Abstract
The electronic structure of transition metal oxides featuring correlated electrons can be rationalized within the Zaanen-Sawatzky-Allen framework. Following a brief description of the present paradigms of electronic behavior, we focus on the physics of rare earth nickelates as an archetype of complexity emerging within the charge transfer regime. The intriguing prospect of realizing the physics of high T c cuprates through heterostructuring resulted in a massive endeavor to epitaxially stabilize these materials in ultra-thin form.
A plethora of new phenomena unfolded in such artificial structures due to the effect of epitaxial strain, quantum confinement, and interfacial charge transfer. Here we review the present status of artificial rareearth nickelates in an effort to uncover the interconnection between the electronic and magnetic behavior and the underlying crystal structure. We conclude by discussing future directions to disentangle the puzzle regarding the origin of the metal-insulator transition, the role of oxygen holes, and the true nature of the antiferromagnetic spin configuration in the ultra-thin limit. *
I. INTRODUCTION
Complex oxides, consisting of transition metal ions offer a vast landscape of fascinating phenomena such as metal-insulator transitions, spin, charge and orbital orderings, high temperature superconductivity, colossal magnetoresistance and multiferroicity etc [1] . The subtle competition between the bandwidth (W ), on-site electron-electron correlations (U ), crystal structure and charge transfer energy between oxygen and transition metal sites (∆), together with the possibility of multiple oxidation states typically available to transition metal ions and a wide range of structural variations results in an unprecedented diversity of interesting phenomena [2, 3] . The quest to understand and control these phenomena has captured the imagination of generations of condensed matter physicists and has fostered the development of advanced experimental probes and theoretical methods.
Thin films and heterostructures add an important new dimension to the problem. Recent advances in atomic precision oxide growth [4] [5] [6] [7] [8] In this review, we focus on the perovskite rare earth nickelate compounds, with chemical formula RENiO 3 where RE = La, Pr, Nd, Sm, Eu ....Lu. This material family exhibits rich physics including charge ordering, strong electron-lattice coupling, MIT and long period magnetically ordered state, all controlled by the interplay of crystal structure and electron correlations. Figure 1 schematically shows the rich diversity of ground state properties and their relationship to different physical parameters that can be controlled via diverse experimental realizations.
A crucial issue in the materials physics of complex oxides is orbital control. In a simple ionic picture, the Ni is in a low-spin d 7 state, with one electron in the two-fold degenerate e g orbitals.
In bulk materials, the occupation probabilities of the two orbitals are nearly equal. An issue that has attracted some recent interest is the extent to which "orbital engineering" (a controllable differential occupancy of the e g orbitals by changing strain and quantum confinement in ultra-thin films) is possible. The issue is important both in the context of the nickelate materials and more generally as an example of control of many-body electronic structure. In this article, we review the known properties of the bulk RENiO 3 materials and then how these are modified in ultra-thin film and heterostructured geometry.
II. CLASSIFICATION OF CORRELATED MATERIALS FROM AN ELECTRONIC STRUC-TURE POINT OF VIEW
As these RENiO 3 are correlated oxides, we begin this review with a basic description of electronic structure parameters of such transition metal compounds. Efforts to classify the electronic structure of transition metal compounds started with attempts to understand why many of these have insulating ground states in spite of having partially filled d levels. Much attention has focused on NiO; the notional electronic configuration of the Ni 2+ ion is 3d 8 in the crystal field split t 6 2g e 2 g configuration, with fully filled t 2g -derived bands and half filled e g -derived bands. One of the early suggestions due to Slater [9] emphasized the doubling of the unit cell due to the ground state antiferromagnetic order of NiO and the consequent opening of a gap in the half filled e g bands.
A density functional theory (DFT)-based ab initio band structure calculation [10] indeed obtained a ground state insulator for NiO. However, this approach is not entirely satisfactory, because the calculated band gap value is an order of magnitude smaller than the experimental value and NiO continues to show insulating behavior above the Néel temperature.
Mott [11, 12] proposed an alternative idea that strong correlation effects in the d-shell can lead to an insulating phase even in a system with partially occupied levels. Hubbard analyzed a theoretical model based on Mott's ideas and showed [13, 14] that a sufficiently large on-site Coulomb interaction strength, U , within a partially occupied level can indeed localize electrons. Fujimori & Minami's [15] analysis of spectroscopic features of NiO established the additional necessity to account explicitly for oxygen 2p levels, since the primary hopping interaction t pd in NiO connect O p and Ni d states. This requires the inclusion of an additional energy-scale, ∆, needed to transfer an electron from the fully-filled oxygen levels to a Ni 3d orbital. The presence of the O p band, arising from p-p hopping interactions between different oxygen sites, in a typical transition metal oxide is shown in Figure 2 (a) for ∆ > U limit. In the opposite limit of ∆ < U , the energy ordering of O p states, LHB, and UHB are as shown in Figure 2 (b) for charge-transfer insulators [2] , with the O p band appearing within the gap between UHB and LHB. In this limit, the band gap, measured between the top of the O p band and the bottom of the UHB, is controlled more by ∆ than by U, in contrast to the case for Mott-Hubbard insulators (Figure 2(a) ). This scenario forms the basis of the name, charge transfer insulator, as the lowest energy excitation for charge transport is achieved here by transferring an O p electron to the transition metal (TM) d orbital.
