Bulk NdNiO3 exhibits a metal-to-insulator transition (MIT) as the temperature is lowered that is also seen in tensile strained films. In contrast, films that are under a large compressive strain typically remain metallic at all temperatures. To clarify the microscopic origins of this behavior, we use position averaged convergent beam electron diffraction in scanning transmission electron microscopy to characterize strained NdNiO3 films both above and below the MIT temperature. We show that a symmetry lowering structural change takes place in case of the tensile strained film, which undergoes an MIT, but is absent in the compressively strained film. Using space group symmetry arguments, we show that these results support the bond length disproportionation model of the MIT in the rare-earth nickelates. Furthermore, the results provide insights into the non-Fermi liquid phase that is observed in films for which the MIT is absent.
Understanding and controlling metal-to-insulator transitions (MITs) of correlated transition metal oxides has been a longstanding goal in materials physics1,2. Identifying the microscopic mechanisms of these MITs is difficult, as various electronic, structural and spin degrees of freedom can compete or cooperate. As a result, the subject continues to be a topic of significant controversy even for seemingly simple materials. A prime example is the rare-earth nickelates (RNiO3, where R is a trivalent rare earth ion, but not La), which are prototypical strongly correlated materials that undergo an MIT as the temperature is lowered. In addition to the temperature-driven MIT, understanding the interplay between atomic structure and electronic degrees of freedom is key to other fascinating aspects of these materials, such as non-Fermi liquid phases3,4,5 and the tunability of their Fermi surface to mimic that of the cuprate superconductors6,7.
RNiO3s adopt the distorted GdFeO3-perovskite-derived structure (space group Pbnm). With decreasing rare-earth ion size, the structural distortion increases, shifting the MIT to higher temperatures8. Hydrostatic pressure5,9,10 or epitaxial film strain4,11,12,13,14,15,16 can also be applied to modify the MIT temperature (TMIT). The direct correlation between TMIT and ionic radius (or strain) suggests that the Ni-O-Ni bond angles play a role, as they determine the electronic bandwidth and magnetic exchange interactions. Early studies thus identified the MIT in the RNiO3s as resulting from a bandwidth controlled charge transfer gap8,17 with concomitant orbital ordering to describe the antiferromagnetic ground state18. More recently, however, subtle symmetry changes from orthorhombic Pbnm to monoclinic P21/n have been detected at TMIT, pointing to a charge ordered ground state and a lifting of the degeneracy of the singly occupied eg band19,20,21. The orthorhombic-to-monoclinic transition permits two inequivalent Ni sites. It should be noted, however, that the ordered ground state may be more correctly described as a bond length ordered state, as it is characterized by alternating NiO6 octahedra with different Ni-O bond lengths21,22 and the nominal charges on the Ni sites may not be very different. For simplicity and since this study focuses on the underlying lattice symmetry, we use the various terminologies (charge/bond order, charge/bond length disproportionation) interchangeably here, following most of the literature. While these new findings offer structural parameters for theoretical calculations, important questions remain as to the relative importance of the electronic, magnetic and structural parameters driving the MIT.
To this end, thin film heterostructures have been proposed as a means for separating the lattice from the electronic and magnetic effects. For example, strain in thin films can affect the octahedral tilt patterns in LaNiO3 films23,24 and, concomitantly, their electronic structure, including band degeneracy25. Meyers et al. did not observe a symmetry change in x-ray absorption spectroscopy and resonant x-ray scattering of ultrathin (15 unit cells) NdNiO3 films as they undergo an MIT, concluding that the magnetic ordering drives the MIT and that it can be decoupled from the structural distortion26. Upton et al. also dismiss charge order or symmetry changes and propose Ni 3d hybridization with O 2p, as well as Ni charge redistribution to Nd 5d states as underlying mechanisms27. These results are in contrast to experimental22,28,29 and theoretical works30,31,32 that associate the MIT with charge/bond length order on the Ni sites. The resolution of this debate hinges on the ability to detect very subtle symmetry changes in strained RNiO3 films as they undergo the MIT. The monoclinic distortion in bulk NdNiO3 is very small19 and would be even more challenging to detect in ultrathin films33. Furthermore, key insights could also be obtained from the opposite case, namely identifying the microscopic reason(s) when the MIT is absent, such as for compressively strained films.
In this work, we use position averaged convergent beam electron diffraction (PACBED) in scanning transmission electron microscopy (STEM) to analyze the structure of strained NdNiO3 films grown on NdGaO3 (tensile) and YAlO3 (compressive). PACBED is sensitive to extremely small structural distortions34, even if they only occur on the oxygen sublattice24,35 and has a high spatial resolution. The overlapping diffraction discs create unique patterns, characteristic of the point group symmetry (or more accurately, Laue symmetry) of the structure. We obtain PACBED patterns above and below TMIT. We show that NdNiO3 films on NdGaO3, which exhibit an MIT, undergo a structural transition while NdNiO3 films on YAlO3, which are metallic at all temperatures, do not. The results, combined with symmetry arguments, provide a complete and remarkably simple understanding of the MIT and its suppression.
