By considering the crystal symmetry of the Dirac semimetal candidate SrMnBi2, it is expected that a substrate based on a square lattice is preferred to form a single-domain growth of a thin film. In this study, however, we observed different schemes of interface formation of SrMnBi2 using molecular-beam epitaxy on two oxide substrates of SrTiO3(001) and LaAlO3(001), both of which are often applied to the growth of the films with square lattices. Although antiphase domains appear in the SrMnBi2 film on SrTiO3(001), a single domain develops on LaAlO3(001) with an abrupt interface. The distinct difference indicates that the surface of the LaAlO3(001) substrate plays a crucial role in the selection of the initial growth plane. Judging from the abrupt interface image in scanning transmission electron microscopy and the four-fold symmetric in-plane x-ray diffraction pattern representing the orientation relationship of SrMnBi2 film //LaAlO3 , the polar surface termination with (AlO2)− or (LaO)+ probably promotes the interface formation of the ionic Sr or Bi plane on the surface, respectively. According to the semimetallic electronic structure of SrMnBi2, the electrical transport properties of the films can be consistently evaluated by the two-carrier model with high-mobility electrons and low-mobility holes. Our demonstration of the single-domain growth of the Dirac semimetal provides a key technique toward the future engineering of heterostructures composed of topological materials.
Two-dimensional Dirac material graphene has been attracting keen interests for the intriguing electrical transport properties stemming from the linear energy dispersion of the electronic structure.1–4 This feature of Diracness has been conceptually expanded to the materials with three-dimensional linearly dispersive bands, classified as Dirac semimetals.5–20 Among a variety of Dirac semimetals, layered compounds AMnBi2 (A = Ca, Sr, and Eu) are the possible candidates for the emergence of the interacting phenomena between Dirac electrons and their magnetism.6,21,22 The angle-resolved photoemission spectroscopy (ARPES) and first principle calculation for SrMnBi2 have revealed that the highly anisotropic Fermi surface of linearly dispersive bands generally originates from the Bi square plane sandwiched by Sr.6,21,23 According to the linear bands, the electron transport in a bulk single crystal of SrMnBi2 exhibits a high mobility of about a few hundred to thousand cm2 V−1 s−1, inducing a large linear magnetoresistance (MR)24 and Shubnikov-de Haas oscillations.6,24 In view of the magnetism, the Mn2+ spins with a half-filled 3d5 electronic configuration induce a long-range antiferromagnetic order, which is coupled to the Dirac electrons.25,26 Owing to the specific structure with the Eu spin adjacent to the Bi square plane in EuMnBi2, the interaction between magnetism on Eu2+ and the Dirac electron is clearly manifested by the appearance of the dramatic variation of the magnetic and electrical transport properties at magnetic transition.22,27 Based on these interacting phenomena with Dirac electrons, the AMnBi2 thin films and heterostructures would provide a platform to explore magneto-transport phenomena originating from the interplay between the Dirac fermion and magnetic moments.22,25–28
The crystal structure of SrMnBi2 has a four-fold symmetry belonging to the space group I4/mmm.6 SrMnBi2 consists of two types of Bi square planes; one is contained within the MnBi layer, and the other is stacked with Sr, as shown in Fig. 1(a).29 The MnBi layer is composed of an MnBi4 tetrahedron, resulting in electronically negative (MnBi)−. In contrast, Sr is not strongly bonded to the two-dimensional Bi square plane although (SrBi)+ can be nominally assigned to hold charge neutrality in the crystal structure.6 There seem three possible terminations at the surface, i.e., Sr or Bi in (SrBi)+, or Bi in (MnBi)−. Since the lattice size of the Bi square plane in the (MnBi)− layer is different from that in the (SrBi)+ layer, interface engineering for such polar layered materials will provide a key contribution to synthesize high-quality films and heterostructures with controllable interface interaction. As the space group of a closely related compound CaMnBi221,23 (the space group P4/nmm) with a layered structure similar to SrMnBi2 is identical to that of other pnictide compounds involving an iron-based superconductor LaFeAsO with (LaO)+ and (FeAs)−,30–32 we may find common features in their growth dynamics and interface stability. In this study, we found the single-domain formation in thin films of a Dirac semimetal candidate SrMnBi2 by applying the LaAlO3(001) substrate using molecular-beam epitaxy, exemplifying the effect of the polar surface for the suppression of twisted-domain formation. Electrical transport properties of the films were described by the two-carrier model, reflecting the semimetallic feature.
