Electronic coupling in square planar La₄Ni₃O₈

The discovery of superconductivity in the infinite-layer thin-film nickelate, Nd_0.8Sr_0.2NiO₂, has motivated the study of compounds with a similar crystal and electronic structure [1]. For instance, single crystal La₄Ni₃O₈ (La-438) has the same square planar oxygen coordination as the new superconducting nickelate, as well as the same preferential orbital occupancy at low temperatures [2–4]. Thus, studies of La-438 can shed light on the local Ni electronic environment that contributes to superconductivity in Nd_0.8Sr_0.2NiO₂.

A striking feature of the Nd_0.8Sr_0.2NiO₂-related square planar compounds LaNiO₂ is the unusual behavior of the dd-like excitations observed in the soft resonant inelastic x-ray scattering (RIXS) spectra [1]. These excitations disperse in energy as the incident energy is changed, unlike true dd excitations, suggesting that the Ni 3d states are delocalized and hybridized with the La 5d orbitals [1]. This unusual energy dispersion is not observed in La-438, meaning that the dd excitation is local, and not extended.

La-438 exhibits a phase transition at 105 K which involves a number of physical properties, including magnetism, resistivity, lattice constants and heat capacity. Below the transition temperature La-438 is an insulating antiferromagnet with charge and spin stripes, whereas above the transition it is a non-magnetic semiconductor [2, 5, 6]. Neutron and x-ray powder diffraction measurements do not show substantial atomic displacements coinciding with this transition [2, 5]. The phase transition at 105 K also coincides with a large change in the heat capacity, indicating a substantial change in the entropy with the transition [2, 5].

There is evidence of unusual electronic coupling in La-438, revealed by the emergence of charge order stripes as observed with x-ray diffraction. Surprisingly, the charge stripes are stacked in phase within the trilayer [2]. Stacking of charge is counterintuitive within a simple electrostatic model because high charge Ni should mutually repel and not be ordered in close proximity. Stacked stripes observed in other compounds have some additional stabilization interaction. For example, charge stacking in half-doped manganites exhibiting ferromagnetic order is stabilized by a magnetic double-exchange interaction, which is more important than the inter-site Coulomb repulsion in these materials [7]. DFT calculations suggest lattice distortions stabilize the charge stacking in La-438 [8].

Here, we report Ni K-edge x-ray absorption scattering (XAS) and RIXS measurements above and below the 105 K transition in La-438. Measurements reveal the energy scale differences between different Ni d and p states and suggest a strong Coulomb interaction between the 3d and 4p_π valence electrons [9]. The closing of the insulating gap is observed as a function of temperature.

Single crystal La-438 (tetragonal with space group I4/mmm with a = 3.9633 Å, c = 26.0373 Å) were prepared using the method described in reference [2]. La-438 consists of three layers of square planar nickel ions separated by La–O layers. The Ni ions are formally assigned as Ni¹⁺ and Ni²⁺ in a 2:1 ratio, corresponding to a formal valence of 3d^+8.66. The two Ni sites have slightly different Ni–O bond lengths. The structure is presented pictorially in figure 1(a).

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All measurements were performed at sector 27 at the Advanced Photon Source at Argonne National Laboratory. The x-ray energy was tuned to the vicinity of the Ni K-edge, 8.34 keV. The incident photons were monochromatized by a four-bounce Si(400) monochromator. For RIXS measurements, a spherical, diced Si(117) analyzer with 2 m-radius was used to select the final photon energy. In order to minimize the elastic background intensity, measurements were carried out in a horizontal scattering geometry for which the scattering angle 2θ was close to 90^o. An overall energy resolution of about 225 meV (FWHM) was obtained.

The Ni K XAS spectra of La-438 are shown in figure 1(b). The spectra show a clear dependence of the XAS signal on the orientation of the incident beam polarization relative to the crystal axis, as is observed in other nickelates [10, 11]. The spectrum plotted with a solid line was measured with the incident polarization perpendicular to the crystal c-axis, and is thus sensitive to the Ni p_σ orbitals. The spectrum plotted with the dashed line was measured with the incident polarization parallel to the c-axis and the main peak corresponds to the Ni 1s to 4p_π transition. The shift of 3 eV between the peaks is indicative of the crystal field splitting in the Ni p states between the 4p_σ and 4p_π orbitals, due to the square-planar coordination of the Ni atoms. This splitting is similar to two octahedrally coordinated charge-stripe compounds that have non-stacked striped phases, La_5/3Sr_1/3NiO₄ (1.24 eV) [10] and LaSrCuO₄ (4.3 eV) [11].

