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Polar metals by geometric design


Gauss’s law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions1. Quantum physics supports this view2, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals3—it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases4. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements5. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra—the structural signatures of perovskites—owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported6,7,8,9,10, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.

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Figure 1: Geometric stabilization of polar NdNiO3 via octahedral tilt engineering.
Figure 2: Non-centrosymmetric NdNiO3 thin films on LaAlO3 (111) substrates.
Figure 3: SHG polarimetry of NdNiO3 (111) thin films.
Figure 4: Coexistence of polar displacements and metallic conductivity in NdNO3 (111) thin films.


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This work was supported by the National Science Foundation (NSF) under Designing Materials to Revolutionize and Engineer our Future grant number DMR-1234096. Transport measurement at the University of Wisconsin–Madison was supported by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences (BES), under award number DE-FG02-06ER46327. The work at Pennsylvania State University was supported by the DOE–BES, under award number DE-SC0012375 (Y.Y., V.G.). The work at Northwestern University was supported by the Army Research Office under award numbers W911NF-15-1-0017 (J.M.R.) and DOE–BES DE-SC0012375 (D.P.). The work at the Argonne National Laboratory is supported by the DOE–BES under contract number DE-AC-02-06CH11357 (H.Z., P.J.R., Y.C., J.W.K.). The computational work made use of the Haise and Kilrain clusters at the Navy DoD Supercomputing Resource Center under the High Performance Computing Modernization Program initiative of the US Department of Defense and NSF XSEDE (ACI-1053575). The work at Cornell University was funded by DMR-1056441 (C.J.F.).

Author information




C.J.F. and C.B.E. conceived the project. T.H.K. and C.B.E. initiated the project, and fabricated and characterized the thin-film samples. C.B.E., M.S.R., V.G. and X.Q.P. supervised the experiments. D.P. and J.M.R. formulated the model and carried out the DFT study. L.X. and X.Q.P. carried out the transmission electron microscopy studies. Y.Y. and V.G. performed the SHG optical measurements. T.H.K., N.C., J.I., Y.M. and M.S.R. carried out the electrical transport measurements. T.H.K., J.P.P., J.R.P., S.R. and H.Z. performed the synchrotron CTR measurements. H.Z., J.R.P., S.R. and Y.Y. performed the COBRA analyses. Y.C., J.-W.K. and P.J.R. carried out the synchrotron diffraction and spectroscopy measurements. T.H.K., D.P., J.M.R., V.G., H.Z., M.S.R. and C.B.E. prepared the manuscript. C.B.E. directed the research.

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Correspondence to C. B. Eom.

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Extended data figures and tables

Extended Data Figure 1 Bond connectivity of heteroepitaxial perovskites along the (111) and (001) orientations.

a, b, Owing to the robust bond connectivity, the NiO6 octahedra is strongly coupled with the underlying AlO6 octahedra in NdNiO3/LaAlO3 (111) heterostructure through three bond contacts (indicated by the broken circle). The modification of oxygen octahedral structures can be better achieved in the perovskite (111) geometry (a) rather than the (001) geometry (b), which shows only one unique bond contact.

Extended Data Figure 2 Phonon frequencies and energy as a function of the tilting angle for C2/c (aac) NdNiO3 with the (111) geometry.

a, At small amplitude of the tilt Θ and the out-of-phase rotation angle ξ = 0° (as defined in the main text), we find two polar modes, Bu and Au, that lift spatial inversion symmetry resulting in the Cc and C2 space groups, respectively (a). The Bu and Au modes describe the polar displacements of Nd, Ni, and O atoms on the (Cc) and (001)pc (C2) planes. These two modes behave as in the aac+ case (Fig. 1b), but become hard at smaller amplitude of tilting angle, 2.45° (Au ) and 6.38° (Bu ). Also, the Bu mode always has a lower frequency than the Au mode. b, For small amplitude of the tilt (Θ) and out-of-phase rotation (ξ) angles, we obtain an energy gain of ~2 meV per formular unit that is smaller than the aac+ case (Fig. 1d).

