Structural study of nickelate based heterostructures

Transition metal oxide compounds,¹ and more specifically, transition metal perovskite oxides with the chemical formula ABO₃,² represent a vast playground for material engineering. This is mainly due to the plethora of physical properties they display, which depend on the choice made for the A and B cations.

Among them, metal-to-insulator transition (MIT) compounds such as rare earth nickelates (RENiO₃) have been deeply studied for understanding both their M–I transition^3,4 and complex magnetic state^5,6 and for their potential applications in novel devices.⁷ The tunability of their MIT temperature also motivated the realization and study of interesting functional heterostructures made of nickelates or combinations of nickelates with other perovskites.⁷ 

As mentioned, nickelates are well known for their MIT, which occurs at a specific temperature (T_MI), ranging from 600 to 0 K depending on the chosen rare earth cation. This value depends on the degree of distortion of the structure, which is in turn determined by the size of the A-cation. Along with this electronic transition, nickelates display a structural transition from a high temperature orthorhombic symmetry (rotation pattern a⁻a⁻c⁺ in the Glazer notation) to a low T monoclinic structure with a similar tilt pattern. In the low T structure, a breathing distortion is observed with alternating large oxygen octahedra (long bond) and smaller ones (short bond).⁷ Due to its twofold nature, the transition can be described by two different order parameters. First, an electronic one, ΔN, which describes the difference in occupation number between the Ni 3d e_g orbitals of two inequivalent nickel sites (Ni-1 and Ni-2 located at the center of the long bond and short bond oxygen octahedra, respectively), is characteristic of the insulating ground state phase. Second, Q is a structural one, which is defined as the size difference between the large and small oxygen octahedra.^8–11 

In previous work (Refs. 12 and 13), superlattices made of two different nickelate compounds (respectively, NdNiO₃ and SmNiO₃) were studied in order to investigate the length scale over which a coexistence between metallic and insulating phases can be established. More recently, in Ref. 11, insulating LaAlO₃ spacer layers were introduced between the nickelate layers to better understand the interfacial behavior of the order parameters controlling the transition (ΔN and Q). These more complex heterostructures were made of repeating stacks of (m NdNiO₃/d LaAlO₃/m SmNiO₃/d LaAlO₃)—m and d being, respectively, the thickness in unit cells of the nickelate layers and LaAlO₃ spacer layers. These structures were grown on top of (001) pseudo-cubic oriented LaAlO₃ substrates and characterized.

In Ref. 11, the transport properties (resistivity vs temperature and Hall effect measurements) of these heterostructures were studied in detail. The main findings of this previous study can be summarized as follows: For d = 0 (no LaAlO₃, SmNiO₃/NdNiO₃ superlattices), below a critical thickness of the nickelate layers, the system displays a single MIT temperature, as expected from the study realized in Ref. 12. However, for all the samples with d LaAlO₃ not equal to zero, d = 1, 2, 3, and 4, the two layers behave independently—and the system displays two different transitions in the resistivity vs temperature curves—indicative of a decoupling of the two layers.

Here, we investigate in detail the structure of these transition metal oxide superlattices through the quantitative analysis of scanning transmission electron microscopy (STEM) data, combined with density functional theory (DFT) calculations. Remarkably, we observe a reorientation of the orthorhombic long axis of the nickelates, whose rotation pattern in Glazer notation is a⁻a⁻c⁺ for the Pbnm structure (c⁺ denoting the so-called long axis, along which the oxygen octahedra rotate in phase). While for nickelate films and superlattices grown on LaAlO₃ substrates, the long-axis is always found to be pointing in-plane (parallel to the substrate interface)—the configuration minimizing macroscopic strain¹⁴—the presence of the spacer layers induces a flip of its direction, which is now found to be pointing out-of-plane across most of the heterostructure. Surprisingly, we also find that the LaAlO₃ spacer layer, rhombohedral in bulk with an a⁻a⁻a⁻ tilt pattern, develops an antipolar motion of the A-site cations below some critical thickness. These experimental findings are corroborated by DFT calculations.