Combining these ideas, Zaanen, Sawatzky & Allen [2] suggested that, instead of a single U c as envisaged by Mott and Hubbard, the metallic and insulating ground states of transition metal compounds are separated by a line in the U − ∆ phase space, with Mott-Hubbard insulators for U c < U < ∆ and charge transfer insulators for U > ∆ > ∆ c . 3d orbitals contract across the 3d transition metal series, leading to a systematic increase in U [16] . Within a related series of oxides, it is also known [17] that ∆ decreases across the Periodic Table due to rapid stabilization of the 3d level with the increasing atomic number. This approach broadly categorizes insulating oxides of early 3d transition metals as Mott-Hubbard type, with larger ∆ and lower U , and those of late 3d transition metals as charge-transfer type, with smaller ∆ and larger U .
For sufficiently small U , the system becomes metallic, as in the Mott's description of the insulator to metal transition, due to the overlap of the top of the LHB with the bottom of the UHB.
Similarly, one would expect that for a small enough ∆ that makes the top of the O p-band overlap the bottom of the UHB , defining the zero of the effective charge transfer energy, ∆ (see Figure   2 (b)), the system will become metallic, as also suggested in the original Zaanen-Sawatzky-Allen phase diagram [2] . However, it was later argued [18] that the insulating state will persist over a region of ∆ < 0, depending on the value of t pd and U , becasue t pd will essentially mix the O p and metal d states, pushing them energetically apart to form a nonzero bandgap, similar to the case of bonding-antibonding splitting formed in molecular orbital theory. This new region in the U − ∆ phase space was termed the covalent insulating regime [18] to stress that the band gap originated from the presence of a sizable t pd mixing between O p and metal d-states or covalency.
This regime has also been referred to in the literature as the negative ∆ insulator [19, 20] , though care should be taken in retaining the distinction between ∆ and the effective charge transfer energy, ∆ , in this context. Explicit calculations [3, 21] showed that this covalent insulator regime is increasingly stabilized with increasing t pd and U . Figure 2 (c) shows the resulting phase diagram, indicating different insulating and metallic regimes and establishing that the late transition metal oxides that are close to MITS, for example, many interesting Ni and Cu compounds, including the nickelates discussed in this review, belong to the covalent regime in their insulating state. Increasing the formal valence of a transition metal ion has the primary effect of lowering ∆ and increasing t pd . Thus, compounds of earlier transition metals, such as Co, Fe, Mn and even Cr may also be in the covalent insulating regime in their higher valence states. The correlation physics is different within the covalent insulating regime from the standard Mott paradigm due to the effective charge transfer energy being negative. One of the direct consequences of this negative effective charge transfer energy is that the ground state wave function has a significant and often dominant contri- The above discussion suggests that localizing effects of increasing U and ∆ are obviously important; however, the delocalizing effects arising from various hopping interactions as well as any other interaction such as the crystal field and the spin-orbit interaction, that may influence the bandwidth are also important and need to be treated on equal footing. This objective has been most successfully achieved through extensive developments of Dynamical Mean Field Theory (DMFT), which provides the basis of most of our discussion of the electronic structure of nickelates in later Altough we begin our discussion of ultra-thin film nickelates by briefly reviewing several key phenomena present in the bulk counterpart, we refer the reader to the reviews by Medarde [25] and Catalan [26] start to separate from each other ( Figure 1 ). Within the insulating phase, the entire family has monoclinic (P 2 1 /n) structure ( Figure 1 and 2(c)) with two inequivalent Ni sites in the unit cell.
Electrical and thermal measurements on the bulk and thin films revealed the signatures of complex multi-band behavior [27] , which has been further corroborated by angle resolved photoemission spectroscopy (ARPES) measurement [28] . Surprisingly, despite sharp changes in conduc-tivity and lattice parameters across the MIT, optical conductivity measurements revealed only a gradual opening of band gap with continuous changes in spectral weight of the Drude peak [29] .
The reported optical gap of ∼ 1 eV is also much larger than the gap (∼ 20 meV) obtained from electrical conductivity data [30] . Recent tunneling experiment showed the opening of a sharp gap (∼ 30 meV) in the insulating state and also the existence of pseudo gap in metallic LaNiO 3 [31] .
In the ionic picture, RENiO 3 compounds have NiO 6 octahedra with Ni 3+ ions in the d 7 low-spin electronic configuration (t 6 2g e 1 g : S =1/2), which are expected to be Jahn-Teller active. However, resonant X-ray diffraction (RXD) experiments showed ordering of local magnetic moments on Ni sites in AFI phase and ruled out any orbital ordering [32, 33] . The magnetic ground state of these spins (Figure 2(c) ) was initially deduced from neutron powder diffraction (NPD) [34] . The magnetic wave vector for the antiferromagnetic state was determined to be (1/2, 0, 1/2) ortho [(1/4, 1/4, 1/4) in pseudo cubic notation]; the spin arrangement of this E -AFM state can be viewed as either a sequence of ↑↑↓↓ or ↑ →↓← pseudo-cubic (1 1 1) planes and the non-collinear spin scenario has been demonstrated by resonant x-ray scattering [35] . Whereas two distinct magnetic moments 1.4 µ B and 0.7µ B consistent with a checker board type charge ordering pattern were determined for YNiO 3 [36] , the magnetic moments in the RE = Pr [34, 37] , Nd [34, 37] , Sm [37, 38] , Eu [37, 38] compounds were found to be similar on each Ni site. This surprising result was further corroborated by RXD experiments, in which a very similar energy dependence of magnetic scattering intensity was recorded across the series, with an similar spectroscopic signature for the local moment on Ni [39] . In view of the strong variation of structural distortion and the magnitude of T MIT in the RENiO 3 series, both measurements raised concern about the true nature of the charge ordering state. A view which aligns many of these facts is the picture where the strong covalency leads to the ground state to be more 3d 8 L, and the charge ordering pattern in this picture resides not on Ni but on the oxygen site (i.e.