Extended Data Figure 3 Epitaxial synthesis and structural characterization of NdNiO3/LaAlO3 (111) thin films.

ac, An atomic force microscopy (AFM) topography image (a) of an as-grown 2.2-nm-thick NdNiO3 film, thickness-dependent evolution of in situ RHEED patterns (b), and intensity oscillation (c) during PLD deposition of a NdNiO3 film. In b, a yellow square shows that a (10) RHEED peak remains up to the 10th layer, but it disappears in thicker layers. This indicates that thin NdNiO3 samples with the film thickness below 10 layers (~2.2 nm) have a high crystalline quality compared with thicker NdNiO3 films. In c, black and red lines represent time-dependent evolution of (00) and peak intensity in b, respectively. d, A schematic diagram of three monoclinic domain variants, which are used for SHG polar fittings, in a NdNiO3 (111) thin film. The crossed circle represents the direction of out-of-plane components of A-site Nd displacements. Open arrows show three possible variants of in-plane components of the A-site Nd displacements. Owing to the three-fold symmetry of the LaAlO3 (111) substrate, three different domains exist with about equal amount. e, Observation of {integer integer half-integer} Bragg peaks in synchrotron X-ray diffraction. Note that the family of {integer integer half-integer} half-order Bragg peaks are directly related to the occurrence of off-symmetry A-site cation displacements in an orthorhombic system.

Extended Data Figure 4 X-ray spectroscopy and resonant X-ray diffraction measurements of epitaxial NdNiO3/LaAlO3 (111) and (001) films.

a, X-ray absorption spectroscopy (XAS) at the Ni K edge shows a clear pre-edge intensity, when the incident X-ray polarization (E) is along [111] of a NdNiO3 (111) film. The near-edge X-ray absorption fine structure (NEXAFS) indicates the Ni displacement is more pronounced along [111]pc of the NdNiO3 (111) film, while weaker along the other two in-plane directions. The response from a NdNiO3 (001) film is similar to the in-plane results from the NdNiO3 (111) film. The weak pre-edge intensity is due to transitions from the 1s to 3d levels. At the K edge, sd electric dipole transition is forbidden for this octahedral case and weak quadrupole transition is allowed. However, as the central Ni atom is displaced from its cubic symmetric site, the displacement breaks the inversion symmetry, mixing p-state symmetry with unfilled d-states and allowing the dipole transition. The strength of the dipole transition is proportional to the square of the displacement along the incident X-ray polarization. b, Resonant X-ray diffraction (XRD) intensity at a film peak in pseudo-cubic notation (that is, equivalent to a (011) Bragg peak in orthorhombic notation) across the Ni K edge is shown. The Ni response at the arises from a combination of the finite size effect of the film (thickness fringes) and monoclinic distortion related to the Ni displacement. The error bars for both the XAS and resonant XRD results are calculated as the square root of the measured intensity.

Extended Data Figure 5 COBRA and STEM analyses of NdNiO3 thin films on LaAlO3 (001) substrates.

ac, A schematic diagram (a), two-dimensional electron density maps sliced through the pseudocubic (110) plane (b), and STEM-ABF images (c) of NdNiO3/LaAlO3 (001) thin-film heterostructures along the pseudocubic [110] zone axis. The interface is marked by yellow dash–dotted lines. d, e, Magnified two-dimensional electron density maps of a NdNiO3 film (d) and a LaAlO3 substrate (e), which are indicated by (i) and (ii) in b, respectively. Red dashed lines represent the positions of oxygen atoms (marked with red colours), which are taken as references to measure the relative off-centre displacements of Nd (green) and La (black) atoms, respectively. No polar displacements of the Nd and La atoms are measured with respect to the oxygen atom positions. f, g, Magnified STEM-ABF images of a NdNiO3 film (f) and a LaAlO3 substrate (g), which are indicated by (iii) and (iv) in c, respectively. Red dotted lines are guidelines to show the tilting of NiO6 and AlO6 octahedra in the NdNiO3 and LaAlO3 layers, respectively. h, Layer-dependent evolution of the NiO6 and AlO6 octahedral tilt angles across the interface in the STEM-ABF image of c. The 0th layer represents the NdNiO3/LaAlO3 interfaces. We extract the error bars by calculating the standard deviation values from the measured tilting angles of about 10 unit cells in each layer. Blue and red dashed lines represent the octahedral tilting angles of bulk LaAlO3 and NdNiO3, respectively. Note that NiO6 octahedra in NdNiO3 (001) thin films exhibit bulk-like tilting angle magnitudes without suppression of octahedral tilt distortion.

