Signatures of topotactic hydrogen in nickelate superconductors

Superconductivity has entered the nickel age marked by enormous experimental and theoretical efforts. Notwithstanding, synthesizing nickelate superconductors remains extremely challenging, not least due to incomplete oxygen reduction and topotactic hydrogen. Here, we present density-functional theory calculations, identify a phonon mode as a possible indication for topotactic hydrogen and discuss the charge redistribution patterns around oxygen and hydrogen impurities.


Introduction
Computational materials calculations predicted superconductivity in nickelates [1] and heterostructures thereof [2][3][4] since decades, mainly based on apparent similarly to cuprate superconductors. Three years ago, superconductivity in nickelates was finally discovered in experiment by Li, Hwang and coworkers [5], breaking the grounds for a new age of superconductivity, the nickel age. It is marked by an enormous theoretical and experimental activity, including but not restricted to . Superconductivity has been found by now, among others, in Nd 1−x Sr x NiO 2 [5,6], Pr 1−x Sr x NiO 2 [7], La 1−x Ca x NiO 2 [8], La 1−x Sr x NiO 2 [9], and most recently in the pentalayer nickelate Nd 6 Ni 5 O 12 [10]. Fig. 1 shows some of the hallmark experimental critical temperatures (T c 's) for the nickelates in comparison with the preceding copper [32] and iron age [33] of unconventional superconductivity. Also shown are some other noteworthy superconductors, including the first superconductor, solid Hg, technologically relevant NbTi, and hydride superconductors [34]. The last are superconducting at room temperature [35], albeit only at a pressure of 267GPa exerted in a diamond anvil cell. All of these compounds are marked in gray in Fig. 1 as they are conventional superconductors. That is, the pairing of electrons originates from the electron-phonon coupling, as described in the theory of Bardeen, Cooper, and Schrieffer (BCS) [36].
Why did it take 20 years to synthesize superconducting nickelates that have been so seemingly predicted on a computer? To mimic the cuprate Cu 3d 9 configuration, as in NdNiO 2 , nickel has to be in the uncommon oxidation state Ni 1+ which is rare and prone to oxidize further. Only through a complex two step procedure, Lee, Hwang and coworkers [65]   year of discovery for selected superconductors. The discovery of cuprates, iron pnictides and nickelates led to enormous experimental and theoretical activities. Hence one also speaks of the copper, iron and nickel age of superconductivity.
able to synthesize superconducting nickelates. In a first step, modern pulsed laser deposition (PLD) was used to grow a Sr x Nd 1−x NiO 3 film on a SrTiO 2 substrate. This nickelate is still in the 3D perovskite phase, see Fig. 2 (left), with one oxygen atom too much and will thus not show superconductivity. Hence, this additional oxygen between the layers needs to be removed in a second step. The reducing agent CaH 2 is used to this end, within a quite narrow temperature window [65]. If all goes well, one arrives at the superconducting Sr x Nd 1−x NiO 2 film (top center). However, this process is prone to incomplete oxidation or to intercalate hydrogen topotactically, i.e., at the position of the removed oxygen, see Fig. 2 (bottom center). Both of those unwanted outcomes are detrimental for superconductivity. In [21,67,68] it was shown by density functional theory (DFT) calculations that NdNiO 2 H is indeed energetically favorable to NdNiO 2 + 1/2 H. For the doped system, on the other hand, Nd 0.8 Sr 0.2 NiO 2 without the hydrogen intercalated is energetically favorable. The additional H or likewise an incomplete oxidation to SrNdNiO 2.5 alters the physics completely. Additional H or O 0.5 will remove an electron from the Ni atoms, resulting in Ni 2+ instead of Ni 1+ . The formal electronic configuration is hence 3d 8 instead of 3d 9 , or two holes instead of one hole in the Ni d-shell. Dynamical mean-field theory (DMFT) calculations [21] evidence that the basic atomic configuration is the one of Fig. 2 (lower right). That is, because of Hund's exchange the two holes in NdNiO 2 H occupy two different orbitals, 3d x 2 y 2 and 3d 3z 2 −r 2 , and form a spin-1. A consequence of this is that DMFT calculations predict NdNiO 2 H to be a Mott insulator, whereas NdNiO 2 is a strongly correlated metal with a large mass enhancement of about five [21].
