Interplay between the magnetic structures and the surface states in MnBi 2Te4from rst-principles studies Zujian Dai1 2Gan Jin1 2and Lixin He1 2

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Interplay between the magnetic structures and the surface states in MnBi2Te4from

ﬁrst-principles studies

Zujian Dai,1, 2 Gan Jin,1, 2 and Lixin He1, 2, ∗

1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, Anhui, China

2Synergetic Innovation Center of Quantum Information and Quantum Physics,

University of Science and Technology of China, Hefei, 230026, China

The antiferromagnetic (AFM) topological insulator MnBi2Te4was believed to have a topologi-

cal surface state (TSS) with large band gap due to the ferromagnetic (FM) order on the surface,

and be able to host the long-sought axion states. However, recent angle-resolved photoemission

spectroscopy (ARPES) experiments indicate that the TSS is gapless, contradicting the theoretical

predictions. Meanwhile, several experiments have suggested that there is robust out-of-plane FM

order on the surface of MnBi2Te4. To understand these seemingly contradictory results, we carry

out comprehensive ﬁrst-principles calculations to investigate the interplay between the surface mag-

netism and the TSS. Our calculations provide direct evidence that in a wide range of parameters,

the (nearly) gapless TSS can coexist with the surface FM order, therefore solving the paradox of the

surface magnetism and the gapless TSS. We further show that proximity eﬀects can be a promising

route to open the gap in the TSS of MnBi2Te4. Our research deepens the understanding of the

relationship between surface magnetism and TSS.

The interplay between magnetism and nontrivial band

topology may lead to rich physical phenomena that not

only are interesting for fundamental physics but also

have important potential applications in spintronic de-

vices [1, 2]. Therefore, MnBi2Te4, the ﬁrst synthesized

intrinsic magnetic topological insulator (MTI)[3–5], has

attracted great attention since its appearance [6–10].

MnBi2Te4has an A-type antiferromagnetic (AFM) struc-

ture, which enables unique thickness-dependent topolog-

ical properties: for a thin ﬁlm with an odd number of

layers, it is the QAH insulator [11–15], whereas for a thin

ﬁlm with an even-number of layers, it is the long-sought

axion insulator[9, 13, 14, 16–24].

However, despite intensive research, the nature of the

topological surface states (TSSs) of this material is still

very controversial[6, 18, 25–38]. First-principles calcu-

lations predicted that MnBi2Te4has a TSS with con-

siderable energy gap (larger than 60 meV) due to the

ferromagnetic (FM) spin order on the surface[6, 8, 9, 25–

27], which is promising for achieving QAH at rather high

temperatures. Nevertheless, the zero-ﬁeld QAHE was

observed only at rather low temperatures (below 1.6 K)

in this system [12, 13]. The gapped TSS was reported

in early ARPES experiments [6, 25–27]. However, more

recent ARPES measurements have observed a nearly per-

fect Dirac cone or a strong reduction of the gap at the

Dirac point on the MnBi2Te4(0001) surface [18, 28–

36, 38].

To understand the origin of the gapless TSS [37], three

scenarios have been proposed, including surface mag-

netic reconstruction [18, 31, 39], geometric reconﬁgu-

ration [36, 40–43] and hybridization of the surface and

bulk bands [44, 45]. For surface magnetic reconstruc-

tion, it has been shown that three types of surface spin

reorientation may led to gapless TSSs, including para-

magnetism (PM), in-plane A-type AFM, and G-type

AFM[29]. However, both time-resolved angle-resolved

photoemission spectroscopy (ARPES)[46], and magnetic

force microscopy [47] suggested that there is robust out-

of-plane FM order on the surface of MnBi2Te4. A key

perplexity here is weather the gapless TSSs can coexist

with surface FM order[46].

In this Letter, we carry out comprehensive ﬁrst-

principles calculations to investigate the interplay be-

tween the surface magnetism and the TSS. Our calcu-

lations provide solid evidence that in a wide range of

parameters, the (nearly) gapless TSSs can coexist with

the surface FM order, therefore solving the paradox of

the surface magnetism and the gapless TSS. We further

show that proximity eﬀects can be a promising route to

open the gap in the TSSs of MnBi2Te4.

The ﬁrst-principle calculations are carried out with

the Atomic orbtial Based Ab-initio Computation at

UStc (ABACUS) code[48, 49]. The Perdew-Burke-

Ernzerhof[50] (PBE) exchange-correlation functional is

adopted and the DFT-D3 correction is used to account

the van der Waals (vdW) interactions[51]. A Hubbard-

like Uvalue of 4.0 eV is used for the half-ﬁlled, strongly

localized Mn 3d orbitals [52, 53]. The ABACUS code

is developed to perform large-scale density functional

theory calculations based on numerical atomic orbitals

(NAO)[48]. The optimized norm-conserving Vanderbilt

(ONCV) [54] fully relativistic pseudopotentials [55] from

the PseudoDojo library[56] are used. The valence elec-

trons for Mn, Bi and Te are 3s23p63d54s2, 5d106s26p3

and 4d105s25p4, respectively, and the NAO bases for Mn,

Bi and Te are 4s2p2d1f, 2s2p2d and 2s2p2d, respectively.