.
IV. EPITAXIAL STABILIZATION
The +2 charge state is the most common oxidation state of Ni and the RENiO 3 requires Ni oxidation state to be +3. Such high oxidation state is stabilized only under a high oxygen pressure P ∼ 200 bar, and an elevated temperature of 1000 • C [41] . Despite the extreme synthesis conditions, to-date only micrometer-sized single crystals have been obtained for these nickelates (except for LNO) [42] , limiting the application of many experimental techniques crucial for understanding the underlying physics of these materials. As an alternate route, the growth of thin films is a feasible solution for obtaining large-size single-crystalline materials. Not surprisingly, many crucial pieces of information discussed in the last section were obtained by using single-crystalline thin films.
A. Thermodynamic Stability:
Whereas thin films of LNO could be grown without high oxygen pressure by pulsed laser deposition (PLD) [43] and sputtering [44] , stoichimetric NdNiO 3 films with a bulk-like MIT were initially achieved only by postannealing under a high oxygen pressure ( ∼115 bar) [45] . Later, epitaxial films for several members of the family were successfully synthesized at much reduced oxygen pressure (< 0.02 bar) by metal-organic chemical vapor deposition (MOCVD) techniques by Novojilov et al. [46] . Following this success, the high quality epitaxy at low oxygen partial pressure has been also realized by PLD [47] , sputtering [48] and all-oxide molecular beam epitaxy (MBE) [49] .
To understand how a single crystalline phase can be obtained outside the thermodynamic phase
of bulk materials, we consider the model of epitaxial stabilization of thin films [50] . In this phenomenological framework, the relative difference between the free energies for the bulk and epitaxially stabilized phases is given by:
Here the superscripts c and ic denote the epitaxially coherent and incoherent (i.e. free from substrate) phases, respectively, h is the film thickness, ∆g v is the Gibbs free energy per unit volume, µ is the shear modulus, ν is a Possion's ratio, is the relative lattice mismatch between the unit cell parameters of the desired phase and the substrate and σ s is the surface tension. Whereas the volume contribution (the first term) is always negative, the surface contribution (the second term)
is always positive. If the energy contributions are such that ∆E > 0, then an epitaxially coherent phase is stabilized [50] . As seen in equation 1, a dramatic reduction in the contribution to the free energy comes from the coherent film-substrate interface, implying that RENiO 3 phases can be stabilized on a perovskite substrate whereas the films on non-perovskite substrates like MgO and ZrO 2 lack the required coherency and enforce the phase decomposition to RENiO 3 → REO x +NiO [51] . Moreover, as indicated by equation (1), the increase of film thickness (h) as well 9 as the larger lattice mismatch ( ) may further amplify the phase decomposition (i.e. RE 2 O 3 and NiO) away from the single phase perovskite film [46] . Because the formation energy of RENiO 3
RT ln(P )] also increases with a decreasing tolerance factor [52] , the epitaxial stabilization of the distorted members of the series becomes much more difficult. In recent years, several groups have overcome this challenge and have successfully stabilized ultra-thin films of RENiO 3 with RE = Pr, Nd, Sm and Eu [53] [54] [55] [56] [57] [58] [59] .
B. Polarity mismatch:
The interest in nickelate heterostructures also brought to light the issue of polar discontinuity at the subtrate-film interface that results in a diverging potential, which is compensated in several ways , e.g. by electronic reconstruction, cationic inter-mixing or oxygen vacancies [60] . In a pure ionic model, because (uc denotes pseudocubic unit cell). Whereas the matched polarity on the LAO substrate yields the desired +3 valence of Ni, the polar mismatched case of LNO on STO yields the first unit cell with Ni in the +2 oxidation state [61] . Careful high-resolution transmission electron microscopy (HRTEM) combined with electron energy loss spectroscopy (EELS) confirmed Ni 2+ O 2− precipitation driven by the interfacial polar fields [62] . This precipitation of the Ni 2+ containing layer can be suppressed by the careful growth of a buffer layer of LAO, which allows for the preservation of Ni 3+ [61] in all nickel containing layers. These experiments highlight the importance of taking into account the polarity mismatch in understanding material properties in heterostructures.
V. GROUND STATE ENGINEERING THROUGH HETEROEPITAXY
Epitaxial stabilization on such perovskite substrate not only provides the desired single crystalline materials, but also allows ground state engineering of nickelates by implementing the effect of strain, confinement, charge transfer etc. The rapid progresses along these directions of research in recent times have been discussed in this section.
A. Epitaxial strain in ultra thin films
Because epitaxial growth on a single-crystalline substrate forces the film to have the same in-plane lattice parameters during the atom-on-atom growth; distortions, lattice symmetry, octahedral tilts and rotations in the resulting thin film may become quite different from the bulk counterpart [63] . Epitaxial strain is conventionally quantified by = (a bulk − a sub )/a bulk , where a bulk and a sub are the pseudo cubic lattice constants of bulk RENiO 3 and the substrate, respectively. However, as some chemical nonstochiometry may be introduced during the growth, actual should be calculated using the experimentally measured lattice constant of an unstrained film (instead of a bulk ). The effect of strain on electronic and magnetic transitions of RENiO 3 series has been thoroughly explored by diverse experimental probes including thermal measurements and Hall effect measurement [58, 64, 65] , synchrotron X-ray diffraction [66, 67] , X-ray absorption spectroscopy [67] [68] [69] [70] [71] , resonant soft X-ray scattering [69, 72, 73] , ARPES [74, 75] , optical spectroscopy [72, [76] [77] [78] . ultra thin films of many perovskite oxides surprisingly do not follow this simple notion [79] .