RIXS spectra were measured at the Ni K edge. Photons incident on the sample promote a 1s core electron to an empty 4p state above the Fermi level. This electron later decays to fill the core hole. In the absence of any further interaction, no inelastic x-ray scattering would be observed. Typically, however, the strong potential exerted by the 1s core hole scatters the 3d electrons, creating an excitation that persists after the 4p → 1s transition. The photoexcited 4p electron can also interact with 3d electrons, but this interaction is usually assumed to be negligible, in what is called the 4p-as-spectator approximation [12, 13].

Figure 1(c) shows RIXS spectra measured at incident energies corresponding to the 1s to 4p_π XAS transition, the 1s to 4p_σ XAS transition and the pre-edge energy, corresponding to 1s to 3d transition. The spectra were measured at the (−4/3 –1/3 23) position, the reciprocal lattice position associated with stripe order. The sample temperature is 20 K. The incident polarization had both in-plane and out-of-plane components, with the angle of the incident beam to the sample surface at 66°. When the incident energy is tuned to the XAS peak associated with the p_π orbitals, the spectrum shows an inelastic excitation at 1.4 eV. By comparison with calculations by Botana et al [8], this peak is identified as a dd transition between ${d}_{{z}^{2}}$ and ${d}_{{x}^{2}-{y}^{2}}$. This peak energy does not disperse with incident energy, as seen in figure 2(a), meaning that it is a local dd excitation, unlike the similar excitations observed in LaNiO₂ [1] and Nd_0.8Sr_0.2NiO₂ [1]. The energy of the excitation is largely in agreement with Botana et al [8], lending support to their assertion that structural distortions stabilize the low temperature stripe configuration. No other electronic excitation peaks were observed in any spectra. All spectra show an insulating gap.

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dd excitations are usually observed at the pre-edge as a result of quadripolar transitions. In the current measurement, however, the dd excitation is not intense enough to be observed at the pre-edge but appears at the main edge, where it is nominally forbidden. The absence of intensity at the pre-edge can be explained by the relatively small pre-edge XAS intensity at this geometry, as can be seen in figure 1(b).

The presence of dd intensity at the main edge is the result of the Coulomb interaction between the 3d and 4p valence electrons [9]. Since the incident energy at which the excitation has maximum intensity corresponds to the 1s to 4p_π transition a strong interaction between the occupied 3d and excited 4p_π Ni electronic states is implied. We believe that this measurement indicates that a photoexcited Ni 4p_π electron is a necessary precondition to observing the dd excitation at the main edge, a possibility predicted in [9].

The intensity of the dd excitation peak as a function of incident polarization is shown in the lower panel of figure 2(c). The geometry of the experiment is defined in figure 2(b). The spectra are fit by a Gaussian peak on top of a Fermi function background. The fitting parameters are the intensity, width and location of the Gaussian peak, the Fermi level intensity and a constant background. The intensity reaches a maximum when the angle of the incident beam relative to the sample surface, α, is low, meaning that the polarization is mostly out-of-plane and closely aligned with the c axis of the sample, as indicated in figure 2(a). This confirms that the dd excitation at this energy is a result of the Ni 3d–4p_π Coulomb interaction.

No dd excitation is observed at the incident energy corresponding to 4p_σ, despite sensitivity to 3d–4p_σ interactions in this geometry as seen in figure 1(b). This implies that the Ni 3d–Ni 4p_σ Coulomb interaction is small or non-existent.

In figure 3(a), RIXS spectra as a function of temperature are shown. Two notable features can be perceived. First, the low energy insulating gap closes suddenly between 75 K and 125 K. Second, the dd excitation does not change in intensity as a function of temperature. The measurable collapse of the insulating gap at the Ni K-edge, shown in figure 3(b) shows that nickel electrons contribute to the conduction.

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In conclusion, a dd excitation is observed in La-438. The incident energy dependence suggests a strong Coulomb interaction between 3d and 4p_π Ni electrons and limited interaction between 3d and 4p_σ Ni electrons. Because of the similar local Ni structure, Ni electrons in Nd_0.8Sr_0.2NiO₂ may also have a strong Coulomb interaction between electrons with 3d and 4p_π character. An insulating gap in La-438 is observed at low temperatures and vanishes above the semiconductor–insulator transition temperature.

This research used resources of the Advanced Photon Source, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. Work in the Materials Science Division of Argonne National Laboratory (crystal growth and characterization), was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. The work at Shandong University was supported by the Qilu Young Scholar Program of Shandong University, and the Taishan Scholar Program of Shandong Province. MHU acknowledges discussions with Jungho Kim, Michael Norman and Thomas Gog.