MINI REVIEW article
Sec. Condensed Matter Physics
Soft X-Ray Spectroscopy of Low-Valence Nickelates
- 1Max-Planck-Institute for Solid State Research, Stuttgart, Germany
- 2Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Ridge, NY, United States
- 3Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA, United States
Low-valence nickelates—including infinite-layer (IL) and trilayer (TL) compounds—are longstanding candidates for mimicking the high-temperature superconductivity of cuprates. A recent breakthrough in the field came with the discovery of superconductivity in hole-doped IL nickelates. Yet, the degree of similarity between low-valence nickelates and cuprates is the subject of a profound debate for which soft x-ray spectroscopy experiments at the Ni L- and O K-edge provided critical input. In this review, we will discuss the essential elements of the electronic structure of low-valance nickelates revealed by x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS). Furthermore, we will review magnetic excitations observed in the RIXS spectra of IL and TL nickelates, which exhibit characteristics that are partly reminiscent of those of cuprates.
Spectroscopy has proven to be a versatile tool for studying the charge, spin, lattice, and orbital degrees of freedom in quantum materials. Arguably, one of the most fascinating families of quantum materials are cuprate high-temperature superconductors [1–3]. Critical insights into cuprates have been provided by electron, neutron, and photon spectroscopy techniques—including photoemission and electron spectroscopy, scanning tunneling microscopy, optical and Raman spectroscopy, as well as inelastic x-ray and neutron scattering [4–10]. More recently, fresh perspectives on the enigmatic ground states of cuprates opened up especially due to resonant soft x-ray spectroscopy studies. For instance, resonant inelastic x-ray scattering (RIXS)  revealed that damped spin excitations persist even for high hole-doping levels far away from the parent antiferromagnetically (AFM) ordered phase [12, 13]. Furthermore, RIXS allowed to probe the three-dimensional (3D) dispersion of low-energy plasmons [14–16], which arise due to the characteristic quasi-2D layered crystal structure of cuprates. Moreover, resonant elastic x-ray scattering (REXS) and RIXS studies found that different types of static and dynamic charge orders emerge ubiquitously in cuprates [17–21]. Nevertheless, a comprehensive understanding of the most prominent phases in cuprates—including the pseudogap, strange metal phase, and superconductivity—remains elusive.
One approach to gain a deeper understanding of cuprates involves the targeted design of materials that mimic cuprate-typical properties, such as their layered quasi-2D crystal structure, 3d9 electronic configuration, spin S = 1/2 magnetic moments with antiferromagnetic (AFM) coupling, strong ligand-oxygen hybridization, and a lifted degeneracy of the active eg orbitals . In principle, the discovery of superconductivity in a material that emulates at least a subset of these properties could allow to identify the hallmarks of cuprates that are crucial for invoking their exceptional high-temperature superconductivity.
In this context, long-standing candidates are Ni-based compounds, as Ni is a direct neighbor of Cu in the periodic table. In early works, it was speculated that doped RE2NiO4 (RE = rare-earth ion), which is the n = 1 member of the Ruddlesden-Popper (RP) homologous series REn+1NinO3n+1 , could become superconducting , as it is isostructural to the cuprate La2CuO4 and possesses similar charge and spin stripe ordered states . The formal electronic configuration of La2NiO4, however, is 3d8 (Ni2+) with S = 1 [26, 27], providing a possible rationalization for the observed absence of superconductivity. Perovskite nickelates RENiO3 are the n = ∞ member of the RP series with a formal 3d7 (Ni3+) configuration and S = 1/2, although x-ray spectroscopic experiments indicated a 3
A breakthrough in the field came with the discovery of superconductivity in hole-doped nickelates with the IL crystal structure . In more detail, epitaxial thin films of Sr- or Ca-substituted RENiO2 obtained via topotactic oxygen reduction of the perovskite phase show superconductivity below 9–15 K [52–58]. The parent compounds of these nickelates formally exhibit the 3d9 (Ni1+) configuration with S = 1/2, which qualifies them as isostructural and isoelectronic to the parent cuprates. Early neutron powder diffraction studies of parent IL nickelates, however, indicated absence of long-range AFM order [59, 60] and electrical transport measurements of films show weakly metallic behavior . This is in stark contrast to parent cuprates, which are AFM Mott (charge-transfer) insulators . Moreover, whereas first theoretical studies proposed that the electronic and magnetic correlations of IL nickelates and cuprates share close similarities , other theoretical works suggested significant distinctions, including a multiband character of nickelates . Along these lines, insights from experiments can help to resolve the controversy about similarities and differences between IL nickelates and cuprates. In particular, recent x-ray and electron energy-loss spectroscopic studies [64–66] unveiled a reduced Ni-O hybridization, presence of a weakly interacting RE 5d metallic band, and overdamped spin excitations with a bandwidth as large as 200 meV in IL nickelates.
