) for MnBi4Te7shows a metallic characteristic with an anomaly aroundTN= 13 K due to the AFM phase transition, as shown in the upper inset of Fig.1(a).This is consistent with the previous results.[27,38,39]Figure 1(a) displays the in-plane reflectivityR(ω)of MnBi4Te7at different temperature up to 6000 cm−1.The lower inset shows the spectrum up to 50000 cm−1at 300 K.It shows a typical metallic response: toward zero frequencyR(ω)approaches nearly unity and increases upon cooling.At higher frequency the reflectivity gradually decreases and drops rapidly near 1500 cm−1,forming a plasma edge.This plasma edge shifts to higher frequency toward lowerT.

Figure 1(b) shows the correspondingT-dependent spectra of the real part of the complex dielectric functionε1(ω).The negative value ofε1(ω) at low frequency is another hallmark of metallic response.The zero-crossing inε1(ω)(marked by the horizontal dashed line) corresponds to the screened plasma frequency, whereωpis the free-carriers plasma frequency andε∞is the high-frequency dielectric constant.The inset shows the detailedTevolution of?.With decreasingT,has a remarkable increase from about 1250 cm−1at 300 K to near 1500 cm−1at 20 K.Moreover, there is a small decrease belowTN, indicating that the AFM order has a weak effect on the charge response.

Fig.1.The measured optical reflectivity and the corresponding real part of the complex dielectric function.(a)T dependence of in-plane reflectivity up to 6000 cm−1 for MnBi4Te7.Insets: T-dependent resistivity(top panel)and reflectivity spectrum up to 50000 cm−1 at 300 K(bottom panel).(b)T dependence of the real part of the complex dielectric function ε1(ω).Inset: temperature evolution of the screened plasma frequency extracted from the zero crossing of ε1(ω).

Figure 2(a)displays theTdependence of the real part of the complex optical conductivityσ1(ω) up to 6000 cm−1.It consists of a narrow Drude peak centered at the origin with a tail extending to about 2000 cm−1.The direct current (dc)conductivity data at 5 K and 300 K(represented by filled circles on they-axis) obtained fromρ(T) in the upper inset of Fig.1(a) agree well with the zero-frequency extrapolation ofσ1(ω).Toward higher frequency above 2000 cm−1,σ1(ω)turns to increase due to the onset of electronic interband transitions.Notably,upon cooling,the Drude peak grows strongly while the onset of region of the interband transitions is suppressed.As shown in the inset,we also compare the full-range spectrum ofσ1(ω)at 300 K between MnBi4Te7and the previously reported MnBi2Te4.[40]The overall feature of the spectrum is very similar for both compounds,consisting of a Drude response at low frequency and two dominant interband transition peaks around 10000 cm−1and 20000 cm−1.Note that the low-frequency ofσ1(ω) for MnBi4Te7is higher than that of MnBi2Te4,indicating a better carrier conduction in the former compound.

Fig.2.The real part of the complex optical conductivity and the integrated spectral weight.(a)T dependence of the real part of the complex optical conductivity up to 6000 cm−1 for MnBi4Te7.The symbols on the y axis denote σdc at 5 K and 300 K from ρ(T)data in the upper inset of Fig.1(a).Inset: spectrum up to 50000 cm−1 at 300 K for MnBi4Te7 and MnBi2Te4.(b) T dependence of the integrated spectral weight within 0–1500 cm−1 and 1500–4500 cm−1.(c)T dependence of the integrated spectral weight within 0–4500 cm−1.

To have a further analysis of the spectral change in MnBi4Te7, we calculate the integrated spectral weight (SW),,whereωcis the cutoff frequency.Figure 2(b)shows theTevolution of SW within two selected integrating ranges.Firstly,the SW below 1500 cm−1is mainly contributed by the intraband response of free carriers.It gradually increases with decreasingTand exhibits a slight decrease belowTN, aligning with the changes ofobserved in Fig.1(b).In contrast, the SW between 1500 cm−1and 4500 cm−1dominated by the interband transitions, decreases upon cooling and shows a small increase belowTN.Moreover,the total SW from 0 to 4500 cm−1keeps nearly a constant under varyingT, as is depicted in Fig.2(c).This suggests a redistribution of spectral weight between the interband and intraband transitions.

Next,we analyze quantitatively the temperature evolution of the free carriers response.A Drude model is introduced to fit the low-frequencyσ1(ω)spectra at all measured temperatures.In this model,the formula writes

whereZ0= 377 Ω is the vacuum impedance.ωp=is the plasma frequency withnandm∗the concentration and effective mass of charge carries, respectively.And 1/τdescribes the scattering rate of carriers.

