Single-domain formation of SrMnBi₂ films on polar LaAlO₃ substrate

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 CaMnBi₂^21,23 (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 $a/2$ 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$2n̲$⁠), indicating [001]-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$14̲$⁠) [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)[100]//SrTiO₃ (001)[100] and “45°-rotated” for SrMnBi₂ (001)[110]//SrTiO₃ (001)[100] 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)[110]//LaAlO₃ (001)[100]] 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 [100] 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 [001] 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 [100] 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 (ρ_xx) and Hall (ρ_yx) resistivities were measured by a standard five-terminal configuration. Figure 4(a) shows temperature (T) dependences of ρ_xx for the 250-nm-thick SrMnBi₂ thin film and the typical bulk crystals.^6,24 The metallic ρ_xx–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, ρ_yx(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 crystals^6,24 so that the two-carrier model should be applied to understand the ρ_yx(H) behavior. We analyze the non-linear ρ_yx(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 (μ_e and μ_h) 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 μ_e and μ_h 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 (E_F) in our thin films is located above the Dirac point. This result is in contrast to the theoretical calculation, showing that E_F is located in the hole side of the Dirac-like linear bands.^6,21,23–25 Disagreement of E_F 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.