Figure 1 displays a characterization of an example of the m NdNiO₃/d LaAlO₃/m SmNiO₃/d LaAlO₃ structures under study. As can be seen from both the high-angle annular dark field (HAADF) STEM images in Figs. 1(a) and 1(b) and the electron energy-loss spectroscopy (EELS) compositional map in Fig. 1(d), the sample displays high crystalline quality and a low degree of chemical intermixing. The structural quality is confirmed by the typical x-ray diffraction θ–2θ scans shown in Fig. 1(c). It is important to note that all the samples investigated here grow coherently on LaAlO₃, i.e., without dislocations or relaxation of the grown structure.¹¹ 

We now leverage STEM imaging to obtain insights into the structural nature of the heterostructures. First, we apply a technique based on the adapted geometrical phase analysis (GPA) of aberration-corrected HAADF STEM images that was developed in Ref. 14 to simultaneously visualize different Pbnm domains within the same image and map the crystallographic orientation across the studied superlattices. As mentioned before, the rotation pattern of the Pbnm structure is a⁻a⁻c⁺. These three rotations couple to an $X5−$ antipolar mode (AM), which corresponds to A-site cation displacements along the [1,0,0]_o and $[1̄,0,0]o$ directions, the previously mentioned antipolar motion. Using the adapted GPA, this antipolar motion is rendered as lines of positive and negative contrasts in a “shear-strain” map. The operating principle behind this is the choice of specific reciprocal-space virtual aperture settings for the strain calculation by the GPA algorithm. These virtual apertures are selected in such a way as to include the half-order peaks associated with the $X5−$ mode. In itself, this mode constitutes a signature of the orthorhombic structure and is not present in the rhombohedral phase.

Figure 2(a) shows a sketch of a 6 NdNiO₃/6 SmNiO₃ superlattice without LaAlO₃ spacer layers. Figure 2(b) displays a HAADF image of the superlattice, with accompanying adapted-GPA mapping of A-site antipolar motion on the right. The vertical stripes of the latter colormap correspond to vertical alternating displacements of the A-cations, henceforth determining that the orthorhombic long-axis lies in-plane as indicated in the figure. The XRD rocking curves (ω scans) displayed in Fig. 2(c) show the presence and absence of $(0,−12,1)pc$ and $(0,−1,12)pc$⁠, respectively. These half order peaks arise because of the aforementioned $X5−$ distortion, which doubles the unit cell along one pseudo-cubic axis. Since only the former peak is present, this confirms the in-plane orientation of the orthorhombic long axis found using the GPA analysis. The same analyses are performed on a 6 NdNiO₃/2 LaAlO₃/6 SmNiO₃/2 LaAlO₃ superlattice, as shown in Figs. 2(d)–2(f). The adapted GPA colormap in (e) reveals horizontal stripes, indicating that the orthorhombic long-axis of the nickelate layers now points out-of-plane. This structural orientation is confirmed by XRD in panel (f). Remarkably, therefore, the insertion of ultra-thin LaAlO₃ spacers between the RENiO₃ layers produces a flip of the long-axis orientation, from in-plane to out-of-plane.

In orthorhombic films grown on substrates having, such as the LaAlO₃ used here, cubic cation sublattices,¹⁴ the strain state of the film is a common determinant of its orientation. Here, the strain state of the nickelate layers is not modified by the insertion of the LaAlO₃ layers.¹¹ Therefore, the observed flip in orthorhombic long-axis orientation may seem surprising. Our DFT calculations do, in fact, confirm that the long-axis in plane is the minimum energy configuration without LaAlO₃ layers, whereas the energy is minimized with a long-axis out-of plane when introducing the spacer layers (see the supplementary material section, Fig. S1). Phenomenologically, a possible explanation for this change in the long-axis orientation derives from the connectivity of oxygen octahedra rotations (OORs). While LaAlO₃ has out-of-phase OOR along all three axes, the long-axis of the orthorhombic nickelate structure has in-phase OOR. If this long-axis points in-plane (as favored by strain state alone), it will create a mismatch with the out-of-phase OOR of the LaAlO₃ layers sandwiching it on either side. It appears that the energetic cost of creating interfaces that couple these mismatched OORs is sufficient to drive the nickelate layers to point their long-axis out-of-plane. This way, the nickelate layers present only out-of-phase OOR in the substrate plane, which then matches better the out-of-phase OOR of the sandwiching LaAlO₃ layers. Evidently, the interfacial energy reduction from avoiding OOR pattern mismatch is sufficient to compensate for the increase in macroscopic strain energy.