Resistivity curves as a function of temperature for the films studied here are shown in Fig. 1, along with corresponding STEM images of the film grown on NdGaO3 at room and cryo temperatures, respectively. Both films were 15 pseudocubic unit cells thick and coherently strained to the substrate (0.85% tensile and −3.6% compressive for NdGaO3 and YAlO3, respectively), as verified by high-resolution x-ray diffraction15. While the film grown on YAlO3 remains metallic down to the lowest temperature, an MIT at ~150 K, with a hysteresis of ~25 K, is observed in the film on NdGaO3. TMIT is comparable to films reported in the literature on this substrate and with this film thickness26, but lower than that of bulk (~200 K8), as is typical for RNiO3 films. The cold stage temperature of 105 K is well within the insulating regime. The complete suppression of the MIT in films under compressive strain for this film thickness is consistent with reports in the literature4,14,36.
Film-Substrate Orientation Relationships
Figure 2a illustrates the orientation relationship of an orthorhombic film grown on a (110)O orthorhombic substrate surface, which is supported by transmission electron microscopy (TEM). While a (001)O//(110)O orientation would have a similar lattice mismatch, interfacial oxygen octahedral connectivity issues make this orientation unlikely. The film is epitaxially constrained along O and O. The orthorhombic a and b lattice parameters change to accommodate the strain, resulting in a characteristic angle γ that deviates from the 90° angle in the bulk. A 2 × 2 × 2 pseudocubic supercell containing the original orthorhombic unit cell is outlined in blue. TEM cross-sections accessed both the O and O projections, each with distinct features in the PACBED pattern, which are similar to those previously observed in orthorhombic films grown on cubic substrates37. A color table has been applied to all patterns in the present study, to better highlight the intensity changes. PACBED patterns along O contain a square-like feature in the central disc, while those along O show a diagonal intensity stripe, as shown in Fig. 2b. These features are reproduced in PACBED simulations and experimentally observed in other perovskite structures with the Pbnm space group (e.g. NdGaO3, YAlO3, GdTiO3). They allow for identification of the zone axis by simple visual inspection. The present paper focuses on the O projection (orange in Fig. 2a), since the PACBED patterns along O are less sensitive to the symmetry changes that are relevant here. While PACBED has been shown to be sensitive to small structural distortions24,34,35, we also employ low-angle PACBED (LA-PACBED) to better distinguish the diffracting discs and gain additional insight into the film structure. The reduction in semi-convergence angle used for LA-PACBED results in a decrease in the resolution of the corresponding high-angle annular dark-field (HAADF) STEM image that is acquired in parallel. However, the 3.4 mrad convergence angle remained sufficient to differentiate the film and substrate during LA-PACBED acquisition.
NdNiO3 Film Symmetry
Figure 3a shows experimental, room temperature LA-PACBED patterns from the substrate and film regions of NdNiO3/NdGaO3, with a simulated orthorhombic NdNiO3 bulk pattern (simulated at 0 K for speed) for comparison. A Sobel edge filter, which highlights sharp changes in intensity, was applied to each pattern and displayed in Fig. 3b, with relevant diffraction discs indexed in the orthorhombic notation. Insets of the 200 and 020 discs for the experimental patterns are also highlighted in Fig. 3b. In the room temperature measurements, we note a characteristic bright band in the LA-PACBED patterns that runs diagonally (bottom left to upper right) in the central disc of the simulated bulk NdNiO3 and substrate NdGaO3. A similar feature appears also in PACBED (Fig. 2b). Furthermore, we see clear differences in diffraction features between 200 and 020 discs: a bright region of intensity near the central beam, as well as 310 reflections, which can be clearly seen in the 200 discs, but are barely observed in the 020 discs. These asymmetric features are a close match with the bulk NdNiO3 simulation and are caused by the octahedral rotations and A-site cation displacements of the orthorhombic Pbnm structure.
In contrast, the LA-PACBED pattern of NdNiO3 on NdGaO3 does not show the asymmetry in the intensity between the 200 and 020 discs, indicating that the strained film has different symmetry than the orthorhombic substrate. In addition, the 200 and 020 disc spacings, corresponding to the a and b orthorhombic lattice parameters, are clearly different for the NdGaO3 substrate, as expected, but a = b for the NdNiO3 film (although we note that the bulk a and b lattice parameters of NdNiO3 are almost identical as well). This result is expected for a tensile strained orthorhombic film38: as the film is constrained along the O and O directions, the strain is accommodated by an increase in the angle γ and a reduction in octahedral tilts along the growth axis (Fig. 3b). We note that this structural change in the film is a result of the strain state, irrespective of the symmetry of the substrate (i.e. cubic or orthorhombic). A measurement of γ from Fig. 2b yields γ = 90.2° and 93.2° for the NdGaO3 substrate and NdNiO3 film, respectively. These results indicate that the octahedral tilts about the O direction are either mostly or completely suppressed.