To understand how the SIOP model is violated, a 10 uc thick film of LaNiO 3 (LNO) was grown on LAO ( = -1.1%) and STO ( = +1.8%) substrates [68] . For the LAO case, X-ray linear dichroism (XLD) measurement showed a 100 meV lowering of the Ni d 3z 2 −r 2 orbital compared to the inversion of the e g orbitals was expected for tensile strain on STO. Surprisingly, no orbital polarization was detected for the STO case, although reciprocal space mapping confirmed that the film was fully coherent with in-plane lattice matched to the STO substrate [67, 68] . This asymmetric orbital-lattice response to epitaxial strain signals the existence of alternative compensation mechanisms for strain accommodation [63, 80] . Density functional theory (DFT) calculations with the experimentally determined lattice constants showed the existence of single type NiO 6 octahedra with different in-plane and out-of-plane Ni-O bonds resulting in finite orbital polarization for compressive strain. In contrast, tensile strain was preferentially accommodated by cooperative octahedral rotations (Figure 3(b) ) and breathing mode distortions (Figure 3(c) ). The importance of these phonon modes is highlighted by the observation of breathing mode distortion, that causes a Ni-O bond-length disproportionation with alternating octahedra of Ni (1) 
Strain induced self-doping
Becasue RENiO 3 belong to a part of U -∆ phase space with an effectively negative charge transfer energy and a high degree of covalency, the ground state of RENiO 3 is a strong admixture
state manifests itself as a characteristic pre-peak around 528.5 eV in O K edge (1s → p) Xray absorption spectra (XAS). Due to the weak core-hole interaction, the O K edge XAS is an approximate measure of oxygen projected unoccupied density of states [82] , and the intensity, position, and width of the pre-peak are the markers of the degree of Ni-O bond covalency. As shown in Figure 3 (e), for the series of LNO films subjected to both tensile and compressive strain, the pre-peak revealed a systematic evolution in the peak energy position with the imposed amount of epitaxial strain. The direct strain control of ligand-hole density was deduced from the nearly linear dependence of the peak position with , Figure 3 ∆ and W implies a strain-induced unusual self-doping effect, which was further substantiated by temperature-dependent Hall coefficient and thermoelectric power measurements [65] .
Strain driven phase engineering
As the nature of the ground states and the transition temperatures depend strongly of Ni-ONi bond angle and Ni-O bond length, epitaxial strain is expected to have a profound impact on the electronic and magnetic properties. To investigate this possibility, Liu et al., [56, 69] investigated 6 nm NNO films as a function of epitaxial strain. The result shown in Figure 4 (a)
indicates that unlike the bulk where T MIT = T N , the transitions get separated, with the degree of separation scaling with tensile strain. On the compressive side, the temperature-induced MIT is completely quenched. Although several reports [46, [83] [84] [85] revealed the preservation of the MIT in compressively strained films, a recent study by Hauser et al. [58] demonstrated that those films are actually partially relaxed, and optimally prepared films under compressive strain are entirely metallic [58, 86] , consistent with the report of Liu and coworkers [56, 69] . These studies found the resistivity of this anomalous metallic state exhibits non-Fermi liquid (NFL) behavior in the vicinity of a quantum critical point akin to the case of bulk PrNiO 3 under external pressure [87, 88] . From those observations, it was concluded that film behavior under increasing tensile strain resembles the A-site replacement by a smaller RE ion of the bulk, whereas the effect of compressive strain is very similar to that of hydrostatic pressure. The exponent of NFL phase is also not affected by the change of film thickness [86] . Although resistance of these films surpasses the Mott-Ioffe-Regel limit at high temperature [89] , unlike the case for the cuprates ρ eventually saturates for nickelates. This behavior was shown to related with the orbital splitting between d x 2 −y 2 and d 3z 2 −r 2 orbitals [86] . . The effect of epitaxial strain was also investigated for the distorted RENiO 3 members with T MIT > T N [70, 71, 73] . Similar to the NNO case, the separation between T MIT and T N decreases as the amount of tensile strain is lowered and the films grown under large compressive strain becomes entirely metallic [73] . 
Selective suppression of order parameters through epitaxy
Although both the antiferromagnetic order and the MIT are preserved in epitaxially grown NNO films with > +1.1%, the next important question is whether the proximity to the substrate of different crystal symmetry can alter the orthorhombic to monoclinic symmetry lowering across the MIT and the concomitant charge ordering. The charge ordering scenario in the bulk-like NNO films was investigated with resonant X-ray scattering experiments at the Ni K-edge [91] . In the high-symmetry orthorhombic metallic phase Ni sites do not contribute to particular reflections,
15
which gain a Ni contribution in the low temperature monoclinic phase and can be used to study the details of the charge ordering phase via the resonant signature [32, 91, 92] . An interesting recent result is that, for an ultrathin (6 nm) NdNiO 3 film grown under tensile strain, even though the film displayed an MIT and magnetic ordering, there was no resonant Ni signal for these reflections even in the insulating phase (Figure 4(c) ). This observation, together with the absence of any detectable temperature dependence of the reflection (Figure 4(d) ), led to the conclusion that P bnm symmetry is preserved deep into the insulating state [81, 90] . This result implies the exceptionally rare case of a purely electronic Mott-Hubbard MIT that is driven by the magnetic ordering.
