Research Update: Orbital polarization in LaNiO₃-based heterostructures Open Access

The orbital configuration of valence electrons, together with the atomic number and electron count, is one of the fundamental properties of the atoms in a material that can greatly influence the material’s behavior. Recently, many researchers have noted the importance of the orbital configuration (independent of the composition and electron density) for physical phenomena in a variety of solid state material systems.¹ The electronic orbital configuration discussed here refers to the energetic alignment and relative occupation of electronic states near the Fermi energy (E_F) that have specific orbital symmetries. While translational symmetry and inter-site hopping lead to hybridization and band formation, the atomic-like orbital symmetries of valence shell states can often dictate key physical properties. For instance, in recently discovered materials exhibiting topological phases (e.g., graphene, topological insulators, and Weyl semimetals), the breaking of the p orbital degeneracy near the Fermi level is essential for formation of topologically protected points in the Brillouin zone.² Furthermore, in topological insulators, the active p orbitals show unique textures near the Dirac points, indicating the importance of the orbital configuration for these and related phenomena.³ 

In transition metal oxides, the pivotal role of the orbital configuration comes to the forefront due to the importance of electronic correlations and the sensitivity of the active d-shell electrons to the lattice structure. Thus, many of the unique and technologically relevant properties in transition metal oxide materials originate from or depend critically on the symmetry and degeneracy of the active orbitals. A non-exhaustive list of such properties includes high-temperature superconductivity in cuprates,^4,5 colossal magnetoresistance and phase transitions in manganites,⁶ spin-state transitions in cobaltates,⁷ and metal-insulator transitions^8,9 and electrochemical activity¹⁰ in numerous oxide systems. The above list primarily represents bulk phenomena where the degree of control is limited; only recently has the development of a comprehensive toolbox for designing and manipulating particular orbital configurations begun to take shape.

In this research update, we review the recent progress in developing such a toolbox for orbital selection in correlated oxides. We highlight the current state-of-the-art with a focus on rare-earth nickelates, LaNiO₃ in particular, a material class where research into engineering orbital polarization has experienced a surge over the past ∼7 yrs (there have been relatively few studies on other nickelates, see Refs. 11–13). The theoretical and experimental advances are generally applicable to other correlated oxide systems and include developments in measurement techniques, correlated electron theory, and design paradigms based on symmetry-breaking and electrostatics. We conclude by offering an outlook along with open questions, future approaches, and potential applications of orbital engineering in oxides.

The rare-earth nickelates, with formula RNiO₃ (R is a rare-earth ion with 3+ formal charge), embody a model system for considering the problem of orbital polarization and provide a fruitful testing ground for experiment and theory. In their bulk form, their ground state has Ni in the (formal) d⁷ ionic configuration, with an octahedral crystal field splitting between the d orbitals of t_2g and e_g symmetry that is sufficient to fill the t_2g levels and to leave a single electron in the doubly degenerate e_g manifold (Fig. 1(a)). Generally, one would expect a Jahn-Teller distortion to break this degeneracy; however, no such distortion has been detected across the bulk nickelate series.¹⁴ The nickelates have a pseudocubic perovskite-like crystal structure (i.e., corner-sharing oxygen octahedra) with orthorhombic or rhombohedral distortions depending on the rare-earth ion. Except for LaNiO₃, which remains paramagnetic and metallic at all temperatures, each member of the rare-earth nickelate family changes from a paramagnetic metal to an antiferromagnetic insulator with the transition temperatures depending on the rare-earth ion size. The underlying mechanism for this transition remains under debate and may result from bandwidth narrowing,¹⁵ a crossover to a Mott insulating state,¹⁶ or from charge disproportionation.^17,18 Furthermore, angle-resolved photoemission, optical spectroscopy, and transport measurements display signs that electronic correlations play a key role in the physics of the nickelates.^19–22 The existence of an isolated, degenerate manifold in a correlated system with strong electron-lattice coupling offers an ideal opportunity to explore the physics of orbital engineering.

Specifically, the nickelates share many of the empirically important qualities of the high-temperature superconducting cuprates—namely, the perovskite-derived structure, strong electron correlations, and an antiferromagnetic ground state. Unlike the nickelates, however, the cuprates exhibit quasi two-dimensional conduction with a Cu d⁹ ground state ionic configuration and strongly broken orbital degeneracy between the e_g states. The d_3z²−r² orbitals are full, while the d_x²−y² levels are partially filled at the Fermi level (Fig. 1(c)). While bulk LaNiO₃ had previously been ruled inoperable as a parent to cuprate-like superconductivity due to such deficiencies,²³ advances in fabricating oxide thin films and heterostructures have opened up new possibilities.