To the best of our knowledge, such a two-orbital, more 3D electronic structure is unfavorable for high-T c superconductivity. The two-dimensionality of cuprate and nickelate superconductors helps to suppress long-range antiferromagnetic order, while at the same time retaining strong antiferromagnetic fluctuations that can act as a pairing glue for superconductivity. In experiment, we cannot expect ideal NdNiO 2 , NdNiO 2 H or NdNiO 2.5 films, but most likely some H or additional O will remain in the NdNiO 2 film, after the CaH 2 reduction. Additional oxygen can be directly evidenced in standard x-ray diffraction analysis after the synthesis step. However, hydrogen, being very light, evades such an x-ray analysis. It has been evidenced in nickelates only by nuclear magnetic resonance (NMR) experiments [69] which, contrary to x-ray techniques, are very sensitive to hydrogen. Ref. [70] suggested hydrogen in LaNiO 2 to be confined at grain boundaries or secondary-phase precipitates. Given these difficulties, it is maybe not astonishing that it took almost one year before a second research group [6] was able to reproduce superconductivity in nickelates. Despite enormous experimental efforts, only a few groups succeeded hitherto.
In this paper, we present additional DFT results for topotactic hydrogen and incomplete oxygen reduction in nickelate superconductors: In Section 3 we provide technical information on the DFT calculations. In Section 3 we analyze the energy gain to topotactically intercalate hydrogen in LaNiO 2 and NdNiO 2 . In Section 4, we analyze the phonon spectrum and identify a high-energy mode originating from the Ni-H-Ni bond as a characteristic feature of intercalated hydrogen. In Section 5 we show the changes of the charge distribution caused by topotactic hydrogen. Finally, Section 6 provides a summary and outlook.

Method
Computational details on E b . In both our previous theoretical study [21] and this article, the binding energy E b of hydrogen atoms is computed as: Here, E[ABO 2 ] and E[ABO 2 H] are the total energy of infinite-layer ABO 2 and hydrideoxides ABO 2 H, while µ[H] = E[H 2 ]/2 is the chemical potential of H. Note that H 2 is a typical byproduct for the reduction with CaH 2 and also emerges when CaH 2 is in contact with H 2 O. Hence it can be expected to be present in the reaction. A positive (negative) E b indicates the topotactic H process is energetically favorable (unfavorable) to obtain ABO 2 H instead of ABO 2 and H 2 /2.
In the present paper, we go beyond [21] that reported E b of various ABO 2 compounds by investigating E b of La 1−x Ca x NiO 2 systems for many different doping levels. Here, the increasing Ca-doping is achieved by using the virtual crystal approximation (VCA) [71,72] from LaNiO 2 (x=0) to CaNiO 2 (x=1). For each Ca concentration, structure relaxation and static total energy calculation is carried out for La 1−x Ca x NiO 2 and La 1−x Ca x NiO 2 H within the tetragonal space group P4/mmm. To this end, we use density-functional theory (DFT) [73,74] with the VASP code [75,76] and the generalized gradient approximations (GGA) of Perdew, Burke, and Ernzerhof (PBE) [77] and PBE revised for solids (PBEsol) [78]. For undoped LaNiO 2 , the GGA-PBEsol relaxations predict its in-plane lattice constant as 3.890 Å whichis close to that of the STO substrate: 3.905 Å. The computations for La 1−x Ca x NiO 2 and LaCoO 2 , LaCuO 2 , SrCoO 2 and SrNiO 2 are performed without spin-polarization and a DFT+U treatment [79], as the inclusion of Coulomb U and spin-polarization only slightly decreases the E b by ∼5% for LaNiO 2 [66] . For NdNiO 2 , an inevitably computational issue are the localized Nd-4 f orbitals. These f -orbitals are localized around the atomic core, leading to strong correlations. In non-spin-polarized DFT calculations this generates flat bands near the Fermi level E F and leads to unsuccessful convergence.  Fig. 4(a,b) are enlarged to a 2×2×2 supercell, while for LaNiO 2 H 0.125 and LaNiO 2.125 the phonon are directly computed with the supercell of Fig. 4(c,d).