Extended Data Figure 6 STEM analyses of octahedral tilt patterns in NdNiO3/LaAlO3 thin films.

a, A STEM image of a NdNiO3/LaAlO3 (111) heterostructure along the pseudocubic zone axis. Dotted red and solid yellow squares represent the NdNiO3 film and LaAlO3 substrate regions for fast Fourier transform (FFT) analyses, respectively. b, c, The corresponding FFT images of the NdNiO3 film (b) and the LaAlO3 substrate (c) regions in a. In c, yellow circles represent half-order spots due to the aaa tilt pattern of the LaAlO3 substrate. In the FFT image of the NdNiO3 film, half-order spots do not appear, indicative of local suppression of in-phase c+ octahedral rotation. d, A STEM image of a NdNiO3/LaAlO3 (001) heterostructure along the pseudocubic [100] zone axis. e, f, The FFT images of the NdNiO3 film (e) and the LaAlO3 substrate (f) regions in d. In e, the dotted red circles represent half-order spots, which usually come from oxygen octahedral rotation. g, h, Simulated electron diffraction patterns of orthorhombic (Pbnm, aac+) NdNiO3 (g) and rhombohedral (Rc, aaa) LaAlO3 (h) along the pseudocubic [100] zone axis. In g, a dotted red circle represents a half-order peak induced by in-phase c+ octahedral rotation in orthorhombic NdNiO3. In rhombohedral LaAlO3, destructive interference occurs and then the half-order peak disappears in h.

Extended Data Figure 7 Thickness-dependent SHG and electrical transport experiments in NdNiO3 (111) thin films.

ac, The temperature-dependent SHG experiments in 1.1- (a), 1.5- (b) and 2.2-nm-thick (c) NdNiO3 (111) thin films. d, The thickness dependence of the SHG responses. The SHG intensity is proportional to the square of the film thickness. e, The temperature-dependent resistance in 1.1-, 1.5- and 2.2-nm-thick NdNiO3 (111) films.

Extended Data Figure 8 SHG polarimetry of LaNiO3 (111) films and a capping-layer effect in NdNiO3 (111) films.

a, b, SHG polar plots of 2.23-nm-thick LaNiO3 thin films on LaAlO3 (111) substrates at a room temperature (RT; a) and 18 K (b). Two SHG components are measured, I2ω|| (blue circles) and I2ω (red circles) under the O1 and O2 sample orientation, depicted in Fig. 3a. The solid lines represent the theoretical fittings of monoclinic (m) point-group symmetry with equivalent three domain variants. c, The temperature-dependent resistivity of a 2.23-nm-thick LaNiO3 thin film on a LaAlO3 (111) substrate. d, Room-temperature SHG polar plots in a NdNiO3 (111) thin film with a LaAlO3 capping layer.

Extended Data Figure 9 Synchrotron CTR measurements in NdNiO3/LaAlO3 thin films.

a, b, CTR scans of processed raw (circles) and simulated (red curves) data along various non-specular CTRs in NdNiO3 (001) (a) and (111) (b) thin film, respectively. The data curves are offset for clarity of comparison. c, d, Schematics of symmetry inequivalent CTRs (HKL) measured in reciprocal lattices defined by the LaAlO3 substrate for both NdNiO3/LaAlO3 (001) (c) and (111) (d) thin films. The monoclinic structure of epitaxial NdNiO3 thin films breaks the high-order symmetry of the LaAlO3 substrate along both (001) and (111) orientations.

Extended Data Table 1 Theoretical NdNiO3 structure metastability for symmetry-unique structures with (111) and (001) film orientations

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Kim, T., Puggioni, D., Yuan, Y. et al. Polar metals by geometric design. Nature 533, 68–72 (2016).

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