In the following, we will review recent soft x-ray absorption spectroscopy (XAS) and RIXS studies at the O K-edge and Ni L-edge of IL and TL nickelates. We will discuss the essential elements of their distinct electronic structure. Furthermore, the spin excitation spectra of IL and TL nickelates observed with RIXS will be reviewed.
2 Electronic Structure
XAS at the O K-edge measures core-hole excitations from O 1s to unoccupied O 2p states and is also a sensitive probe of the covalent mixing between O 2p and transition-metal d states . In particular the O-K pre-edge fine structure can provide valuable information about Ni-O hybridized states and the associated electronic structure, for instance in the cases of NiO and perovskite RENiO3 [28, 67, 68]. In both materials, Ni 3d-orbitals strongly hybridize with oxygen ligands, giving rise to a pre-peak in the absorption spectra near the O K-edge (Figure 1A). Due to different relative energy scales between the charge-transfer energy Δ and the Coulomb interaction U, according to the Zaanen–Sawatzky–Allen (ZSA) scheme , the former material falls into the regime of charge-transfer insulators, whereas the latter is a negative charge-transfer compound. In contrast, the O K-edge absorption spectra of the IL nickelates LaNiO2 and NdNiO2 lack a prominent pre-edge peak (Figure 1A), suggesting a substantially weaker effective mixing between oxygen and the unoccupied 3d states of the upper Hubbard band (UHB) of the Ni1+ cations . In the case of cuprates, a prominent pre-peak feature is present in O K-edge absorption spectra . This is known to originate from the charge-transfer nature of these materials, with Δ smaller than U, and O 2p states mixed with both the lower Hubbard band (LHB) and the UHB of the Cu 3
FIGURE 1. Electronic structure of nickelates. (A) Upper panel: O K-edge XAS of NiO, LaNiO3 and LaNiO2. Red arrows mark the pre-edge peaks indicative of Ni–O hybridization. Lower panel: O K-edge XAS of NdNiO3 and NdNiO2. Dashed vertical lines indicate features of the SrTiO3 (STO) substrate (solid grey line) in the XAS spectra of NdNiO3 and NdNiO2 due to the film thickness being thinner than that of the La-based films in the upper panel. Spectra are vertically offset for clarity. (B) Ni L3-edge XAS of NiO, LaNiO3, LaNiO2, and NdNiO2. The La M4-line was subtracted from the LaNiO3 and LaNiO2 spectra. (C) Comparison of the O K-edge pre-peak intensities (shaded areas) of a TL nickelate (La4Ni3O8), a hole-doped cuprate (La1.85Sr0.15CuO4), and a hole-doped IL nickelate (Nd0.775Sr0.225NiO2). (D) RIXS intensity map of NdNiO2 measured as a function of incident photon energy across the Ni L3-edge. (E) Representative RIXS spectra of LaNiO3, LaNiO2, and NdNiO2. Black arrows highlight the 0.6 eV features of LaNiO2 and NdNiO2. (F) Calculated RIXS map and XAS (solid black line) of LaNiO2 for a 3d9 + 3d8R ground state, with R denoting a charge-transfer to the La cation. The dashed box highlights the same feature as the box in panel D. Panels adapted from Refs. [49, 64].
Further insights into the electronic structure can be obtained from Ni L-edge XAS, corresponding to 2p-3d multiplet transitions, reflecting the valence configuration of the Ni ions. In the cases of NiO and perovskite RENiO3 (2p63d8–2p53d9 and 2p63d8Ln–2p53d9Ln transitions, respectively) distinct multi-peak structures emerge across the L3-edge (Figure 1B) [28, 64, 73]. Conversely, the line shapes of the IL nickelates LaNiO2 and especially of NdNiO2 (Figure 1B) resemble rather the single-peak XAS spectrum of IL cuprates with only one possible final XAS state (2p63d9-2p53d10 transition). In more detail, the L3-edge XAS of LaNiO2 and NdNiO2 is dominated by a main peak A (Figure 1B), while LaNiO2 shows an additional minor low energy shoulder A′ at slightly lower energies.1 Figure 1D displays the RIXS intensity map of NdNiO2 as a function of the incident photon energy and Figure 1E shows RIXS spectra for selected incident energies. Importantly, the RIXS spectra of LaNiO2 and NdNiO2 exhibit a distinct feature around 0.6 eV energy loss (Figures 1D,E), which is visible in the RIXS spectra with incident energies coinciding with the XAS peak A (A’). Furthermore, this feature emerges exclusively in the IL compounds and not the perovskite nickelate LaNiO3 (Figure 1E). Using exact diagonalization, the general XAS and RIXS features can be reproduced (Figure 1F) and the 0.6 eV feature can be assigned to the hybridization between the Ni 3
3 Magnetic Correlations
3.1 Magnetic Excitations in Infinite-Layer Nickelates
Despite of the involvement of rare-earth 5d states, the fact that the electronic structures of the Ni 3d states resemble a cuprate-like 3d9 system raises a curious question: whether the Mott-physics, a key ingredient in the cuprate phenomenology , also play an important role in sculpting the electronic structures in IL nickelates. Since a strong AFM interaction is a consequence of Mott physics due to strong onsite Coulomb interaction, information about the magnetic structures in IL nickelate is imperative to gain further insight into this issue. Early investigations of bulk polycrystalline LaNiO2 and NdNiO2 found no evidence of AFM order [59, 60], which appeared to suggest a significantly weaker magnetic interaction than in cuprates. On a different ground, theories have been debating the energy scale of magnetic interactions in the IL nickelates. Some theories predict a small AFM interaction (∼ an order of magnitude smaller than that of cuprates) because of the larger charge transfer energy Δ [91–94]. Conversely, other theories argue that the magnetic interactions are comparable to those in cuprates [74, 92, 95]. Experimental information about magnetic excitations is crucial to clarify this important issue.