Computational details on electron density. The electron density distributions of LaNiO 2 , LaNiO 2 H, LaNiO 2 H 0.125 , and LaNiO 2.125 are computed using the WIEN2K code [82] while taking the VASP-relaxed crystal structure as input. The isosurfaces are plotted from 0.1 (yellow lines) to 2.0 (center of atoms) with spacing 0.1 in units of e/Å 2 . Fig. 3 shows the results of the hydrogen binding energy E b for the infinite layer nickelate superconductors Nd 1−x Sr x NiO 2 [5,62,63] and La 1−x Ca x NiO 2 [8]. To reveal the evolution of E b when the B-site band filling deviates from their original configurations (3d 9 in LaNiO 2 when x=0 and 3d 8 in CaNiO 2 when x=1), we also show the binding energy of LaCoO 2 (3d 8 ), LaCuO 2 (3d 10 ), SrCoO 2 (3d 7 ) and SrNiO 2 (3d 8 ).

Energetic stability
Let us start with the case of La 1−x Ca x NiO 2 [8]. Here, the unoccupied La-4 f orbitals make the computation possible even without spin-polarization and Coulomb U for La-4 f , whereas for NdNiO 2 this is not practicable due to Nd-4 f flat bands near E F . Positive (negative) E b above (below) the horizontal line in Fig. 3 indicates topotactic H is energetically favorable (unfavorable). When x=0, i.e. for bulk LaNiO 2 , the system tends to confine H atoms, resulting in oxide-hydride ABO 2 H with E b = 157 meV/H. As the concentration of Ca increases, E b monotonously decreases, reaching -248 meV for the end member of the doping series, CaNiO 2 . The turning point between favorable and unfavorable topotactic H inclusion is around 10% to 15% Ca-doping. Let us note that E b = 0 roughly agrees with the onset of superconductivity, which for Ca-doped LaNiO 2 emerges for x>15% Ca-doping [8]. To obtain E b in NdNiO 2 a much higher computational effort is required: firstly, the Nd-4 f orbitals must be computed with either treating them as core-states or including spin-splitting. Secondly, for the spin-polarized DFT(+U) calculations, an appropriate (anti-)ferromagnetic ordering has to be arranged for both Ni-and Nd-sublattices. In oxide-hydride ABO 2 H compounds, the δ-type bond between Ni and H stabilizes a G-type anti-ferromagnetic order by driving the system from a quasi two-dimensional (2D) system to a three dimensional (3D) one [21]. Given the large computational costs of E b for Nd 1−x Sr x NiO 2 by using antiferromagnetic DFT+U calculations for both Nd-4 f (U ∼7 eV) and Ni-3d (U=4.4 eV) orbitals, we merely show here the results of NdNiO 2 (x=0), Nd 0.75 Sr 0.25 NiO 2 (x=0.25) and SrNiO 2 (x=1), which are adopted from [21]. With 25% Sr-doping, the E b of NdNiO 2 is reduced from 134 meV to -113 meV. Please note that E b of (Nd,Sr)NiO 2 is slightly smaller than in (La,Ca)NiO 2 , at least in the low doping range. This can be explained by shorter lattice constants in NdNiO 2 , in agreement with the finding [21] that compressive strain plays an important role at reducing E b .
One can speculate that this suppression of topotactic hydrogen may also play a role when comparing the recently synthesized (Nd,Sr)NiO 2 films on a (LaAlO 3 ) 0.3 (Sr 2 TaAlO 6 ) 0.7 (LSAT) substrate [64] with the previously employed SrTiO 3 (STO) substrate [62]. Lee et al. [64] reported cleaner films without defects and also a higher superconducting transition temperature T c ∼ 20 K for the LSAT film, as compared to T c = 15 K and plenty of stacking fault defects for the STO substrate [62]. As for (La,Ca)NiO 2 , E b = 0 falls in the region of the onset of the superconductivity for (Sr,Nd)NiO 2 , which is x ∼10% Sr-doping in LSAT-strained defect-free films [64] and x ∼12.5% at SrTiO 3 -substrate states [62]. Topotactic hydrogen might play a role in suppressing superconductivity in this doping region.