Figure 3(a) shows an example of the Drude fit for the data at 5 K.The fitting curve is composed of two Drude terms (referred to as Drude 1 and Drude 2) characterized by small and large scattering rates, respectively.Such a fitting method by multiple Drude terms has been widely used in iron-based superconductors[41–43]and the recently discovered kagome superconductors[44]due to the multiband response.The two-Drude fit indicates that MnBi4Te7has two types of charge carriers with very different scattering rates.This observation is consistent with the multiband characteristic near the Fermi level (EF), as supported by the ARPES measurements and band structure calculations in MnBi4Te7.[34]The fitting parameters,ωpand 1/τ, for the two Drude terms are plotted against temperature in Figs.3(b) and 3(c), respectively.The narrow Drude term (Drude 1) exhibits strong temperature dependence with an enhancedωpand a reduced 1/τat lower temperature.The broad Drude term (Drude 2) withωp=9000 cm−1and 1/τ=850 cm−1does not change withT,which can also be inferred by the nearly unchange of the Drude tail inT-dependentσ1(ω), as shown in Fig.2(a).To further understand the responses of these two types of free carriers,we outlined the band structure of MnBi4Te7in inset of Fig.3(a).This schematic highlights the presence of two distinct conduction bands, denoted as CB1 and CB2.Accordingly, we can attribute the narrow Drude peak to the intraband transitions of CB1, as CB1 is located shallowly below the Fermi level,making it highly sensitive to the thermal effect.In contrast,the broad Drude peak corresponds to intraband transitions of CB2, which is located deeper below the Fermi level and thus is less sensitive to the thermal effect.Additionally,the optical excitations at higher energy involve transitions across the direct band gap,from the valence band(VB)to the empty states in CB1 and CB2,as indicated by the green arrows.

Fig.3.Drude fitting and the fitting parameters.(a) Drude fitting of σ1(ω) at 5 K for MnBi4Te7.Inset: schematic of the band structure.(b)and(c)The T dependence of the two fitting parameters,plasma frequency and the scattering rate,respectively.

Next, we focus on the influence of antiferromagnetic order on the carrier response.Figure 4(a) presents theσ1(ω)up to 2500 cm−1at three temperatures above and belowTN=13 K for MnBi4Te7.AboveTN,σ1(ω) is nearly unchanged.However,belowTN,we observe a slight decrease inσ1(ω)below 1000 cm−1and an increase at higher frequencies.These features can be seen clearly in the difference spectra ofσ1(ω)in Fig.4(b).The anomalous change highlights a transfer of spectral weight and suggests a band reconstruction occurring in the presence of antiferromagnetic order.This band reconstruction is caused by the band folding alongkzand splitting of conduction and valence bands,which lifts the band degeneracy due to the unit cell doubling in the AFM state.Such a band splitting is also seen in recent ARPES study.[22]

Finally, it is worthy to compare the results between MnBi4Te7and MnBi2Te4.In Fig.4(a), we also plotσ1(ω)of MnBi2Te4at three temperatures above and belowTN=24 K.In MnBi2Te4,a clear bump-like feature can be observed around 1100 cm−1, while it is not discernible in MnBi4Te7.This feature is attributed to the interband transitions between the CB1 and CB2.Here,the featureless response in MnBi4Te7suggests a lower joint density of states for such interband transitions.Another different spectral feature is the change of low-frequencyσ1(ω) belowTN, which is enhanced below 500 cm−1in MnBi2Te4while it is suppressed in MnBi4Te7.This result is consistent with the enhancement of Drude SW belowTNfor MnBi2Te4and the suppression of which for MnBi4Te7.As outlined in MnBi2Te4,[40]the anomalous change of Drude SW is related to the shift of center of the splitting conduction bands belowTNwith respect to the conduction band aboveTN.Thus, the opposite change of Drude weight implies an opposite shift of center of the splitting conduction bands in MnBi4Te7.

Fig.4.Anomaly of the optical conductivity across TN.(a)The σ1(ω)spectra below 2500 cm−1 at selected temperature above and below TN for MnBi4Te7 and MnBi2Te4.(b) The difference plots of σ1(ω) for MnBi4Te7 and MnBi2Te4.

4.Conclusion

In summary,we measured the optical conductivity of the antiferromagnetic topological insulator MnBi4Te7over a wide frequency range both above and belowTN.Our optical data reveal the presence of two Drude peaks in the low-frequency region,providing evidence for a multiband free carrier response.Meanwhile,we observe a series of interband transitions originating from valence band states to unoccupied states above the Fermi level,with an onset of interband transitions around 2000 cm−1.With decreasing temperature, we find a transfer of spectral weight from interband transitions to the Drude response.Moreover, the antiferromagnetic transition leads to anomalies in the charge response, affecting the plasma frequency and the transfer of spectral weight belowTNdue to the band reconstruction.Our study provides a deep understanding of the interplay between magnetism and electronic properties,and is also helpful in discovering more magnetic topological insulators.

Acknowledgements

Project supported by the the National Natural Science Foundation of China (Grant No.12274442) and the National Key R&D Program of China(Grant No.2022YFA1403901).