Electron doped layered nickelates: spanning the phase diagram of the cuprates

TL;DR

This study uses ab initio calculations to show that Ce-doped layered nickelates mimic the electronic structure of cuprates' antiferromagnetic insulating phase, indicating potential for superconductivity at specific doping levels.

Contribution

It demonstrates the stability and electronic similarity of Ce-doped nickelates to cuprates, proposing a new pathway to explore superconductivity in nickel-based oxides.

Findings

Ce-doped Pr4Ni3O8 has cuprate-like electronic structure.

Substantial Ce-doping is thermodynamically stable.

Intermediate doping levels near 1/8 may host superconductivity.

Abstract

Pr$_4$Ni$_3$O$_8$ is an overdoped analog of hole-doped layered cuprates. Here we show via ab initio calculations that Ce-doped Pr$_4$Ni$_3$O$_8$ (Pr$_3$CeNi$_3$O$_8$) has the same electronic structure as the antiferromagnetic insulating phase of parent cuprates. We find that substantial Ce-doping should be thermodynamically stable and that other 4+ cations would yield a similar antiferromagnetic insulating state, arguing this configuration is robust for layered nickelates of low enough valence. The analogies with cuprates at different $d$ fillings suggest that intermediate Ce-doping concentrations near 1/8 should be an appropriate place to search for superconductivity in these low-valence Ni oxides.

Tables

Table 1. Table 1: Nearest neighbor Pr-O, Ce-O and Ni-O distances for Pr 3 CeNi 3 O 8 in Å  for Ce substitution on the Pr1 and Pr2 sites. The Pr/Ce environment is square antiprismatic with eight oxygen ions as nearest neighbors. The R ion is positioned asymmetrically inside the polyhedra. For this reason, two different R-O distances are listed in the table. In undoped Pr438 the Pr-O distances are (in Å) 2.48, 2.59 for Pr1 (IL), and 2.32, 2.74 for Pr2 (F). The Ni is in a square planar environment of oxygens. For undoped Pr438 the Ni-O distance is 1.97 Å.

	Pr3CeNi3O8(IL)		Pr3CeNi3O8(F)
$Ce-IL$	2.39, 2.54	$Ce-F$	2.30, 2.63
$Pr-IL$	2.46, 2.59	$Pr-F$	2.40, 2.63
$Pr-F$	2.33, 2.74	$Pr-IL$	2.53 2.59
$Pr-F$	2.32, 2.79	$Pr-IL$	2.55, 2.58
$Ni$	1.96	$Ni$	1.96

Full text

Cuprate-like electronic structures have been pursued in other oxides since soon after high temperature superconductors were discovered.Norman (2016); Pickett (1989); Keimer et al. (2015); Dagotto (1994) Cuprates are layered materials with an underlying CuO2 square lattice. The parent compounds (Cu2+: d9, S= 1/2) have d${}_{x^{2}-y^{2}}$ as the active orbitals, with strong antiferromagnetic correlations, as well as a substantial hybridization of Cu-$d$ and O-$p$ states. Upon doping the CuO2 planes away from a stoichiometric Cu2+ oxidation state, the antiferromagnetic state is suppressed, then superconductivity appears, and at higher dopings a Fermi liquid phase arises.Pickett (1989) A schematic phase diagram with respect to filling of the $d$ levels for hole doping is shown in Fig. 1.

Given the proximity of Ni and Cu in the periodic table, an interesting conjecture is whether these phenomena could also occur in nickelates, since if so, this could tell us a lot about the nature of high temperature superconductivity. LaNiO3-based heterostructures Chaloupka and Khaliullin (2008); Middey et al. (2016) and doped single layer nickelates (La2-xSrxNiO4) Kajimoto et al. (2003); Zhong et al. (2017) have been intensively studied, but the challenge is finding a nickelate that has a similar electron count (Ni1+ and Cu2+ being isoelectronic) with Ni in a square planar environment.