Figure 3c illustrates the most likely Glazer tilt configuration39 of the tensile strained NdNiO3 film, which is the same as previously found by Vailionis38. Here, we use the convention of denoting the axis of zero tilt as the a-axis. The phase of the rotations remains the same as in the bulk, but the magnitudes change, with negligible tilt along O. This space group is more accurately described as orthorhombic Cmcm and the in-phase and out-of-phase tilts are likely different. In particular, the in-phase tilt is probably small. LA-PACBED simulations (not shown) indicate that the similarities in intensity between 200 discs from Fig. 3a, as well as the absence of 120 reflections, are likely indicators of significantly reduced octahedral tilts along the projected direction (O). While the present study does not represent a rigorous determination of the space group symmetry based on electron diffraction40, due to experimental challenges (thinness of our samples and stability issues), it still presents compelling evidence of the structural symmetry and octahedral rotations that are consistent with previous results from literature38 and geometric arguments of allowed tilts within the respective space groups41.
Figure 4 shows LA-PACBED patterns of the same sample at 105 K. While the substrate pattern shows similar features as the room temperature pattern (expected since NdGaO3 does not undergo a structural transition42), we see a noticeable difference in the NdNiO3 film. Most markedly, there is a strong intensity asymmetry between 110 and 10 reflections, which can be seen as bright overlaps in the central disc. This difference indicates a reduction in symmetry, most likely a monoclinic transition to P21/n, similar to what occurs in the bulk. In particular, similar peak splittings between 40/404 reflections were observed by synchrotron powder diffraction in polycrystalline NdNiO3 and taken as a sign of the monoclinic transition19. At low temperatures, γ decreases to 91.1°, indicating an increase in octahedral rotations about the growth direction (O), consistent with P21/n.
Figure 5a shows LA-PACBED patterns of compressively strained NdNiO3 grown on YAlO3. These films are expected to be monoclinic (P21/m)38 in this strain state. Patterns from the substrate (not shown) were similar to the NdGaO3 substrate patterns at both temperatures. From Fig. 5a, we do not observe any noticeable differences between the room temperature and 105 K patterns, although the 220 and 20 reflections may have slight differences in intensities. The NdNiO3 film grown on YAlO3 contained structurally disordered regions in HAADF STEM, likely as a result of the very large compressive strain that makes it more susceptible to TEM sample preparation and beam damage, which might explain overall weaker diffraction intensities. A schematic of the most likely octahedral tilt rotations of the compressively strained NdNiO3 is shown in Fig. 5b. The angles, γ and α, from the figure are consistent with angle measurements from the LA-PACBED pattern (γ = 88.1° and α = 89.4°). The tilt configurations for both compressive and tensile strained films are determined from geometric considerations based on the lattice parameters of the film and the substrate epitaxial constraints8,41,43. A detailed explanation for determining the tilt systems of similar films can be found in ref. 38.
At first glance, it may seem curious that the compressively strained film, which we believe to be monoclinic and have a similar tilt pattern as bulk NdNiO3 (Figs 3c and 5b), does not undergo an MIT. To explain this observation, we first highlight the fact that the expected space group of the strained compressive film (P21/m) is not the same as the low temperature bulk NdNiO3 space group (P21/n). In general, the presence of order, i.e., charge or bond length disproportionation, will always result in a loss of symmetry, usually involving a loss of translational symmetry since neighboring octahedral sites are no longer equivalent. As discussed by Woodward41, 1:1 order in the Pbnm space group results in a symmetry reduction to P21/n and this is indeed observed in bulk nickelates. Likewise, introducing 1:1 order into the P21/m space group would reduce the symmetry of the unit cell to P (triclinic). However, any epitaxially strained film on a cubic or (110) orthorhombic substrate (90° in-plane angle) is bound to contain higher symmetry elements than the triclinic system. Therefore, by symmetry arguments, compressively strained films are unable to reduce to a charge or bond ordered state upon cooling. These simple considerations, which are consistent with the charge/bond length order driven MIT, explain why these films remain metallic and do not undergo a MIT.