The lattice mismatches of SrMnBi2 to SrTiO3 and LaAlO3 substrates are compared in Fig. 1(b). The Bi–Bi distances in the (SrBi)+ and (MnBi)− layers correspond to and a, respectively, where a corresponds to the in-plane lattice constant of SrMnBi2 (a = 4.565 Å6). When we estimate the lattice mismatch based on anion distances, the lattice mismatches of the Bi–Bi distance in (SrBi)+ and (MnBi)− with the O–O distance of SrTiO3 (3.905 Å) are −17.1 and +16.9%, respectively. Those values for LaAlO3 (3.789 Å) are −14.5% and +20.5%, respectively. Although all the values are rather large in view of usual epitaxial interfaces (roughly less than a few %), the Bi plane in (SrBi)+ with the smallest mismatch may be preferable on LaAlO3. Another distinct difference between these two substrates is electric polarity. The surface of LaAlO3 has a polar feature with (LaO)+ and (AlO2)− although that of SrTiO3(001) has charge-neutral (SrO)0 and (TiO2)0.33 Figure 1(c) shows the atomic force microscopy (AFM) image of the surface of the LaAlO3(001) substrate (Furuuchi Chemical Corporation) after sonification in deionized water for 3 min, in acetone for 1 min, and in isopropyl alcohol for 1 min. The step-and-terrace structure, the step height of which corresponds to one unit cell of LaAlO3, implies the singly terminated polar surface with either the (AlO2)− or (LaO)+ plane.34–36 With reference to the previous literature,36 the LaAlO3(001) substrate sonicating in the deionized water may remove the residual LaO plane at the surface. In addition, according to the temperature dependence of surface termination,37 (AlO2)− termination seems more stable on LaAlO3(001) at room temperature. While the effect of surface polarity on the preferable interface formation has not been apparently discussed in the thin-film growth of pnictide compounds on oxide substrates, it may play a role in the fabrication of polar layered structures such as SrMnBi2.
The SrMnBi2 thin films were grown on the SrTiO3(001) and LaAlO3(001) substrates at 400 °C followed by annealing at 600 °C in a base pressure of about 8 × 10−7 Pa. Before the growth, both the SrTiO3 and LaAlO3 single-crystal substrates (Furuuchi Chemical Corporation) were sonicated in the identical process explained above for the AFM image [Fig. 1(c)]. After the installation of the substrates into the growth chamber, pre-annealing was performed at 600 °C for 1 h in the vacuum. During pre-annealing, the surface termination of LaAlO3 might be switched from (AlO2)− to (LaO)+.37 Beam equivalent pressures of Mn, Sr, and Bi were 1.4 × 10−6 Pa, 3.5 × 10−6 Pa, and 1.4 × 10−5 Pa, respectively, leading to a growth rate of 0.89 nm/min. The Bi-rich flux, 10 times larger than the Mn flux, was employed to avoid Bi deficiency, resulting in the roughly stoichiometric composition in the films as detected by energy-dispersive x-ray spectroscopy (EDS). After the growth, the film was capped by a MnSe amorphous layer deposited below 150 °C. Lattice constants and in-plane orientation were determined from x-ray diffraction (XRD) patterns with Cu–Kα excitation.