In 2008, Chaloupka and Khaliullin²⁴ proposed using two-component superlattices consisting of metallic LaNiO₃ layers and insulating barrier layers (Fig. 2) to achieve an orbital polarization of the Ni e_g states, leading to a cuprate-like single band Fermi surface with d_x²−y² character (Fig. 1(b)). They suggested that suppression of the out-of-plane hopping due to the insulating barrier combined with tensile strain would lower the energy of the d_x²−y² states relative to d_3z²−r² states, and they devised a low-energy effective Hamiltonian (with two sites and two orbitals) to model the electronic correlations in the NiO₂ planes. Their mean field treatment suggests that an antiferromagnetic phase with only d_x²−y² orbitals is stabilized, as in the undoped cuprates. Furthermore, based on the observation that the hybridization with an axial orbital in the cuprates enhances T_c, the model predicts potentially higher T_c in nickelates due to the empty d_3z²−r² orbitals being above E_F.

Theoretically, the orbital polarization can be calculated from first-principles density functional theory (DFT) by integrating the computed projected density of states for each orbital up to E_F to find the occupancy of an orbital. However, such computed occupancies are not unique due to the multiple possible choices for the localized orbital basis. That is, one may choose atomic orbitals or instead construct and employ Wannier functions for the relevant occupied bands. In the case of Wannier functions, due to Ni–O hybridization (discussed in more detail below), one can create localized, atomic-like or extended Wannier functions by reproducing energy bands within different energy ranges around E_F, which can have a significant impact on the computed orbital polarization largely due to differences in n_eg.^28,29 As a result of such considerations, recent publications have adopted the hole occupation ratio, r, instead of P, as a more useful quantity to consider with regard to orbital configuration because it can be directly compared to experiment and is computationally robust with respect to the choice of localized basis.^28,30 Below, we discuss both of these quantities, but emphasize the utility of the hole ratio, r, for future work.

Following the proposal of Chaloupka and Khaliullin,²⁴ strained, two-component LaNiO₃ based superlattices have been theoretically and experimentally examined in great detail. The key questions concern whether structural and chemical effects validate the proposed approach. Structurally, in order to lower (lift) the energy of the d_x²−y² (d_3z²−r²) orbital, a sufficient structural deformation of the Ni–O octahedra is needed to reduce the apical Ni–O bond distance (d_ap) relative to the in-plane one (d_inp) (Fig. 1(b)). In addition, the insulating barrier in the proposed two-component superlattices acts to reduce the out-of-plane hopping and thus the d_3z²−r² bandwidth; however, the hybridization between Ni e_g states and the influence of O p states must also be considered.

Initially, the proposal was reinforced by DFT calculations taking the band structure and lattice into account, which predicted relatively large orbital polarizations in LaNiO₃-based superlattices under tensile strain. Han et al.³¹ compute an optimal orbital polarization P > 50% from the combined effects of strain, quantum confinement, and chemical composition of the insulating layer. The lower band edges are predicted to split by as much as Δ_eg ∼ 1 eV for 2% strain (d_ap/d_inp ∼ 0.98). Despite this effect, the DFT band structure remains degenerate at E_F. Merging DFT results with dynamical mean field theory (DMFT) calculations to include electronic correlations within the two-band, d-only Hubbard model yields a completely non-degenerate single Fermi “sheet.”³² 

These encouraging results spurred experimental efforts to fabricate LaNiO₃-based superlattices using pulsed laser deposition (PLD),^33,34 RF magnetron sputtering,³⁵ and molecular beam epitaxy (MBE).³⁶ The common observation of a crossover between metallic and insulating transport with decreasing LaNiO₃ layer thickness, along with indications of antiferromagnetic order in the insulating state,³³ supported the proposed ground state. However, measurements of the orbital occupancy of such superlattices do not detect the predicted large orbital polarizations (Fig. 3(c)). XLD experiments³⁷ on (LaNiO₃)₁/(LaAlO₃)₁ superlattices grown on SrTiO₃ substrates (imparting ∼2% tensile strain) find a lowered d_3z²−r² occupancy (hole ratio r > 1), but only by ∼5% and with a small splitting of Δ_eg ≲ 0.1 eV. Orbital reflectometry on similar structures with thicker LaNiO₃ layers reveals comparable results, with the Ni ions at the interface with LaAlO₃ experiencing slightly enhanced polarization (P = 7%) relative to those in the interior layers.²⁷ As anticipated, changing the insulating barrier and the substrate-induced strain improves the measured polarization.²⁹ A maximum hole ratio of r = 1.19 is found with Δ_eg ∼ 0.3 eV, corresponding to an orbital polarization of either P = 25% or 8%, depending on the assumed n_eg. This result exceeds previous efforts but appears to place an upper bound on the experimentally achievable orbital polarization using strain and confinement in two-component nickelate heterostructures. Further, the orbital polarization values are smaller than expected by theory (for LaNiO₃/LaAlO₃ superlattices, by almost an order of magnitude).