In this context, the recently synthesized low valence layered nickelates (R4Ni3O8, R438, with R= La or Pr) with an average Ni valence of +1.33, are promising candidates to investigate.Botana et al. (2016); Zhang et al. (2016); Pardo and Pickett (2010); Poltavets et al. (2010); Lacorre (1992); Aproberts-Warren et al. (2011); Sarkar et al. (2011); Guo et al. (2017) Particularly, Pr438, a 1/3 self hole doped (relative to d9) line compound, stands among the closest bulk analogs to high-Tc cuprates. It shows metallic behavior and a large orbital polarization with holes in the planar d${}_{x^{2}-y^{2}}$ states, as well as a high degree of O-$p$–Ni-$d$ hybridization.Zhang et al. (2017) Fig. 1 illustrates where metallic Pr438 lies within the cuprate phase diagram, sitting in the overdoped Fermi liquid region.

Electron doping this new phase is an obvious strategy to explore the analogy with cuprates. If we consider as a starting point that the physics of high-Tc superconductivity in cuprates is brought about by doping a 2D Mott insulator with strong antiferromagnetic correlations, a natural question is whether this type of “parent phase” arises at $d^{9}$ filling for electron-doped Pr438.Lee et al. (2006) As pointed out almost 20 years ago by Anisimov et al.,Anisimov et al. (1999) “only if the Ni ions are forced into a planar coordination with the O ions can a S=1/2 magnetic insulator be realized with the difficult Ni1+ oxidation state”. Here, we show using DFT-based calculations that doping Pr4Ni3O8 with a 4+ ion allows going from a Fermi liquid phase at a nominal d8.67 filling to a parent antiferromagnetic insulating phase at d9 filling, effectively spanning the hole-doped cuprate phase diagram (see Fig.1).

Our electronic structure calculations were performed within density functional theory using the all-electron, full potential code wien2k based on the augmented plane wave plus local orbitals (APW+lo) basis set.Blaha et al. (2001); Sjöstedt et al. (2000) For the structural relaxations we have used the Perdew-Burke-Ernzerhof version of the generalized gradient approximation (GGA).Perdew et al. (1996) Volume and $c/a$ optimizations, as well as a full relaxation of all the internal atomic coordinates, were carried out. To deal with strong correlation effects, we apply the LDA+$U$ scheme that incorporates an on-site Coulomb repulsion $U$ and Hund’s rule coupling strength $J_{H}$.Lichtenstein et al. (1995) We use typical values: $U$= 5 eV for Ni-$3d$, $U$= 8 eV for Pr-$4f$, and $U$= 5 eV for Ce-$4f$. $J_{H}$ has been set to 0.7 eV for Ni-$d$ and 1 eV for Pr and Ce-$f$. Experience with the cuprates and other transition metal oxides shows LDA+$U$ to be a reliable method to predict the electronic structure. For example, the antiferromagnetic insulating state of the stoichiometric cuprates is correctly reproduced.Anisimov et al. (1997, 2004); Blaha et al. (2005)

Pr438 crystallizes in a tetragonal unit cell,Zhang et al. (2017) with space group I4/mmm (no. 139) and lattice parameters a= 3.9347 Å, c= 25.4850 Å. The structure, pictured in Fig. 2, consists of three NiO2 infinite-layer (IL) planes separated by layers of Pr ions. On either side of this trilayer lies a fluorite (F) Pr-O2-Pr block. With an average Ni valence of ${1.33+}$, Pr438 is isoelectronic with (hole) overdoped cuprates involving a mixture of Ni1+ and Ni2+ ions. The electronic structure of Pr438 is found to be metallic, consistent with a 2/3-filled Ni-d${}_{x^{2}-y^{2}}$ band crossing the Fermi level hybridized with O-$p$ states as described in Ref. Zhang et al., 2017.

By substituting trivalent Pr with a tetravalent ion in Pr438, the electron count on the Ni-O layer can be changed, moving the material towards the left of the phase diagram shown in Fig. 1. In principle, the ionic count required for reaching the parent insulating state (with Ni1+: $d^{9}$) would need 25% substitution on the Pr site with a 4+ cation (Pr3RNi3O8, R= Ce, Th). However, the low oxidation state Ni1+ is hard to stabilize. The bulk synthesis of the Ni1+ infinite-layer compound LaNiO2 is difficult and because of these materials issues, it is unclear whether an insulating state is achieved.Crespin et al. (1983); Hayward et al. (1999); Lee and Pickett (2004) LDA+$U$ calculations give a stable solution with antiferromagnetic ordering of S=1/2 ions,Anisimov et al. (1999) but experimentally there is no evidence for long range order. In principle, the on-site energy difference between the $p$ and $d$ levels is smaller for Cu2+ than for Ni1+, favoring larger hybridizations in the former. However, we will see that substantial oxygen hybridization can occur for the layered nickelates studied here.