Recently, magnetic excitations in Nd1−xSrxNiO2 have been revealed using RIXS at the Ni L3-edge . As shown in Figure 2A, a branch of dispersive magnetic excitations has been observed in NdNiO2, whose energy-momentum dispersion resembles the spin wave excitations of AFM coupled spins in a square lattice. Importantly, the bandwidth of the magnetic excitations is approximately 200 meV, corresponding to a nearest neighbor spin interaction J1 ∼ 65 meV. This is about half of the J1 in cuprate superconductors and similar to that in the TL nickelates , but is notably higher than in the stripe-ordered single-layer (n = 1) nickelates [25–27], perovskite nickelates (n = ∞) , and cubic NiO [97, 98]. Therefore, the observation of the high energy scale of J1 in IL nickelates confirms the presence of a strong onsite Coulomb interaction, indicating that the strong correlation effect associated with the Mott-physics is likely also at play in the nickelate superconductors. Notably, distinct from the sharp magnetic modes observed in undoped cuprates, the magnetic excitations in the undoped parent compound of IL nickelates are damped, which is likely due to the coupling to the metallic Nd 5d states.
FIGURE 2. Magnetic excitations in nickelates. (A) Magnetic excitations in NdNiO2. Solid and open symbols are mode energy and the damping parameters, respectively, extracted from fitting RIXS spectra to a damped harmonic oscillators (DHO). The dashed curve is the linear spin wave fit to the extracted energy-momentum dispersion. The horizontal dashed line represents the energy resolution of the RIXS measurement. (B) Doping dependence of the spectral weight (upper) and mode energy (lower) deduced from the DHO fitting. (C) The structural unit cell of La4Ni3O8 with Ni/O/La atoms shown as purple/gray/green spheres. (D) The electronically active TL nickel-oxide plane structures in La4Ni3O8, showing the diagonal stripe-ordered state . Ni sites with additional hole character are in purple, whereas spinful Ni up (down) sites are depicted in red (blue). (E) Measured magnetic excitations in La4Ni3O8. Black squares are the extracted energies of the magnetic excitations. The dark gray line is the fit to the experimental dispersion, which is composed of three modes plotted in blue, orange, and green, respectively. The doubling of the modes from
Upon hole doping, the magnetic excitations become less dispersive as a function of momentum and significantly damped. By fitting the spectrum to a damped harmonic oscillator function, it is found that mode energies soften accompanied by slightly reduced spectral weight (Figure 2B). The observed doping dependence is consistent with spin dilution in a Mott insulator. This is in fact different from those observed in cuprates, in which the mode energy and spectral weight do not decrease with increasing doping . The doping dependence of the magnetic excitations in cuprates has been attributed to the longer-range charge dynamics emergent with increasing hole doping, for example, the three site terms in a Hubbard model [100, 101]. Such dynamics appear to be less prominent in the doped IL nickelates, likely due to the larger charge transfer energy Δ and the presence of the rare-earth 5d metallic state, calling for further investigation.
We note the next nearest-neighbour exchange interaction J2 extracted from the magnetic excitations dispersion possesses an opposite sign to the nearest neighbor J1, which should favor the formation of AFM ordering at (0.5, 0.5). Unfortunately, RIXS at the Ni L3-edge cannot reach (0.5, 0.5) due to insufficient momentum transfer of the photons, preventing a direct scrutinization on the putative AFM order. Notably, recent susceptibility measurement on bulk powder samples indicated spin glass behaviors, but signatures of an AFM phase transition were still not observed. Thus, it would be interesting to investigating why IL nickelates are a failed AFM. However, one should be cautious about the difference between bulk and thin film samples, as well as the disorders in both types of materials, which were significantly reduced over time along with the optimization of material synthesis protocols.