For samples with thicker LaAlO₃ spacer layers (at least 4 u.c.), it was shown that the interface roughness increases.¹¹ At the same time, we no longer observe a uniform flip of the orthorhombic long axis (see the supplementary material, section Fig. S2). This observation is likely due to the small difference in energy between the two configurations (in-plane or out-of-plane long-axis), which was found to be 2 meV/5 atom f.u. in our DFT calculations. The increase in interfacial disorder in these samples, tied to a decrease in the density of interfaces, probably affects the OOR coupling, making the two configuration possibilities very close in energy, such that neither of them predominates.

An open question is why this mechanism does not occur for single nickelate films or heterostructures (without LaAlO₃ spacer layers) since they are grown on a rhombohedral LaAlO₃ substrate. A possible explanation is linked to the fact that, in these new superlattices, we have thin nickelate layers both grown on LaAlO₃ and capped with LaAlO₃. The OOR coupling thus occurs on both sides of each nickelate layer, giving a relatively strong energetic influence. In comparison, for structures without spacer layers, the OOR coupling occurs only at the single substrate/film interface; it appears insufficient to induce a long axis reorientation away from that favored by the macroscopic strain state, given the low energy difference between the two configurations found in DFT calculations as discussed above.

Since this difference in energy is small, there should also be in superlattices with LaAlO₃ spacer layers a critical thickness of the nickelate individual layers, above which the macroscopic strain energy (that increases with the thickness of the nickelate layer) will win against the interfacial cost linked to oxygen octahedra coupling, which instead does not depend on thickness. This should lead to a long axis in-plane reorientation.

Having studied the nickelate layers, we now turn our attention to the structure of the LaAlO₃ spacer layers in the superlattices as a function of their thickness. First, we note that, in bulk, LaAlO₃ is a large bandgap insulator, which crystallizes in a rhombohedral $R3̄c$ structure with, as mentioned above, a Glazer tilt rotation pattern a⁻a⁻a⁻. This corresponds to out-of-phase rotations of the AlO₆ octahedra along the three pseudocubic axes with identical rotation amplitudes. Phonon spectra calculations using a cubic structure of LaAlO₃¹⁵ show that the system displays three unstable modes at the high symmetry R point, which condense in the 0 K calculations and lead to the rhombohedral ground state structure. Furthermore, phonon spectra for cubic LaAlO₃ do not reveal any other unstable modes at any other high symmetry points. The system is thus not close to in-phase octahedral or polar distortion instabilities. DFT calculations of the LaAlO₃ structure show, in particular, that it is very costly to try enforcing an in-phase rotation in one of the directions. It is also worth mentioning that the Imma (I4/mcm) phase of the LaAlO₃—with Glazer notation a⁻a⁻c⁰ (a⁻b⁰b⁰)—can be achieved by applying tensile (compressive) strain as this phase is energetically very close to the ground state $R3̄c$ phase. The calculations thus show that, although one or two of the out-of-phase rotations can be suppressed in LaAlO₃, it is very challenging to impose the in-phase rotations. Clearly, this is consistent with the observed imposition of an out-of-plane orthorhombic long-axis on the nickelate layers, such that out-of-phase OOR can be maintained in the LaAlO₃ spacer layers.

Despite this, an unexpected distortion is observed in the thinnest LaAlO₃ spacer layers. Figure 3(a) shows a section of a STEM-HAADF image of one superlattice of the series, specifically (6,3,6,3). Figure 3(b) presents the adapted GPA of this image section; it displays horizontal stripes, consistent with the out-of-plane orthorhombic long axis direction of the nickelate layers. From the full high-resolution image, which measures 54 pseudocubic unit cells in width, the average displacement of the A-site cation has been extracted for each atomic layer, as displayed in Fig. 3(c). Plotting the absolute value of the AM in panel (d) reveals two aspects. First, the AM distortions in the nickelate slabs are reduced when in proximity to the LaAlO₃ layers. Second, surprisingly, the AM is not completely suppressed in the nominally rhombohedral LaAlO₃ thin layers (for which no antipolar motion is expected) but rather propagates across them.