In the self-consistent and band structure calculations, the

energy cutoﬀ for the wave functions is set to 120 Ry. Ex-

perimental lattice parameters [57] have been used. The

atomic positions are fully optimized until all forces are

less than 0.01 eV/˚

arXiv:2210.14009v1 [cond-mat.mtrl-sci] 25 Oct 2022

FIG. 1. (a)The unfolded band spectra of MnBi2Te4in the PM phase. (b) Comparison of unfolded band spectra of MnBi2Te4

in the PM and A-type AFM phases around the Γ point. The color shows the spectra intensity, which is broadened by 4 meV.

BCB and BVB denote the bulk conduction bands, and bulk valence bands respectively. The energy band splitting of BCB and

BVB in the AFM phase is denoted by ∆Cand ∆V, respectively.

The MnBi2Te4has a vdW stacking structure (space

group R¯

3m) with a MnTe bilayer sandwiched by Bi2Te3.

The unit cell consists of a Te-Bi-Te-Mn-Te-Bi-Te septuple

layer (SL)[27, 58, 59]. Below the N´eel temperature TN=

25K, the spins within each SL are found to be parallel

to the out-of-plane easy axis but antiparallel within the

adjacent SLs[6, 27, 59, 60]. The conduction and valance

band splittings in MnBi2Te4below the N´eel temperature

were reported, due to the spins ordering below the N´eel

temperature [28, 45].

We ﬁrst examine the impact of magnetism on the bulk

band structures, by comparing the band structures of

MnBi2Te4in the PM and A-type AFM phases. To sim-

ulate the band structure of the bulk MnBi2Te4in the

PM phase, we construct a 4×4×4 supercell. The Ising-

like spins on Mn ions [46] are randomly initialized. We

neglect the structure relaxation due to diﬀerent spin con-

ﬁgurations.

The band structures calculated in the supercell are un-

folded to the nonmagnetic unit cell[61, 62]. We ﬁnd that

the unfolded band structures of diﬀerent random spin

conﬁgurations are almost the same, which suggests that

the supercell is large enough to describe the PM state.

The unfolded band structures of the PM phase are shown

in Fig. 1(a), which shows a sharp and well-deﬁned band

spectra around the Γ point. However, the bands become

blurred around the Zand Fpoints. This is because,

around the Γ point, where the Bloch states have long

wave length, the spin conﬁgurations are well averaged

within the wave length range. In contrast, when the wave

length of the Bloch states is short, the short range spin

ﬂuctuation blurs the band structure.

The band structures of MnBi2Te4in the PM phase

around the Γ point are compared to those in the AFM

phase in Fig. 1(b). In addition to some diﬀerences in de-

tails, there is a signiﬁcant diﬀerence between the AFM

bands and PM bands, i.e., the highest valence band and

the lowest conduction bands of PM states split into two

bands in the AFM states. The energy splitting of the con-

duction band minimum(CBM) is approximately 90 meV,

which is larger than that from ARPES experiments[28]

(50 meV at 7.5 K). The diﬀerence might come from that

the magnetic state near the surface is not perfect AFM

in experiments.

We now turn to the surface states of the MnBi2Te4un-

der diﬀerent magnetization. We construct a slab contain-

ing 4×4×6 MnBi2Te4unit cells. There are 96 Mn atoms

in the slab. We change the spin orientations of Mn ions

in the slab to realize diﬀerent magnetic conﬁgurations. A

15 ˚

A vacuum is added to avoid the interactions between

the slab and its periodic images. The atomic positions of

the slab is relaxed under the A-type AFM conﬁguration.

The band structure of the perfect A-type AFM

MnBi2Te4slab is shown in Fig. 2(a). We determine the

surface states by analyzing the real space distributions

of the wave functions. The surface state has a consid-

erable gap of 65 meV, which is consistent with previous

theoretical results [6, 8, 9, 25–27].

When the temperature is above the N´eel temperature,

the experiment shows that MnBi2Te4becomes PM and

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InterplaybetweenthemagneticstructuresandthesurfacestatesinMnBi2Te4fromrst-principlesstudiesZujianDai,1,2GanJin,1,2andLixinHe1,2,1CASKeyLaboratoryofQuantumInformation,UniversityofScienceandTechnologyofChina,Hefei230026,Anhui,China2SynergeticInnovationCenterofQuantumInformationandQuantumPhysics,Univ...

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Interplay between the magnetic structures and the surface states in MnBi 2Te4from rst-principles studies Zujian Dai1 2Gan Jin1 2and Lixin He1 2

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