Despite the absence of both the lattice symmetry change and Ni charge disproportionation, the transition was found to be accompanied by a peculiar charge redistribution from the Ni 3d to Nd 5d orbitals that may play a role in the MIT [81] . Although the relevance of Mott-Hubbard picture about the nature of the MIT was highlighted by the mid-gap spectral weight transfer in optics measurements [76] , the charge redistribution which involves the A-site states questions the simple picture of the conventional Mott transition. The K-edge RIXS measurement and the resonant x-ray scattering data suggest that the MIT is neither pure Mott-Hubbard nor charge-transfer.
In contrast to the case for NdNiO 3 , the bulk-like charge ordering pattern remains unaltered in ultra-thin films of highly distorted EuNiO 3 [93] . Those experiments stress the exquisite sensitivity of the electronic structure in the insulating state to various type of structural distortions [94] including the Jahn-Teller distortion (NdNiO 3 ) and breathing mode distortion (EuNiO 3 ), under epitaxial constraint. The issue of charge ordering in such geometry was also investigated by Raman scattering [72] , and phonon modes characteristic of the charge ordering were indeed observed in insulating state of thin film and superlattices of PrNiO 3 (of thickness ∼ 12 nm) under tensile strain. Interestingly, these Raman modes were absent in superlattices under compressive strain, which are weakly metallic but retain E antiferromagnetic ordering. Such an antiferromagnetic, metallic phase does not exist in the bulk nickelate and has been referred to as a spin-density wave phase [72] , which was predicted theoretically by Lee and co-workers [95, 96] .
B. Quantum confinement in heterostructures
The ability to grow these materials with sub-unit cell precision has opened another new dimension to explore highly two-dimensional electronic and magnetic phases in the quantum confinement regime. The SL structure consisting of an electronically active material and a wide band gap insulator (one side can be vacuum) blocks electron hopping along the confining direction (i.e.
across the interface), the specific choice of confining interface further determines the boundary condition in this quantum well geometry. In this section, we explore how heterostructures can be used to tune the electronic and magnetic states of nickelates.
Dimensionality and Carrier Localization
The correlated metallic behavior of bulk LNO provides a perfect play ground to test the itinerant behavior of d-electrons down to the atomic scale. Toward this goal, several group explored the effect of dimensionality along with electron-electron correlations was explored by growing a series of single layer films and SL structures of LNO of different thicknesses [48, 75, [97] [98] [99] [100] [101] . As an example, consider the results in Figure 5 (a), showing the temperature dependent resistivity behavior for a series of LNO films grown on LAO substrates by oxide molecular beam epitaxy [75] .
Although the room temperature conductivity decreases with decreasing film thickness, the metallicity over the entire temperature range is maintained down to 4 uc. Upon approaching the 2 uc limit, the LNO film becomes insulating. Although all groups have reported this confinement induced MIT, the critical film thickness at which the insulating behavior sets in is strongly dependent on the strain value and the architecture (i.e. film vs. SL). With respect to dimensionality effects in single layer films, one issue is the presence (or lack) of a polar discontinuity, which may explain the differences between the results on LAO [75] vs. STO [97] . Resonant X-ray absorption spectroscopic measurements on Ni L 3,2 -edge complemented by first principle calculation [98] and soft, hard X-ray photoemission spectroscopic measurements [100, 102] revealed a gradual evolution of electronic structure including the charge transfer gap. X-ray diffraction showed a change in atomic arrangement, in terms of both decreased Ni-O-Ni bond angle and lattice rumpling near the interface with a reduced number of unit cells [101] . In addition, layer-resolved studies established that the suppression of DOS is more pronounced near the interface [103] , where the octahedral tilts are larger than in layers away from the interface [101, 104] . All of these results indicate at the bandwidth control is an important component for the MIT as is the case for bulk nickelates [25, 26] .
Recent ARPES studies [75] dimension [75] .
Magnetism in Confined Architectures
Because all bulk rare earth nickelates that display a MIT also undergo magnetic transition, the observation of the insulating state in the few unit cell limit prompted several groups to investigate its spin degree of freedom. Ultrathin superlattices were initially investigated by muon spin rotation (µSR) [99] , and metallic 4-uc LNO/4-uc LAO SLs were found to remain paramagnetic down to the lowest temperatures, as for the case of bulk LNO, but antiferromagnetism was clearly detected in the insulating phase of a 2-uc LNO/2-uc LAO SL. Because µSR cannot determine the ordering pattern, a series of LNO SLs with dielectric spacers were grown on several substrates and were investigated by resonant soft x-ray diffraction [105] . (Figure 6(b) ), this magnetic state has been interpreted as spin-density wave.
The disappearance of the spin-density wave states for N = 3, 4 SL was attributed to the increasing three-dimensional Fermi surface that in turn suppresses the tendency for nesting together with the onset of the metallic phase. Such a nesting driven mechanism behind magnetic ordering was further corroborated by very recent ARPES measurements [106] . Similar polarization-dependent magnetic scattering experiments with azimuthal scans for thin films spanning the whole RENiO 3 series are clearly necessary to probe any variation in the spin orientation with the change in the Ni-O-Ni bond angles.
Orbital polarization
From the electronic structure standpoint, due to the strong similarity between RENiO 3 and high -T c cuprates (i.e. one electron vs. one hole on the e g orbital), Chaloupka & Khaliullin [109] proposed, as an analog for high T c superconductors, a single unit cell LNO layer heterostructured with a band insulator. In their model, it was assumed that tensile strain would enforce the electron in to the d Disa et al [114] also recently confirmed this zero orbital polarization. In contrast, the same SL grown under tensile strain on STO showed only ∼ 5% orbital polarization and most importantly no splitting between the e g orbitals. Ab-initio calculations [113, 115] found that the coordination between the Al and the Ni resulted in a chemical mismatch that influenced the hole density on the apical oxygen and subsequently the Ni d 3z 2 −r 2 orbital. A new approach termed orbital reflectometry (a combined analysis of XLD and resonant X-ray reflectivity) [107] applied to a 4-uc LNO/4-uc LAO superlattice (SL) on a STO substrate also detected a similar value of the orbital polarization.