Analogous analyses of a (6,2,6,2) superlattice show very similar behavior (Fig. S3 of the supplementary material section). It is important to note that there is a certain imprecision in this finding because of the finite miscut angle of the substrate and the film deposition method, meaning that the atomic column projections observed by STEM at any superlattice interface can contain a mixture of both compounds on either side, resulting in a 1 u.c. error bar on the thickness of the layers. Nevertheless, when inspecting superlattices with thicker LaAlO₃ layers such as the (6,4,6,4) sample, which, as previously described, have lower structural quality and decreased symmetry-imposition of orthorhombic orientation on the nickelate layers, no analogous AM is observed in the LaAlO₃ spacer layers, thereby indicating that the observation of AM in the thinnest LaAlO₃ layers is not an artifact.

Given that the orthorhombic long-axis (having in-phase OOR) of the nickelate layers is out-of-plane, it can be questioned why LaAlO₃ develops an antipolar motion. The coupling of rotations is typically weak along an out-of-plane axis.^16–19 Combined with in-phase OOR being highly unfavorable in LaAlO₃, it is, therefore, unlikely that the thinnest LaAlO₃ spacer layers take on the OOR pattern of an orthorhombic compound, as typically associated with an A-cation AM. Alternatively, a possible reason comes from the A-cations themselves. At interfaces, the La cations of the LaAlO₃ spacer layers experience the potential landscape of the Nd and Sm cations of the adjacent layers. Since the latter atoms are displaced in-plane by their AM, their interaction with the La “lattice” may induce an antipolar motion in the LaAlO₃ layers. This may explain the surprising change in the LaAlO₃ structure, which, in these superlattices, is no longer “purely” rhombohedral.

To better understand the structure of the thin LaAlO₃ layers and, in particular, to confirm the observation of antipolar motion in them, DFT calculations are performed for different structures. In these simulations, the orthorhombic long axis of the nickelate layers is imposed to point in the out-of-plane direction, as observed experimentally in the superlattices containing LaAlO₃ studied here. This configuration is also the one that minimizes the energy in the DFT calculations (Fig. S1). Figures 4(c) and 4(d) display the results of DFT calculations performed on a (3,1,3,1) and (3,2,3,2) NdNiO₃/LaAlO₃/SmNiO₃/LaAlO₃ superlattices, while Figs. 4(a) and 4(b) constitute a study on simpler structures, respectively, four layers of strained NdNiO₃ and 3–1 layers of NdNiO₃-LaAlO₃. From the latter structure, it is clear that the proximity to LaAlO₃ influences both the OOR and the AM pattern of the A-cation in the nickelate layer. Without the LaAlO₃ spacer, Fig. 4(a), the out-of-phase OOR angles ϕ_a/ϕ_b display an amplitude of 7.66°, while an amplitude of the in-phase rotations ϕ_c of 6.99° is obtained, which differs from bulk NdNiO₃ due to the epitaxial strain (see the supplementary material section, Fig. S4). Furthermore, the antipolar motion, shown in Å in the last column in Fig. 4(a), perfectly cancels out in consecutive Nd layers. Upon the introduction of 1 unit cell of LaAlO₃ [Fig. 4(b)], the values of the OOR in the c-direction for NiO₆ octahedra are modified. Tied to this, the A-cation displacements are modified; not only do the La cations adopt a non-zero displacement, giving a first hint of the experimental observation in the more complex superlattices, but the Nd cations take non-uniform absolute displacement values.

Turning to Fig. 4(c) and the results for the optimized structure of a (3,1,3,1) superlattice, one can observe that the suppression of the LaAlO₃ in-phase rotations (ϕ_c) is larger at the NdNiO₃ interfaces than at the SmNiO₃ ones. This may be the consequence of the smaller bulk rotation amplitudes of NdNiO₃ as compared to the ones of SmNiO₃. One also notices a strongly reduced in-phase rotation close to the La plane, in line with the difficulty noted earlier in developing in-phase rotations in LaAlO₃. In addition, observed is that the antipolar motion of the La-cations mostly follows the alternate motion of the Sm and Nd layers, a result consistent with the experimental observations described above. Together, this leads to a non-cancellation of the net A-site cation displacements.