Figure 2(a) shows the out-of-plane XRD pattern for the 50-nm-thick SrMnBi2 thin film on SrTiO3(001). Most of the diffraction peaks from the films are consistent with SrMnBi2(00), indicating -oriented growth. From the SrMnBi2(006) peak, the c-axis length is estimated to be 22.99 Å. In addition, the peaks around 8.6 and 26.0° are assigned to the other segregated phases (supplementary material, Fig. S1). As shown in the in-plane phi-scans for SrTiO3(111) [Fig. 2(b)] and SrMnBi2(11) [Fig. 2(c)], the appearance of eight peaks for the film implies the formation of twisted SrMnBi2 domains that are aligned “parallel” for SrMnBi2 (001)//SrTiO3 (001) and “45°-rotated” for SrMnBi2 (001)//SrTiO3 (001) because both SrTiO3 and SrMnBi2 have a four-fold symmetry. By contrast, both out-of-plane [Fig. 2(d)] and in-plane [Fig. 2(f)] XRD patterns for the film on LaAlO3(001) clearly represent an almost single-domain crystalline structure without segregated phases. Moreover, the peaks in the in-plane XRD pattern of the SrMnBi2 film [Fig. 2(f)] shift by 45° from that of the LaAlO3 substrate [Fig. 2(e)]. This result suggests that the “45°-rotated” domain [SrMnBi2 (001)//LaAlO3 (001)] is preferably grown on LaAlO3(001). The lattice parameters c = 23.01 Å [Fig. 2(d)] and a = 4.58 Å of the thin film (supplementary material, Fig. S2) agree well with the bulk values c = 23.123 Å and a = 4.565 Å,6 indicating a negligibly weak strain effect due to the rather large lattice mismatch [Fig. 1(b)]. The single-domain formation uniquely obtained on the polar surface of LaAlO3(001) sheds light on the different growth dynamics on the charge neutral surface of SrTiO3(001), possibly related to the electrostatic stability of the interface.
The lattice arrangements of the SrMnBi2 films on the SrTiO3 and LaAlO3 substrates were imaged with high-angle annular dark field-scanning transmission electron microscopy (HAADF-STEM) shown in Fig. 3. All images were taken with the incident electron beam parallel to the  direction of the substrates. It should be noted that the observed patchy contrasts in all HAADF-STEM images are not related to the local variation of chemical composition but the damage during the polishing process, as revealed by uniform EDS mapping (Fig. S3). As expected from the XRD results for the film on SrTiO3, two types of domains are observed, as separated by the white dashed line in Fig. 3(a). In an enlarged HAADF-STEM image in Fig. 3(b), the layered contrast with atoms of bright whitish color is clearly visible in both domains, corresponding to the largest atomic number of the Bi plane in (SrBi)+. The interlayer distance between the Bi bright planes is estimated to be 11.5 Å, which is consistent with the half value of the c-axis length of SrMnBi2 [Fig. 1(a)]. Interestingly, the layered structure is displaced by c/4 along the  direction across the boundary.38 Although the interface atomic arrangement is hardly recognized because the atomic number Z contrast was tuned to SrMnBi2 or the incident electron beam was slightly deviated from the  direction of SrTiO3, each domain is likely grown from either the (SrBi)+ or (MnBi)− layer.
In contrast, the antiphase domains are not detected in the film on LaAlO3, as shown in Fig. 3(c). The uniform domain without dislocation in the wide STEM image despite the large lattice mismatch implies that the film starts to grow in a relaxed manner; thanks to the layered structure. A magnified view in Fig. 3(d) and EDS mapping (supplementary material, Fig. S3) demonstrate the abrupt interface and uniform distribution of constituent elements. Between the whitish Bi planes in (SrBi)+, two Bi planes in (MnBi)− can also be identified in a magnified STEM image of the interface between SrMnBi2 and LaAlO3 [Fig. 3(e)]. The lattice arrangement of the topmost plane of the LaAlO3 substrate is hardly resolved at the interface due to the small atomic number of Al. Here, we discuss the origin of single-domain formation on the LaAlO3 substrate. The Bi planes in (MnBi)− and (SrBi)+ are regularly stacked down to the nearby interface. However, additional atomic planes seem necessary to occupy the gap between the topmost visible LaO plane and the bottommost Bi plane [Fig. 3(e)]. One plausible interface plane is the Sr plane in the (SrBi)+ layer when the surface of the LaAlO3 substrate is terminated with the (AlO2)− plane. The other is the Bi plane on the (LaO)+ terminated surface. A high-resolution TEM capable of capturing a large dynamic Z range should be able to capture the interface structure of Bi/Sr/(AlO2)− or Bi/(LaO)+ in a future study.