As illustrated in Figure 6 (c), the power of this method is the ability to differentiate the orbital polarization across the layers. By careful choice of spacer layers and application of high tensile strain, large orbital polarization (up to 25%) was reported for a 4-uc LNO/4-uc GdScO 3 SL [108] ( Figure 6(d) ). A very recent study of a 4-uc PrNiO 3 /4-uc PrAlO 3 SL revealed the presence of smaller orbital polarization (P av ) of ∼ 5% [116] , which also decreases across the MIT. Interestingly, no significant temperature dependence of P av was observed across the magnetic transition of compressively strained SLs, which had earlier been assigned as a spin density wave phase [72] .
C. Interfacial charge transfer
The redistribution of charge at the interface between two dissimilar materials is one of the key concepts behind modern electronics. The difference in the chemical potential may cause charge transfer across the interface; which in-turn it can alter spin and orbital sectors, resulting in novel electronic and magnetic states emerging in complex oxide heterostructures [5] [6] [7] [8] . For example, electronic reconstructions have been explored for LNO by forming interface with manganites [117] [118] [119] [120] [121] [122] and titanates [114, 123, 124] .
Although bulk CaMnO 3 (CMO) is an antiferromagnetic insulator, interfacial ferromagnetism limited within one unit cell of CMO from the interface was uncovered in N -uc CMO/M -uc LNO superlattices when the thickness (M ≥ 4) was sufficient to make the system metallic [120] . Because no sizable charge transfer was observed, the origin of ferromagnetism connected to the (Figure 7(a) ). As illustrated in Figure 7 (b), this artificially generated buckled honeycomb lattice provides a unique opportunity to investigate physics of d electrons in graphene-like geometry [127] [128] [129] . Similarly, the dice lattice shown in Figure 7 the weakly correlated limit a number of topological phases (e.g. Dirac half-metal phase, quantum anomalous Hall insulator phase, and spin nematic phase) driven exclusively by interactions and without spin-orbit coupling were predicted [128, 129] .
Because all popular perovskite substrate such as STO (LAO, NdGaO 3 , YAlO 3 ) are polar along [111] with alternating +4e, -4e (+3e, -3e) charges per plane, epitaxial thin film growth along this direction is rather undeveloped due to the possibility of complex structural, chemical and electronic reconstructions that act to compensate for the polarity jump. To elucidate the issue, the unit cell by unit cell growth was investigated by monitoring the growth progression with in-situ reflection high energy electron diffraction (RHEED) of LNO on STO (polar interface) and LAO (non-polar in-terface) (111) substrates [134] . The measurements showed the presence of non-perovskite phases within the first 5 unit cells on the STO substrate; a combination of X-ray diffraction and resonant X-ray spectroscopy identified the formation of La 2 Ni 2 O 5 phase. In contrast, a stoichiometric LNO was successfully grown on a LAO (111) substrate, thus confirming that the absence of the polar mismatch at the interface is the key for the [111] oriented heterostructures [135] .
Followed by the theoretical predictions [128, 129, [131] [132] [133] , the behavior of d 7 Mott electrons on the honeycomb lattice was investigated by growing 2-uc NNO/4-uc LAO SL on a LAO (111) substrate. The resultant system exhibits a new ground state characterized by antiferromagnetic correlations and orbital ordering, and this lattice-geometry stabilized new ground state is unattainable in either bulk NNO or in analogous heterostructures grown along the conventional [001] direction [136] . Although design of RE nickelates with new lattice geometries is still in its infancy, the potential of this interesting concept for the ground state engineering was recently highlighted also by a report of markedly larger charge transfer in [n LNO/n LMO] (111) SLs with n = 5, 7
compared to the equivalent (001) SLs [122] .
VI. THEORETICAL UNDERSTANDING
The most important task of the theory of the RE nickelates is to link the atomic physics of the strongly correlated Ni d-orbitals to the behavior of actual materials. Issues of current importance include the nature of the MIT and its connection to lattice distortions and to magnetic ordering, the degree to which orbital occupancy can be varied by strain or other external parameters, and the nature and origin of the observed magnetic states.
An important issue in the context of transition metal oxides generally and RENiO 3 materials in particular is orbital engineering: the degree to which the electronic structure and, in particular the occupancy of different d-orbitals and the number of bands crossing the Fermi level can be changed by strain or by heterostructuring [7] . Following the proposal of Chaloupka and Khalliulin [109] that under appropriate circumstances LNO might exhibit a one-band Fermi surface analogous to that of the high-T c cuprates, many groups [67, 68, 107, 108, 113, 116, 137] have investigated the degree to which orbital occupancies of RENiO 3 materials can be manipulated. As far as is known, in bulk materials the relevant Ni d-orbitals are roughly equally occupied. The key finding [67, 68, 107, 108, 113, 116] is that in strained SLs a differential orbital occupancy of up to at most 25% can be achieved. Understanding the limits of orbital engineering is a second challenge 24 to theory.
We begin the theoretical discussion by consideration of the electronic configuration of Ni sites, which is a superposition of states with 6, 7, 8, or 9 Ni d-electrons. We can schematically write
The Hund's and ligand field energies are such that the t 2g -symmetry d orbitals are fully filled and the relevant electronically active Ni d orbitals are the e g states. Thus d 6 corresponds to an empty Ni e g shell, d
7 to an e g shell with one electron, and so forth. Although the Hund's coupling is evidently not strong enough to overcome the ligand field, it is believed to be strong enough to ensure that the dominant d 8 configuration is high-spin (S=1, with one electron in each e g orbital).