In light of these experiments, several theoretical works have re-examined the orbital physics in nickelates and other correlated transition metal oxide systems in more detail. The key conclusions are two-fold. First, epitaxial strain may be accommodated by the oxide through mechanisms other than c axis (tetragonal) expansion/contraction of the Ni–O octahedra.^11,13,38,39 In particular, octahedral rotations can alleviate strain and actually lead to larger orbital polarization due to larger Ni–O bond distortions,²⁸ as determined by recent high-resolution scanning transmission electron microscopy on two-component superlattices.⁴⁰ Alternatively, several theoretical predictions indicate a propensity for charge disproportionation for LaNiO₃ films and heterostructures under tensile strain. This mechanism has been posited as a possible explanation for low orbital polarizations due to the resulting breathing mode ordering of Ni–O octahedra on adjacent sites whose orbital effects cancel;^41,42 however, the predicted magnetic ordering in this state may contradict experimental findings, so further investigation is required.

Second, charge transfer effects and Ni–O hybridization in the rare-earth nickelates significantly modify the orbital polarization. Typical two-band, Hubbard models of electronic correlations consider the d orbitals only. Incorporating correlations via such models tends to increase the d orbital splitting and polarization relative to DFT. However, applying four-band models that include the O p states explicitly always decreases the orbital polarization relative to DFT. This outcome stems from the change in electron occupation of the d manifold due to change transfer from the oxygen ligand together with the suppressing effect stemming from enhanced Hund’s coupling.^28,43 DMFT^44,45 and slave-rotor⁴⁶ calculations based on pd Hubbard models, as well as DFT + U,⁴² and self-consistent GW⁴⁷ calculations all find a reduction in the orbital polarizations in LaNiO₃ based superlattices and a degenerate Fermi surface, in line with the experimental evidence. A recent DFT + DMFT (pd model) study on LaNiO₃ layers, that included octahedral distortions, computes hole occupation ratios as function of strain and finds agreement with the relevant experimental measurements.²⁸ 

The above discussion reveals that while the intended effects of confinement and strain on LaNiO₃ (reducing the d_3z²−r² bandwidth and inducing a crystal field e_g energy splitting) are realized via two-component heterostructuring, the effectiveness of such techniques may be limited (best cases provide P ∼ 20% and Δ_eg ∼ 0.3 eV) due to competing structural and correlated electronic effects. These limitations point to the need for a new approach, such as breaking the symmetry of the Ni–O bonding environment, if the goal of a cuprate-like, single band system is to be achieved. This approach requires large stretching or shrinking of the Ni–O bonds by means other than substrate-induced epitaxial strain (see Fig. 1).

A most recent development towards this end is the introduction of a symmetry-breaking paradigm that borrows from observations on single-component nickelate thin films. In particular, transport and photoemission experiments show that thin films of (001)-oriented LaNiO₃ undergo a metal-insulator transition as the thickness of the LaNiO₃ is reduced below 3-5 unit cells.^19,48–51 In addition, XLD measurements on thin films indicate an asymmetric response of the orbital configuration to strain.⁴¹ Both of these effects originate from the polarity and reduced coordination at the surface of the LaNiO₃ film, which lead to picoscale polar distortions, Ni–O bond stretching, and symmetry breaking.^48,52 As a result, DFT calculations for the surface layers find a large d_ap/d_inp ratio of 1.07, a 1.3 eV e_g energy splitting, and a hole occupation ratio r ∼ 0.3 (corresponding to a “negative” orbital polarization, see Fig. 1(c)), indicating d_3z²−r² orbitals that have significantly higher occupancy (lower energy).⁵³ 