For the single-domain film on LaAlO3, longitudinal (ρxx) and Hall (ρyx) resistivities were measured by a standard five-terminal configuration. Figure 4(a) shows temperature (T) dependences of ρxx for the 250-nm-thick SrMnBi2 thin film and the typical bulk crystals.6,24 The metallic ρxx–T curve was obtained though the residual resistivity ratio (RRR) of the film is smaller than that of the bulks. As the two-dimensional Fermi surface of Dirac electrons in Bi square planes is expected,24 the conduction of SrMnBi2 is dominated by the carrier transport within the Bi plane rather than hopping between the planes. Therefore, the smaller RRR indicates the existence of defects in the Bi planes in the film. As shown in Fig. 4(b), the steep and non-saturating magnetoresistance (MR) exceeding 120% up to 19 T observed at 2 K is comparable with the MR values in the previous study on the SrMnBi2 bulk single crystal.24 In addition, ρyx(H) at T = 2 K in Fig. 4(c) exhibits a highly non-linear dependence. Here, the SrMnBi2 film likely possesses the same semimetallic band features as bulk crystals6,24 so that the two-carrier model should be applied to understand the ρyx(H) behavior. We analyze the non-linear ρyx(H) data for the SrMnBi2 film using the two-carrier model given as follows:39
With this analysis, the carrier densities of electrons and holes (n and p) and their mobilities (μe and μh) can be estimated independently. The experimental data are well fitted with Eq. (1), as shown in a black solid line in Fig. 4(c). The carrier density n and p of 4.3 × 1019 and 5.7 × 1020 cm−3, respectively, and mobility μe and μh of 765 cm2 V−1 s−1 and 235 cm2 V−1 s−1, respectively, were obtained. Considering the previous literature with electrical transport and ARPES,6,24 the electronic structure of SrMnBi2 consists of the Dirac-like linear bands along the Γ–M line and a 3D-like hole pocket at the Z-point. The size of the Fermi surface of the Dirac-like linear bands is smaller than that for the 3D-like hole band.6 Here, we expect that the carrier density reflects the size of the Fermi surface and the carrier mobility is larger for the Dirac-like linear bands than that for the 3D-like hole band. The lower density and higher mobility of electrons than those of holes in the analysis imply that the electrons and holes are derived from the Dirac-like and the 3D-like bands, respectively. It means that the Fermi level (EF) in our thin films is located above the Dirac point. This result is in contrast to the theoretical calculation, showing that EF is located in the hole side of the Dirac-like linear bands.6,21,23–25 Disagreement of EF between the experiments (both bulk crystals and films) and the band calculation may be relevant to defects in those samples. To make the Dirac-band contribution to be more dominantly observed, the suppression of the conduction in the bulk band is required via precisely tuning the Fermi level into the Dirac band by chemical doping and/or by electrostatic doping in a field-effect transistor configuration.
In summary, we demonstrate the single-domain growth of Dirac semimetal candidate SrMnBi2 on LaAlO3(001) owing to the suppression of the formation of the twisted domain. In contrast to the films grown on SrTiO3 exhibiting antiphase domains, a clear layered structure with an abrupt interface is obtained on LaAlO3. The electrostatic polar effect of the LaAlO3 substrate likely plays a critical role in the interface formation of SrMnBi2. This concept may be applied to other polar materials such as Fe-based pnictide compounds. Electrical transport measurements reveal that electrons and holes comparably contribute to conduction, reflecting the semimetallic band structure of SrMnBi2. The demonstration of the domain control of the Dirac semimetal provides a key guideline toward future electronic devices based on the topological materials.
See the supplementary material for the results of the 2 theta-omega scan of the XRD pattern for the SrMnBi2 film on the SrTiO3 substrate (Fig. S1), reciprocal space mapping of XRD (Fig. S2), and chemical composition mapping of the STEM image (Fig. S3) for the SrMnBi2 film on the LaAlO3 substrate.
The data that support the findings of this study are available from the corresponding author upon reasonable request.
The high-field measurements up to 19 T were performed at the High Field Laboratory for superconducting materials at Tohoku University. The STEM images were taken at, Analytical Research Core for Advanced Materials, Institute for Materials Research, Tohoku University. This work was supported by the Japan Society for the Promotion of Science KAKENHI (Grant Nos. JP15H05853 and 19K23415) and JST CREST (Grant No. JPMJCR18T2).