In Pr438 there are two different Pr sites: Pr1 within the NiO2 trilayer and Pr2 within the fluorite blocks that separate NiO2 trilayers (see Fig. 2). Both types of substitutions were tried, giving rise to a very similar outcome for the electronic structure (which will be described in detail below). Concerning the most appropriate 4+ dopant atom, Ce is the most obvious choice given its proximity to Pr in the periodic table and because Ce-doping has been realized in T*′-cuprates giving rise to electron-doped phases. For instance, T′-Pr2-xCexCuO4 shows superconductivity with an optimum doping level x= 0.135 and Tc*= 27 K.Tokura et al. (1989); Scalapino (2012); Krockenberger et al. (2008) In T*′*-Nd2CuO4 superconductivity develops by doping with both Ce and Th.Takagi et al. (1989); Naito et al. (2016)

To test the possibility of in-plane checkerboard magnetic (AFM) ordering in Pr3CeNi3O8, a \sqrt{2}$$a $\times$ \sqrt{2}$$a $\times$ $c$ cell was used. After the substitution of Pr by Ce in a 3:1 ratio, the optimized volume results in a reduction with respect to that of Pr438 of 1 to 2 % (see Fig. 2) – the ionic radius of Ce4+ in an 8-fold coordination is 0.97 Å vs the ionic radius of Pr3+ of 1.13 Å, so a decrease in lattice constants can be anticipated.Shannon and Prewitt (1969) Small distortions of the Ni-O and Pr/Ce-O distances take place after structural relaxation as shown in Table 1. Ce-substitution within the F block is energetically favorable by 96 meV/unit cell with respect to substitution in the IL block. The standard enthalpy change $\Delta$H can be obtained at T= 0 from the calculated total energies: E(Pr3CeNi3O8)+ $\frac{3}{4}$E(O2)- $\frac{3}{2}$E(Pr2O3)- E(CeO2)- 3E(NiO) giving a value of -814 $kJ/mol$.

Within GGA, the band structure is metallic with an in-plane AFM coupling within the NiO2 planes. Application of a Coulomb $U$ to the Ni-$d$, Pr-$f$ and Ce-$f$ states is enough to open a gap of $\sim$0.6 eV for doping in the IL block and $\sim$0.3 eV in the F block (see Fig. 3). The gap is smaller for substitution in the F block due to the unoccupied Ni-$d$ states from the outer planes being closer in energy to the Ce-$f$ bands, leading to a level repulsion effect (see Fig. 4). The magnetic moments inside the Ni muffin-tin sphere are approximately $\pm$0.9 $\mu_{B}$ with checkerboard (AFM) ordering within the NiO2 planes as well as between planes. All in all, our LDA+$U$ band structure, shown in Fig. 3, exhibits a correlated S=1/2 AFM insulator analog of the parent cuprate materials. Holes would hence go into the Ni-$d$ band of $x^{2}-y^{2}$ character that is highly hybridized with O-$p$ states (see below). Calculations confirm that this state comprised of AFM-ordered Ni layers is more stable than a ferromagnetic one by a sizable 0.2 eV/Ni, implying a superexchange interaction comparable to that of cuprates.