The nickelates are believed to be strongly correlated materials in which interaction effects be- The basic picture emerging from standard DFT calculations is that the mean Ni d-valence slightly greater than 8 [112] and that in the ideal structure two bands, of mixed Ni e g and O 2p origin, cross the Fermi level (in the actual materials, monoclinic or GdFeO 3 -type distortions increase the unit cell so that it contains 4 Ni ions; the associated backfolding leads to multiple band crossings).
Structural relaxation calculations indicate an increasing degree of GdFeO 3 distortion as the RE ion is changed from Nd across the series to Lu, consistent with experiment, and provide valuable information regarding rotational changes in SLs [94] . Pure DFT calculations generally predict a metallic and non-magnetic ground state in all members of the family.
The +U extensions of DFT do find a charge ordered ground state for reasonable values of U [138] but greatly overestimate the critical pressure required to destroy the charge ordering. [139, 140] . Jahn-Teller effects associated with lifting the degeneracy of the two e g states were considered
by He & Millis [141] and were found to become relevant at large (∼ 4%) strains. In addition, the +U methodologies predict a ferromagnetic ground state, rather than the long-period E or E state observed experimentally. However, for a reasonable range of U , Bellaiche and co-workers [142] were able to stabilize the E antiferromagnetic state (two inequivalent Ni atoms, one, associated with the long-bond octahedron and carrying a non-zero moment and, the other associated with the short-bond octahedron and carrying zero moment) as a metastable state. Puggioni et al. [143] as well as Bruno et al. [71] used hybrid functional methods for strained films of the nickelates to
show that the experimentally observed ground state is reproduced in these calculations.
An alternative family of theoretical approaches uses model calculations based on simple physical pictures following the assumption that, in the ground stat,e only one valence is dominant. The
Mott-Hubbard picture is based on the assumption that the relevant valence is d 7 . In this picture, the main charge transfer process involves removing an electron from one site (creating a d 6 configuration) and adding it to an adjacent site, creating a d 8 configuration, so that the key energy is
. One expects U > 0, in which case the important physical effects are the Mott transition (conductivity is blocked if U is too large relative to the bandwidth) and Jahn-Teller physics associated with cubic-tetragonal distortions that lift the degeneracy of the d state. Also important is the Hunds coupling, J H , which favors high-spin configurations.
To study this situation one considers a Hubbard-like model, with two bands (representing the Ni e g states, or, in a more sophisticated interpretation, the e g -O 2p antibonding bands, and that are subject to the U , J H and perhaps an electron-phonon interaction. Several researchers have taken this approach [95, 96, 109, 110, 138] . Mazin and co-workers [138] (using an approach based much more closely on DFT calculations) observed that at the crossover between itinerant and localized behavior ( with a bandwidth comparable to the Coulomb repulsion) interesting physics can occur;
in particular, if the intra-atomic exchange interaction strength J H is large enough, it may drive charge ordering.
Hansmann and collaborators [110] surface nesting leads to a susceptibility χ (q) peaked close to the q value at which the magnetic ordering has been observed in experiments. Lee and co-workers noted that, for site-centered but not bond-centered spin-density waves, symmetry considerations imply that the magnetic ordering would lead also to a charge ordering (with an amplitude of charge order proportional to the square of the magnetic order parameter), providing a possible theoretical explanation of PrNiO 3 and NdNiO 3 for which the magnetic and charge ordering coincide. However, this reasoning cannot be extended to those nickelates for which the magnetic ordering and MIT were separated unless unreasonably large values of J H are assumed.
If ∆ is positive and reasonably large (but less than U ) and β (Eq. 2) is still reasonably close to 1, one finds that the Mott-Hubbard picture provides a reasonable first-order description of the physics, with ∆ playing the role of U . This picture yields, for example, the basic understanding of the high-T c cuprates [144] [145] [146] . However in the RE nickelates, ∆ may be negative, implying different physics. As noted above, DFT calculations indicate that the dominant electronic config- [112] and that ∆ is negative. Mizokawa et al., [40] explored the potential relevance of the negative charge transfer energy situation to nickelate physics in the context of a Hartree-Fock analysis of an extended Hubbard model that also included oxygen orbitals. In this situation, holes are present on the oxygen, and a purely electronic mechanism for insulating behavior requires ordering of the oxygen holes. Ordering of oxygen holes occurred only for extremely unphysically large magnitudes of charge transfer energy (∆ −7eV ), so these authors concluded that the combination of breathing-mode distortions and strong correlations on the Ni site was essential for stabilizing the insulating state.
Marianetti, one of us, and co-workers [112, 139, 140, 147] more quantitatively examined the negative charge-transfer energy scenario using a DFT+DMFT methodology in which the correlated states were taken to be atomic-like Ni states constructed from Wannier functions defined over the full energy range of the Ni-O band complex and the O states were explicitly retained in the DMFT self-consistency equation. As with all beyond-DFT approaches, the results depend to some degree on the values chosen for the interaction parameters U and J and for the doublecounting correction [145, 146, 148, 149] . electrons are correlated by the Hunds coupling into an S = 1 state. On the long-bond site, the S = 1 is decoupled from the environment, so the prediction is that, for example, an NMR measurement in the paramagnetic state would reveal a freely fluctuating S = 1 local moment. On the other site, the S = 1 is strongly hybridized to the two holes on the O-sites, leading to a singlet. The DFT+DMFT calculations provide an explicit realization of this state, which is insulating. As with other DFT+ methodologies, the DFT+DMFT methodology indicates a ferrimagnetic ground state, rather than the long-period antiferromagnetic state observed experimentally. In the ferrimagnetic state, the moment size alternates: it is small on the short-bond site and large on the long-bond site.
