Key role of lattice symmetry in the metal-insulator transition of NdNiO3 films

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.

be decoupled from the structural distortion 26 . 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 mechanisms 27 . These results are in contrast to experimental 22,28,29 and theoretical works [30][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 RNiO 3 films as they undergo the MIT. The monoclinic distortion in bulk NdNiO 3 is very small 19 and would be even more challenging to detect in ultrathin films 33 . 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 NdNiO 3 films grown on NdGaO 3 (tensile) and YAlO 3 (compressive). PACBED is sensitive to extremely small structural distortions 34 , even if they only occur on the oxygen sublattice 24,35 , 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 T MIT . We show that NdNiO 3 films on NdGaO 3 , which exhibit an MIT, undergo a structural transition while NdNiO 3 films on YAlO 3 , 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.

Results
Transport Properties. 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 NdGaO 3 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 NdGaO 3 and YAlO 3 , respectively), as verified by high-resolution x-ray diffraction 15 . While the film grown on YAlO 3 remains metallic down to the lowest temperature, an MIT at ~150 K, with a hysteresis of ~25 K, is observed in the film on NdGaO 3 . T MIT is comparable to films reported in the literature on this substrate and with this film thickness 26 , but lower than that of bulk (~200 K 8 ), as is typical for RNiO 3 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 literature 4,14,36 .  Corresponding STEM images for the film grown on NdGaO 3 at room and cryo temperatures are shown on the right. Arrows mark the approximate interface between the film and substrate. Images were acquired using fast acquisition and crosscorrelated over many frames for higher signal-to-noise.

Film-Substrate Orientation Relationships.
are less sensitive to the symmetry changes that are relevant here. While PACBED has been shown to be sensitive to small structural distortions 24,34,35 , 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.
NdNiO 3 Film Symmetry. Figure 3a shows experimental, room temperature LA-PACBED patterns from the substrate and film regions of NdNiO 3 /NdGaO 3 , with a simulated orthorhombic NdNiO 3 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 NdNiO 3 and substrate NdGaO 3 . 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 NdNiO 3 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 NdNiO 3 on NdGaO 3 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 NdGaO 3 substrate, as expected, but a = b for the NdNiO 3 film (although we note that the bulk a and b lattice parameters of NdNiO 3 are almost identical as well). This result is expected for a tensile  Figure 3c illustrates the most likely Glazer tilt configuration 39 of the tensile strained NdNiO 3 film, which is the same as previously found by Vailionis 38 . 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 [110] 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 ([001] O ). While the present study does not represent a rigorous determination of the space group symmetry based on electron diffraction 40 , 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 literature 38 and geometric arguments of allowed tilts within the respective space groups 41 . 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 NdGaO 3 does not undergo a structural transition 42 ), we see a noticeable difference in the NdNiO 3 film. Most markedly, there is a strong intensity asymmetry between 110 and 110 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 P2 1 /n, similar to what occurs in the bulk. In particular, similar peak splittings between 404/404 reflections were observed by synchrotron powder diffraction in polycrystalline NdNiO 3 , and taken as a sign of the monoclinic transition 19 . At low temperatures, γ decreases to 91.1°, indicating an increase in octahedral rotations about the growth direction ([110] O ), consistent with P2 1 /n. Figure 5a shows LA-PACBED patterns of compressively strained NdNiO 3 grown on YAlO 3 . These films are expected to be monoclinic (P2 1 /m) 38 in this strain state. Patterns from the substrate (not shown) were similar to the NdGaO 3 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 220 reflections may have slight differences in intensities. The NdNiO 3 film grown on YAlO 3 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 NdNiO 3 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

Discussion
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 NdNiO 3 (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 (P2 1 /m) is not the same as the low temperature bulk NdNiO 3 space group (P2 1 /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 Woodward 41 , 1:1 order in the Pbnm space group results in a symmetry reduction to P2 1 /n, and this is indeed observed in bulk nickelates. Likewise, introducing 1:1 order into the P2 1 /m space group would reduce the symmetry of the unit cell to P1 (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 NdNiO 3 films is accompanied by a symmetry-lowering structural distortion. They likely belong to the P2 1 /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 [110] O substrate, is orthorhombic, we note that tensile strained films grown on cubic substrates, such as (LaAlO 3 ) 0.3 (Sr 2 AlTaO 6 ) 0.7 (LSAT) or SrTiO 3 , 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 a 0 b + 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 measurements 4 suggest otherwise: films grown on LSAT and SrTiO 3 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.

Conclusions
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 NdNiO 3 is best described with a larger centered unit cell (Cmcm) with Glazer tilt pattern a 0 b + c − , while compressively strained films (P2 1 /m) retain the [110] O out-of-phase rotations and have tilt patterns a + b − c − , with octahedral tilts similar to those of bulk NdNiO 3 (a + b − b − ). Thus even at room temperature, strained NdNiO 3 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 RNiO 3 s, 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 RNiO 3 films and bulk materials for which the MIT is suppressed 4,5 . 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.

Methods
15 unit cell (~6 nm) NdNiO 3 films were grown by RF magnetron sputtering on NdGaO 3 and YAlO 3 substrates, in an Ar/O 2 gas mixture, with a 9 mTorr growth pressure, as described in detail elsewhere 15 . 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 [001] O and [110] 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 (C s = 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 LN 2 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 code 44 at 0 K.