In general, Ce can be trivalent as well as tetravalent. Using the same structural parameters and $U$ values described above, as well as a checkerboard AFM configuration within the NiO2 planes, a solution where Ce is 3+ was obtained. However, this state turns out be energetically unfavorable by 0.34 eV/unit cell with respect to that where Ce is tetravalent. The derived electronic structure is metallic with a magnetic moment of 1 $\mu_{B}$ developing on Ce. An in-trimer charge ordered solution results with AFM ordering in the NiO2 planes: Ni1+ in the outer layers, and Ni2+ (high spin) in the inner layers. Wu (2013)

As can be observed in Fig. 4, for Ce4+ substitution, the top of the valence band consists of a mixture of $d_{x^{2}-y^{2}}$ and $d_{z^{2}}$ states, whereas the Ni-$d$ unoccupied bands are $x^{2}-y^{2}$-only in character. At around 1 eV above the Fermi level lie the Ce-$f$ states whereas Pr-$f$ states appear mostly above $\sim$ 4 eV. It is clear from the density of states (DOS) that both inner and outer Ni1+: $d^{9}$ (S=1/2) ions have a single hole in the minority-spin $d_{x^{2}-y^{2}}$-like band. Hybridization between the Ni-$d$ and O-$p$ states is clear in the DOS, being most noticeable for the planar O ions as a result of the strong pd$$\sigma bond. The lobes of the $x^{2}-y^{2}$ orbital point directly to the $p$ orbital of the neighboring oxygen, forming a strong covalent bond with a large hopping integral $t_{pd}$= 0.3 eV. The strong directionality of the bond can be observed for Pr3CeNi3O8 in Fig. 5. Let us recall that bond covalency sets the unusually high energy scale for the exchange interaction in cuprates. Small moments are induced on the oxygen ions as a consequence of hybridization along with low-site symmetry: $\mu_{O1}$= -0.05 $\mu_{B}$ (inner NiO2 plane), $\mu_{O2}$=-0.07 $\mu_{B}$ (outer NiO2 plane), $\mu_{O3}$= -0.02 $\mu_{B}$ (F block). Importantly, the Ce cation bonds with neighboring O ions (as implied in the DOS, clearly reflecting the hybridization between O-$p$ and Ce-$f$ states). Previous results show that Ce substitution in R2CuO4 (R= Pr, Nd) enhances the phase stability given that tetravalent Ce has a firmer grip on surrounding O2- ions by stronger electrostatic force than trivalent rare earth ions.Naito et al. (2016); Idemoto et al. (1992); Kanai et al. (1997)

To check the robustness of the obtained electronic structure, Th substitution on the Pr site was also tried as well as smaller 4+ cations like Zr and Te. For Th substitution, the same type of calculations give rise to a smaller volume reduction of only 0.5-1% (the ionic radius of tetravalent Th4+ in an 8-fold environment is 1.06 Å, larger than that for Ce4+).Shannon and Prewitt (1969) The electronic structure is very similar except for the $f$-states missing at the tail of the unoccupied Ni-$d$ states (see Fig. 3) arguing that the derived insulating AFM state is robust in Pr3RNi3O8. Zr and Te are smaller ions Shannon and Prewitt (1969) so substitution with these gives rise to bigger distortions in the structure. However, the main features of the electronic structure obtained for Th doping remain for both Zr and Te doping.

If the likelihood of promoting superconductivity in these layered nickelates is to be analyzed, the similarities with cuprates are important to characterize. The state we have obtained in Pr3CeNi3O8 (for a Ni1+ oxidation state) has insulating, AFM planar order in common with the cuprates, as well as obvious similarities in structure with common MO2 (M= Ni, Cu) square lattice planes. Even though we are dealing with hypothetical structures, our calculations show that substantial Ce-doping should be thermodynamically stable and that several other 4+ cations would yield a very similar antiferromagnetic insulating solution, suggesting this configuration is robust in layered nickelates of low enough valence. Intermediate Ce-doping concentrations near 1/8 should be the appropriate place to search for superconductivity in these low-valence Ni oxides. Our results show that planar nickelates directly analogous to the high-Tc superconducting cuprates are a realistic possibility, especially given their similar superexchange interaction.

The authors acknowledge fruitful discussions with Peter Blaha, Warren Pickett and John Mitchell. ASB and MRN were supported by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the US DOE, Office of Science, under Award No. DE-AC0298CH1088. VP thanks MINECO of Spain for financial support through project No. MAT2016-80762-R. We acknowledge the computing resources provided on Blues, the high-performance computing clusters operated by the Laboratory Computing Resource Center at Argonne National Laboratory.