Figure 4(d) shows the results for an energy-minimized structure in which the number of LaAlO₃ layers inside the heterostructure is increased to 2 u.c. but the thickness of the ReNiO₃ layers remains 3 u.c. Such a (3,2,3,2) replicates more closely the experimentally measured samples. Here, we see a very large suppression of the rotation amplitude of the oxygen octahedra in between the two AlO planes. For the octahedra sandwiched between AlO and NdO, the rotations are non-vanishing but are again more strongly reduced than the ones of the octahedra in between AlO and SmO planes. Nevertheless, LaAlO₃ seems to partly recover its bulk-like out-of-phase rotation in all directions. However, that depends strongly on the cation environment and again leads to a non-uniform pattern in the A-cation motion. This resulting complex pattern should introduce a net polarization, which in turn could provide a path toward producing in-plane improper ferroelectricity.

In conclusion, high crystalline quality heterostructures made of SmNiO₃ and NdNiO₃ with LaAlO₃ spacer layers were grown and characterized in-depth by means of XRD, AFM, and STEM. The structural study presented here reveals that the insertion of the LaAlO₃ layers has a strong effect on the orientation of the orthorhombic long-axis of the nickelate layers. While the long-axis is always in-plane when growing single compound films and superlattices made only of nickelates on LaAlO₃ substrates (as expected from the macroscopic strain state), when 2 or 3 u.c. LaAlO₃ spacer layers are inserted between the nickelate layers, the orthorhombic long-axis flips out-of-plane. This result is in agreement with DFT calculations, which further reflect this phenomenon when just a single u.c. of LaAlO₃ is inserted as a spacer layer. The observed change in the orientation of the long-axis can be explained by considering OOR coupling at the multiple interfaces between materials displaying different crystal structures in their bulk-like form. This study illustrates how the lattice orientation in Pbnm systems can be manipulated by combining the Pbnm layers (a⁻a⁻c⁺) with rhombohedral $R3̄c$ ones, which instead display a bulk a⁻a⁻a⁻ rotation pattern. Such manipulations might be important for controlling the electronic properties of some transition metal oxides. For instance, magnetism in LaMnO₃/GdScO₃ was found to depend on the orientation of the long-axis.²⁰ Between experiments and simulations, we also find that the crystallographic structure of ultra-thin LaAlO₃ spacer layers sandwiched between nickelate layers changes; they both develop an antipolar motion and display markedly reduced out-of-plane rotation amplitudes. This very unusual finding can possibly be explained by the electrostatic interaction between the A cations at interfaces. Since it is well known that rather small changes in the crystallographic structure of a correlated material can drastically modify its displayed properties, our findings provide a possible path to engineering functional properties by controlling the long axis orientation and antipolar motion.

The supplementary material contains the following: 1. Additional DFT calculations for a (3,1,3,1) superlattice. 2. STEM image and GP analysis of a (6,4,6,4) superlattice. 3. High resolution STEM image and antipolar motion pattern relative to (6,2,6,2) SL. 4. Simulated amplitude of the octahedral rotations in bulk SmNiO3, NdNiO3, and LaAlO3.

This work was supported by the Swiss National Science Foundation—Division II (Grant Nos. 200020_179155 and 200020_207338). The authors acknowledge the access to the electron microscopy facilities at the Interdisciplinary Center for Electron Microscopy, École Polytechnique Fédérale de Lausanne.

The authors have no conflicts to disclose.

Lucia Varbaro: Data curation (equal); Investigation (equal); Writing – original draft (equal). Bernat Mundet: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Subhadeep Bandyopadhyay: Data curation (equal); Formal analysis (equal); Writing – review & editing (equal). Claribel Domínguez: Conceptualization (equal); Writing – review & editing (equal). Jennifer Fowlie: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal). Lukas Korosec: Conceptualization (equal); Data curation (equal); Writing – review & editing (equal). Chih-Ying Hsu: Data curation (equal); Formal analysis (equal). Duncan T. L. Alexander: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Philippe Ghosez: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal). Jean-Marc Triscone: Conceptualization (equal); Investigation (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available at Yareta repository upon reasonable request.