In Fig. 3, we further show additional infinite layer compounds LaCoO 2 , LaCuO 2 , SrCoO 2 and SrNiO 2 for comparison. Their E b is predicted to be 367, -42, 69 and -134 meV, respectively. Combining the results of LaNiO 2 and CaNiO 2 , we summarize several tendencies on how to predict E b of ABO 2 : (1) the strongest effect on E b is changing the B-site element. However this seems unpractical for nickelate superconductors as the band filling is strictly restricted to be 3d 9−x (x ∼ 0.2). For both trivalent (La, Nd) and bivalent (Sr, Ca) cations, E b decreases when the B-site cation goes from early to late transition metal elements, e.g. from LaCoO 2 (3d 8 ) to LaNiO 2 (3d 9 ) to LaCuO 2 (3d 10 ). (2) Compressive strains induced by either substrate or external pressure can effectively reduce E b and we believe that this might be used for growing defect-free films. (3) According to our theoretical calculations, E b mainly depends on lattice parameters and band filling of the B-site 3d-orbitals, but much less on magnetic ordering and Coulomb interaction U.

Phonon dispersion
As revealed by previous DFT phonon spectra calculations [16], NdNiO 2 is dynamically stable. One of the very fundamental question would be whether topotactic H from overreacted reduction and/or O from unaccomplished reductive reactions affect the lattice stability. To investigate this point, we perform DFT phonon calculations and analyze the lattice vibration induced by H/O intercalation, as shown in Fig. 4.
The phonon spectrum of LaNiO 2 [4(a)] is essentially the same as in Ref. [16], all the phonon frequencies are positive, indicating it is dynamically stable. In Fig. 4(b), the oxideshydride LaNiO 2 H is also predicted to be dynamically stable. Please note that the phonon dispersions between 0 and 20 THz are basically the same as those in LaNiO 2 [ Fig. 4(a); note the different scale of the y-axis]. However, one can see new, additional vibration modes from the light H-atoms at frequencies of ∼27 THz and ∼43 THz. Among these vibrations, the double degenerate mode at lower frequency is generated by an in-plane (xy-plane) vibration of the topotactic H atom. There are two such in-plane vibrations of H atoms, either along the (100) or (110) direction (and symmetrically related directions), as indicated by the orange arrows in Fig. 4(b). The mode located at the higher frequency ∼43 THz is, on the other hand, formed by an out-of-plane (z-direction) vibration and is singly degenerate.
We explain these phonon modes in detail by computing the bonding strength between H-1s-Ni-d z 2 and H-1s-La-d xy orbitals. Our tight-binding calculations yields an electron hopping term of -1.604 eV between H-1s and Ni-d z 2 while it is -1.052 eV from La-d xy to H-1s. That is, the larger H-1s-Ni-d z 2 overlap leads to a stronger δ-type bonding and, together with the shorter c-lattice constant, to a higher phonon energy. Additionally, the shorter c-lattice in LaNiO 2 should also play a role at forming a stronger H-1s-Ni-d z 2 bond.
In our previous analysis of the band character for LaNiO 2 H [21], the H-1s bands were mainly located at two energy regions: a very flat band that is mostly from the H-1s itself at ∼-7 to -6 eV, and a hybridized band between H-1s and Ni-d z 2 at ∼-2 eV. Together with the higher phonon energy this indicates that the topotactic H atoms are mainly confined by a Ni sub-lattice via bonding and anti-bonding states formed by H-1s and Ni-d z 2 orbitals, instead of the La(Nd) sub-lattice.
The complete (full) topotactic inclusion of H, where all vacancies induced by removing oxygen are filled by H, is an ideal limiting case. Under varying experimental conditions, such as chemical reagent, substrate, temperature, and strain, the H-topotactic inclusion may be incomplete, and thus ABO 2 H δ (δ<1) be energetically favored. Hence, we also compute the phonon spectrum at a rather low H-topotactic density: LaNiO 2 H 0.125 , achieved by including a single H into 2×2×2 LaNiO 2 supercells as shown in Fig. 4(c). Also such a local H defect, as revealed by the positive frequency at all q-vectors in the lower panel of Fig. 4(c), does not destroy the dynamical stability of the LaNiO 2 crystal. In fact, the only remarkable qualitative difference between the complete and 12.5% topotactic H case is the number of phonon bands at 0 THz to 20 THz. This is just a consequence of the larger 2×2×2 LaNiO 2 supercell, with eight times more phonons. Some quantitative differences can be observed with respect to the energy of the phonon mode: The out-of-plane vibration energy is enhanced from ∼43 THz in LaNiO 2 H [ Fig. 4(b)] to ∼47 THz in LaNiO 2 H 0.125 [ Fig. 4(b)], and the in-plane vibration mode frequency is reduced from ∼27 THz in LaNiO 2 H [ Fig. 4(b)] to ∼21 THz LaNiO 2 H 0.125 [ Fig. 4(c)]. This is because the H-intercalation shrinks the local c-lattice, i.e., the distance between two Ni atoms separated by topotactic H, from 3.383 Å in [LaNiO 2 H: Fig. 4(b)] to 3.327 Å [LaNiO 2 H 0.125 : Fig. 4(c)]. The bond length between H and La is, on the other hand, slightly increased from 2.767 Å in [LaNiO 2 H: Fig. 4(b)] to 2.277 Å [LaNiO 2 H 0.125 : Fig.  4(c)]. This lattice compression (enlargement) explains the enhancement (reduction) for the out-of-plane (in-plane) phonon frequencies (energies).