Meanwhile, Figs 3 and 4 show clear evidence that the MIT in tensile ultrathin NdNiO3 films is accompanied by a symmetry-lowering structural distortion. They likely belong to the P21/n space group, which is consistent with our observation that octahedral tilts along the growth direction are re-introduced. In addition, while the tensile-strained film, grown on a O substrate, is orthorhombic, we note that tensile strained films grown on cubic substrates, such as (LaAlO3)0.3(Sr2AlTaO6)0.7 (LSAT) or SrTiO3, would contain a tetrad axis along the growth direction and therefore possess tetragonal symmetry. While seemingly trivial, the most likely Glazer tilt pattern with a tetragonal space group would be a0b+b+, meaning the out-of-phase tilt in Fig. 3c would change to in-phase. Although such a change might seem to have a large effect on the transport properties, transport measurements4 suggest otherwise: films grown on LSAT and SrTiO3 show MITs, which shift to slightly higher temperatures with increasing tensile strain. These observations all support the view that the symmetry lowering structural distortion is a key requirement for the MIT; the exact high temperature symmetry starting structure is not as important as long as it permits a transition to a lower-symmetry ordered state. This is possible in case of the tensile strained films but not for the compressive strained films.
In summary, we have shown that LA-PACBED allows for the detection of subtle symmetry changes in ultrathin films due to epitaxial film strain and the MIT, which may be missed in other diffraction methods. Epitaxial film strain affects the high-temperature (above the MIT) octahedral rotations and space group symmetry. Tensile strained NdNiO3 is best described with a larger centered unit cell (Cmcm) with Glazer tilt pattern a0b+c−, while compressively strained films (P21/m) retain the O out-of-phase rotations and have tilt patterns a+b−c−, with octahedral tilts similar to those of bulk NdNiO3 (a+b−b−). Thus even at room temperature, strained NdNiO3 films are structurally dissimilar from their bulk counterparts and the modified structure, rather than the bulk Pbnm space group, should be used as the starting structure in future theoretical work describing the MIT of coherently strained films and associated phenomena, such as orbital polarization and Fermi surface tuning. Furthermore, the results provide a remarkably simple understanding of the modified MIT in thin films: in the case of tensile strained film, transition to a symmetry consistent with charge order is allowed by the high-temperature space group, thus permitting the MIT, while the opposite is true for compressively strained films which therefore have to remain metallic.
More broadly, the results present compelling evidence for charge/bond length order being inextricably linked to the insulating state of the RNiO3s, the transition to which we have shown to be highly reliant on the high temperature “parent” space group symmetry. The ability to tune the MIT by epitaxial film strain, in conjunction with sensitive measurements of the film symmetry, provides strong evidence that the charge or bond length ordered state is firmly linked to the MIT of the nickelates, which does not occur without it.
Finally, we note that the results also provide insights into the nature of the non-Fermi liquid phase that is observed in RNiO3 films and bulk materials for which the MIT is suppressed4,5. In particular, the results show that the non-Fermi liquid phase in the thin films coincides with a phase whose lattice symmetry is incompatible with reaching the long-range ordered state. It would be interesting to determine if a similar mechanism, namely a suppressed or frustrated symmetry-lowering ordered ground state, may explain the appearance of non-Fermi liquid phases in other correlated systems.
15 unit cell (~6 nm) NdNiO3 films were grown by RF magnetron sputtering on NdGaO3 and YAlO3 substrates, in an Ar/O2 gas mixture, with a 9 mTorr growth pressure, as described in detail elsewhere15. Neither film is relaxed. The in-plane longitudinal resistivity was measured as a function of temperature in a Quantum Design Physical Properties Measurement System (PPMS). TEM cross-sections along O and O (the subscript indicates the orthorhombic orientation) were prepared using a focused ion beam with final milling energies of 5 kV Ga ions. High-angle, annular dark-field (HAADF)-STEM imaging and (LA-)PACBED experiments were conducted on a 300 kV FEI Titan S/TEM (Cs = 1.2 mm). A convergence semi-angle of 9.6 mrad was used for high resolution STEM imaging, while 9.6 and a reduced angle of 3.4 mrad was used for PACBED. LA-PACBED patterns are obtained from roughly a 12 × 12 unit cell area. An FEI double-tilt holder was used for room temperature PACBED and high resolution imaging, while a Gatan 636 double-tilt LN2 holder was used for low temperature experiments. All cold-stage experiments were carried out a temperature of 105 K, which remained stable throughout the data acquisition. PACBED simulations were carried out using the Kirkland multislice code44 at 0 K.
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We thank Nelson Moreno for help with the film growth. The microscopy work was supported by the U.S. Department of Energy (grant number DEFG02-02ER45994). The film growth and transport measurements were supported by FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA. Facilities used in this work were supported by the UCSB Materials Research Laboratory, an NSF-funded MRSEC (DMR-1121053).
The authors declare no competing financial interests.
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Zhang, J., Kim, H., Mikheev, E. et al. Key role of lattice symmetry in the metal-insulator transition of NdNiO3 films. Sci Rep 6, 23652 (2016). https://doi.org/10.1038/srep23652
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