A design based on three-component superlattice composed of LaNiO₃, LaTiO₃, and an insulating barrier was shown to emulate the surface effect: inversion symmetry about the LaNiO₃ layer is broken and charge transfer from Ti to Ni leads to dipole-field induced polar distortions stretching the apical Ni–O bond (Fig. 2), similar to the LaNiO₃ surface.⁵³ A related scheme using the ordering of polar cation layers in Ruddlesden-Popper compounds has been shown to manipulate cation-oxygen bonds through internal electric fields and large changes of the band gap have been predicted.^54–56 The charge transfer and polar field mechanisms are confirmed experimentally in compressively strained LaTiO₃/LaNiO₃/LaAlO₃ superlattices,³⁰ and XLD measurements agree with the predicted hole occupation ratio r ∼ 0.5 and Δ_eg ∼ 0.8 eV (Fig. 3(d)). These results significantly improve upon those in strained, two-component superlattices. Additionally, as in the two-component case, changing the insulating barrier can improve the orbital polarization. Theoretically, hole occupation ratios in the range r ∼ 0.1–0.6 are accessible (which may be further modified with strain), providing extensive tunability of the orbital configuration.

This three-component approach provides an architecture for orbital engineering based on symmetry-breaking and polar fields to manipulate the Ni–O bonding environment, opening up a number of exciting possibilities and future directions. For one, the agreement with DFT calculations that do not explicitly include localized electronic correlations contrasts with the confinement and strain scenario in two-component superlattices. Experimentally, the influence of Ni–O hybridization and octahedral rotations can be addressed by advanced microscopy techniques, as have been applied to two-component superlattices recently.^40,57,58 Another important note is that these three-component designs lead to a lowering of the d_3z−r² orbital energy (Fig. 1(c)) to a sufficient degree to approach a single-band Fermi surface with d_x²−y² character due to d_3z−r² filling from internal electron transfer. To fully reach a cuprate-like configuration, the system requires further electron doping, which may be achieved through chemical substitution or field effect gating using ionic liquids or ferroelectrics.^59–61 Alternatively, one could devise an approach to reverse the polar field (e.g., by hole transfer rather than electron transfer) and contract the apical Ni–O bond to arrive at a lower energy d_x²−y² orbital, which would not require significant further doping to emulate the cuprates (Fig. 1(b)). Finally, the nature of the transport, magnetic, and the low-energy electronic properties in these orbitally non-degenerate nickelates remains an open research direction. Experimentally exploring the orbital tunability mentioned above, combined with doping, offers enticing opportunities that may lead to the emergence of new phenomena, potentially including unconventional superconductivity.

Viewed broadly, many of the developments in understanding and controlling orbital properties in nickelates can be applied to other systems and/or be combined with other cutting-edge techniques to provide an extensive toolbox for manipulating properties in correlated oxides. For example, the modification of orbital states due to confinement and strain has been tied to spin state control in cobaltate superlattices,⁶² magnetization enhancement in manganite thin films,⁶³ and exotic non-collinear magnetism in nickelate heterostructures,⁶⁴ making these systems ripe for applying the polar, symmetry breaking approach to further enhance these effects.⁶⁵ Another potential direction is to leverage ultrafast optical control of lattice distortions, which has been shown to enhance superconductivity in cuprates,^66,67 and to transiently augment a wider variety of structural distortions. Promising motifs discovered using transient methods can then be designed into superlattice geometries. Ferroelectric field effect modulation⁶⁸ can also be used in this manner to construct switchable, picometer-scale structural distortions that affect the energies of orbital states, as was recently demonstrated at a manganite/ferroelectric interface.⁶⁹ Conversely, applying the techniques of orbital engineering discussed here to the cuprates might provide a route to statically enhance their superconductivity. Emerging research into correlated, topological states of matter potentially realized on (111)-oriented perovskite oxides^70,71 may also benefit from the control of the valence orbital configuration.

In summary, the research into orbital polarization in nickelates over the last several years has highlighted the complex interplay of structure, chemistry, and electronic correlations in influencing the relative energies and occupations of electrons, showing the efficacy of established epitaxial approaches. One path forward uses symmetry-breaking and atomic distortions on the picometer-scale, which provides a flexible model that can interface with a variety of materials and methods to enable the exploration of new orbital physics.

The authors are supported by NSF MRSEC DMR 1119826 (CRISP), FAME, and ONR-BRC.