These results pave a new way to detect the formation of topotactic H in infinite nickelate superconductors: by measuring the phonon modes. The existence of localized phonon modes with little dispersion at ∼25 THz and ∼45 THz indicates the presence of topotactic hydrogen, which otherwise would be extremely hard to detect. These frequencies correspond to energies of 103 meV and 186 meV, respectively, beyond the range <80 meV measured for La 1−x Sr x NiO 2 in [83].
Lastly, we further study the case representing an incompleted reduction process: LaNiO 2.125 , achieved by intercalating a single O into a 2×2×2 LaNiO 2 supercell [LaNiO 2.125 : Fig. 4(d)]. As the same consequence of employing a supercell in phonon computation, the number of phonon bands is multiplied by a factor of 8 in the frequency region between 0 THz to 20 THz. One obvious difference between undoped LaNiO 2 [ Fig. 4(a)] and LaNiO 2.125 [ Fig. 4(d)] is, that the additional O leads to an unstable phonon mode near q=X(π,0,0) [blue region in Fig. 4(d)]. This phonon mode is formed by an effective vibration of the additional O along the xy plane in the (001) or (110) direction (and symmetrically related directions depending on the exact q-vector) of locally cubic coordinate. Such a mode is related to the structural transition from cubic Pm-3m to a R-3c rhombohedral phase as in bulk LaNiO 3 , with the Ni-O-Ni bond along the z-direction deviating from 180 • . Our simulations for other concentrations of additional O atoms (not shown) also indicate that incomplete oxygen reduction reactions generally result in local instabilities of LaNiO 2+δ with δ>0.

Charge distribution
In this Section, we perform electron density calculations for LaNiO 2 , LaNiO 2 H, LaNiO 2 H 0.125 and LaNiO 2.125 compounds to investigate the bond types resulting from intercalated H and O atoms. Fig. 5 (a) and (b) show the electron density of LaNiO 2 at the NiO-plane and La-plane (light green planes of the top panels). In Fig. 5(a), a strong Ni-O bond is observed while the low electron density between each Ni-O layers reveals a very weak inter-layer coupling, indicating the strong quasi-2D nature of the infinite layer nickelates. In Fig. 5(b), no bonds are formed between the La (Nd) atoms. The A-site rare-earth elements merely play the role of electron donors.  Fig. 5(a-b) and those with H are akin to Fig. 5(c-d). This indicates that the effects induced by topotactic H are indeed very local, i.e., they only affect the the nearest Ni and La atoms.
In Fig. 5 (g) and (h), for LaNiO 2.125 , the additional O increases the local c-lattice (Ni-Ni bond length via the additional O) from the LaNiO 2 value of 3.338 Å to 4.018 Å which is even larger than the DFT-relaxed value of LaNiO 3 : 3.80 Å. This lattice expansion can be clearly seen in Fig. 5(g). The large electron density between Ni and O along the z-direction indicates the strength of this Ni-O bond in the z-direction is comparable with the ones along x/y directions. From Fig. 5(h), we conclude that similar La-O bonds are formed after intercalating additional O atoms, the La-La distance is shrunken by the additional O atom from 3.889 Å (LaNiO 2 ) to 3.746 Å between the La atoms pointing to the additional O. However, from the electron density plot, the La-O bond strength seems not stronger than the La-H bonding in Fig. 5(c,e). This can be explained by the fact that both O-p x and -p y orbitals do not point to orbital lobes of La-d xy , leading to a comparable bond strength as the La-H bond in LaNiO 2 H x .