These conclusions were subsequently reproduced by Johnson et al [151] who performed exact diagonalization studies of the one-and three-dimensional Ni-O clusters.
More recently, Park et al. [139, 140] Further exploration of this and other theoretical approaches seems highly desirable.
VII. CONCLUDING REMARKS AND FUTURE ISSUES
With a brief introduction to the classification of electronic structure for correlated oxides, we review above the recent progress in the field of interface-controlled ground-state engineering of the heterostructuring route has also resulted in several unconventional phases such as insulating states without charge order, NFL metallic phases and antiferromagnetism in the metallic state, which are unattainable in the bulk. Here, we highlight several important issues for future consideration.
A. Exploration of crystals beyond simple perovskites
Although pushing synthesis of thin films of the highly distorted member of the series RE [156, 157] . The large tetragonal distortion or absence of the apical oxygen in these compounds gives rise to strong variations in the crystal field that can be used to tune orbital energies. In this series, thin film growth also offers opportunities to also tune orbitals via cation ordering [158] . Another option, ANiO 2 compounds such as LiNiO 2 that display interesting electronic and magnetic states [159, 160] , remains largely unexplored from the perspective of epitaxial control.
B. Role of oxygen in electronic and magnetic transitions
Resonant X-ray absorption spectroscopy has firmly established the presence of holes on oxygen and the theoretical studies have also emphasized the ordering of the ligand holes in a particular fashion across the transitions. Although the checker board type charge ordering and the E magnetic structure of the Ni sublattice have been firmly established by resonant X-ray scattering in bulk, the ligand hole ordering and magnetism associated with the oxygen sub-lattice have not been
experimentally verified yet due to limitations of scattering geometry. An experimental answer to these crucial issues can be the key to disentangling the puzzle of charge and E magnetic ordering.
C. Ground State Engineering Using External Stimuli
So far, this review focuses around metastable states created using different architectures during growth. In this section, we explore the opportunities to drive these systems non-adiabatically even further away from equilibrium via external driving forces, and we focus on two areas: optical control with visible and mid-IR sources and ionic control by applying strong electrochemical gradients. Both approaches have unique portions of phase space that can be accessed as described below.
Ultrafast Dynamics in Nickelate Heterostructures
Stimulating phase changes using optical pulses is a well-established way to control ground states in complex oxides [161] and offers the ability to drive a system far off the equilibrium axis as a means to trigger phase transitions or seek out wholly new emergent states. Initial work on nickelates focused on tracking the time response of the carrier dynamics [29, 162] and coherent phonon excitation to probe the nature of electron-phonon coupling [163] , but recently this ap-proach was extended using ultrafast soft X-rays to track the response of magnetism to optical excitation [164] . In NdNiO 3 , the collapse of the antiferromagnetic order as probed by resonant scattering at the AFM Bragg peak revealed an ultrafast collapse of the ordering of the Ni moments, followed by much slower dynamics for the parasitic magnetism related to low-temperature ordering of the Nd moments. Direct exploration of the magnetic order gives important insight into the interaction between the MIT and magnetism. However, the recovery process is much more difficult to understand due to the high energy of optical excitation, the system equilibrates on the longer time scale of several picoseconds due to heat generated during the carrier relaxation process via electron-lattice coupling.
To circumvent this issue, researchers have been exploring mode-selective excitations that can efficiently transfer the energy in the optical excitation in to the system. One very intriguing approach demonstrated recently is the direct excitation of collective modes by light in the Thz-tomid-IR regime [161, 165, 166] . This approach was first demonstrated in bulk complex oxides as a route to control the MIT by pumping specific phonon modes in the mid-IR that couple to the electronic degrees of freedom [167] and was later shown to be a route to dynamically control the superconducting phase in cuprates [168] . Caviglia et al. [84] also applied this approach to nickelate films to control the MIT. The experiment demonstrated that, by pumping a substrate phonon mode that generates an ultra fast strain wave, the system could be converted to the metallic phase [84] . By merging the mode-selective pumping with ultra fast soft X-ray scattering, Caviglia and colleagues [169] were also able to measure the propagation of the phonon from the substrate into the film by following the spatial collapse of the magnetic state. This result confirmed that the non-linear nature of the phonon excitation is a key component for triggering the transition [165] .
Very recently, a DMFT theoretical framework has appeared to predict the couplings to design materials for far more efficient dynamic control [170] . In the future, this approach has the potential to offer new ways to efficiently manipulate correlated electron systems.
Ionic Control
Another new control avenue for nickelates is through the use of electric fields applied to thin-film samples to manipulate carrier doping, analogous to gate control in semiconducting devices [171] . Ionic liquids have emerged in this area as a means to apply large electric potentials through the use of a molecular electric double layer that forms on the surface of a sample. Al-31 though this approach was efficiently used to control the MIT in several systems [83, [172] [173] [174] [175] [176] [177] , the recent picture of charge carrier doping turned out to be more related to doping via the injection of oxygen vacancies under large applied electrochemical potential gradients [178, 179] . Although the timescale of this method is much slower due to doping via ionic diffusion, this process still offers the ability to change a material's phase through large stoichiometric changes, that were not available via gating in more conventional oxide devices [171] . Recently, in another interesting approach, the ionically gated RE nickelates were used to construct new classes of electronics based on neuromorphic (i.e. brain-like) principles [180, 181] . 

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