Conclusion and outlook
Our theoretical study demonstrates that the parent compounds of infinite-layer nickelate superconductors, LaNiO 2 and NdNiO 2 , are energetically unstable with respect to topotactic H in the reductive process from perovskite La(Nd)NiO 3 to La(Nd)NiO 2 . The presence of H, which reshapes the systems from ABO 2 to the hydride-oxide ABO 2 H, triggers a transition from a quasi-2D strongly correlated single-band (d x 2 −y 2 ) metal, to a 2-band (d x 2 −y 2 +d z 2 ) antiferromagnetic 3D Mott insulator. Our predictions [21] have been reproduced by other groups using DFT+U calculations for other similar ABO 2 systems [67,68]. The recent experimental observation [84] of Ni 2+ (3d 8 ) in nickelates indicates the existence of topotactic H, as do NMR experiments [69]. The presence of H and its consequence of a 3D Mott-insulator is unfavorable for the emergence of superconductivity in nickelates. However, it is difficult to detect topotactic H in experiment. Three factors contribute to this difficulty: (1) the small radius of H makes it hard to be detected by commonly employed experimental techniques such as x-ray diffraction and scanning transmission electron microscopy (STEM). (2) As revealed by our phonon calculations, the dynamical stability of La(Nd)NiO 2 does not rely on the concentration of intercalated H atoms. Hence the same infinite-layer structures should be detected by STEM even in the presence of H. (3) As revealed by electron density distributions, the topotactic H does not break the local crystal structure either (e.g. bond length and angle); the H atoms merely affect the most nearby Ni atoms via a Ni-d z 2 -H-1s δ-bond. This is different if we have additional O atoms instead of H: O atoms do not only induce a dynamical instability but also obviously change the local crystal by enlarging the Ni-Ni bond length and angle visibly. Oxygen impurities also lead to unstable phonon modes in LaNiO 2+x and thus a major lattice reconstruction.
The ways to avoid topotactic H revealed by our calculations are: in-plane compressive strains and bivalent cation doping with Sr or Ca. This draws our attention to the recently synthesized (Nd,Sr)NiO 2 films [64] , which has been grown on a (LaAlO 3 ) 0.3 (Sr 2 TaAlO 6 ) 0.7 (LSAT) instead of a SrTiO 3 (STO) substrate, inducing an additional 0.9% compressive strain. These new films were shown to be defect-free and with a considerably larger superconducting dome from 10% to 30% Sr-doping and a higher maximal T c ∼20 K [64], compared to 12.5%-25% Sr-doping and T c ∼15 K for nickelate films grown on STO which show many stacking faults [5,62,63]. The compressive strain induced by replacing the STO substrate (a=3.905 Å) by LSAT (a=3.868 Å) may tune the positive E b to negative, thus contributing to suppressing defects and recovering a single d x 2 −y 2 -band picture.
Besides avoiding topotactic H, compressive strain is also predicted as an effectively way to enhance T c . Previous dynamical vertex approximation calculations [27,66] reveal the key to enhance T c in nickelates is to enhance the bandwidth W and to reduce the ratio of Coulomb interaction U to W. Based on this prediction, we have proposed [27,66] three experimental ways to enhance T c in nickelates: (1) in-plane compressive strain, which can indeed be achieved by using other substrates having a smaller lattice than STO, such as LSAT (3.868 Å), LaAlO 3 (3.80 Å) or SrLaAlO 4 (3.75 Å). The smaller in-plane lattice shrinks the distance between Ni atoms thus increases their orbital overlap, leading to a larger W and a smaller U/W. Recent experimental reports have confirmed the validity of this approach by growing (Nd,Sr)NiO 2 on LSAT [64] and Pr 0.8 Sr 0.2 NiO 2 on LSAT [85]. (2) Applying external pressure on the films plays the same role as in-plane strain for the, essentially 2D, nickelates. This has been experimentally realized in [86]: under 12.1 GPa pressure T c can be enhanced monotonously to 31 K without yet showing a saturation. (3) Replacing 3d Ni by 4d Pd. In infinite-layer palladates such as NdPdO 2 or LaPdO 2 and similar compounds with 2D PdO 2 layers and separating layers between them, the more extended 4d orbitals of Pd are expected to reduce U/W from U/W ∼ 7 for nickelates to U/W ∼ 6 for palladates. Further experimental and theoretical research on the electronic and magnetic structure and the superconductive properties of palladates are thus worth to perform.