Interestingly, the IL nickelates add one more case in which the magnetic correlations are in proximity to superconductivity in the phase diagram, similarly to a number of unconventional superconductors, such as cuprates, iron-based superconductors, and heavy fermion superconductors . It might be tempting to attribute magnetic fluctuations as a candidate mechanism of superconductivity. However, among these superconducting compounds, including the nickelate superconductors, there appears no clear correlation between the energy scale of the magnetic excitation and the superconducting transition temperature, casting doubt on this notion. In any case, the relationship between magnetic fluctuations and the superconductivity remains an important issue in nickelate superconductors.
3.2 Magnetic Excitations in Trilayer Nickelates
In parallel with the measurement of magnetic excitations in the IL material Nd1−xSrxNiO2, magnetic excitations were also measured in the TL materials La4Ni3O8 and Pr4Ni3O8 . The crystal structure of La4Ni3O8 is shown in Figure 2C. This material has some features that indicate that it might be especially promising as a cuprate analog. The rock salt RE-O layers present in its structure make it more two-dimensional than IL compounds and the rare-earth orbitals that are populated in IL are predicted to have a less significant role in TL systems [48, 103, 104]. As explained in the introduction, this compound is naturally self-doped and has a nominal hole concentration of 1/3. A disadvantage of the La4Ni3O8 series is that they have, to date, proven difficult to chemically dope. Like cuprates, and some other complex oxides, La4Ni3O8 has charge and spin order [47, 105]. This structure, illustrated in Figure 2D, features diagonal rows of Ni sites with enhanced hole character and neighboring diagonal stripes of up and down spin-ordered sites with reduced hole character. The overall magnetic dispersion, measured with Ni L3 edge RIXS, is plotted in Figure 2E and features a bandwidth of ∼ 80 meV with a downturn near
The leading value of J1 = 69(4) meV in La4Ni3O8 is strikingly close the 65(1) meV value obtained for NdNiO2. It should be noted that this similar value arises from a much smaller magnetic bandwidth, as within the stripe-ordered state, each Ni will have only two magnetic neighbors. An approximate extrapolation of the magnetic dispersion of Nd1−xSrxNiO2 to a doping of x ∼ 1/3 implies that it would have a bandwidth comparable to La4Ni3O8 at this doping; yet, whether stripe order or fluctuations exist in the IL nickelates, like those found in the TL nickelates, remains an important open question. Overall, this suggests that the local correlated physics in these reduced RP cousins is very similar provided they are compared at the same effective doping, although their precise low-energy ground states might be more different.
In summary, soft x-ray spectroscopic studies have provided valuable insights into the physics of RP-phase and RP-derived nickelates. Nevertheless, for low-valence nickelates there is still limited consensus on the essential ingredients of their electronic structure. Along these lines, we anticipate that advances in sample synthesis and the application of complementary experimental techniques, including ARPES and quantum oscillation measurements, will be helpful. Moreover, the role of disorder and capping layers, as well as the apparent differences between film and bulk samples need further clarification. These insights could point the way towards improved low-valance nickelate superconductors, including multilayer systems . Finally, a pertinent question is whether suitable sample preparation allows to realize other cuprate-typical ground states in nickelates, such as antiferromagnetism, pseudogap, as well as nematic, charge, and spin orders.
The manuscript was written by MH, MD, and W-SL.
Work at SLAC National Lab was supported by United States Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. Work at Brookhaven National Laboratory was supported by the United States Department of Energy, Office of Science, Office of Basic Energy Sciences. The use of resources at the SIX beamline of the National Synchrotron Light Source II, a United States Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704, is acknowledged. The Max Planck Society is acknowledged for funding of the open access fee.
Conflict of Interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
The authors thank K. Fürsich for useful discussions and comments.
1The A′ feature in XAS is only visible in LaNiO2 films without a SrTiO3 (STO) capping layer. Based on our recent measurements on LaNiO2 films with a STO capping layer, the A′ feature, which arises from the resonance of the ∼ 0.6 eV feature in the RIXS map, coincides with the main XAS peak and becomes invisible. In other words, the XAS of La- and Nd-based infinite layer nickelates (with a STO capping layer) are essentially the same
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Keywords: infinite-layer nickelates, trilayer nickelates, low-valence nickelates, spectroscopy, RIXS, XAS, electronic structure, magnetic correlations
Citation: Hepting M, Dean MPM and Lee W-S (2021) Soft X-Ray Spectroscopy of Low-Valence Nickelates. Front. Phys. 9:808683. doi: 10.3389/fphy.2021.808683
Received: 03 November 2021; Accepted: 30 November 2021;
Published: 22 December 2021.
Edited by:Veerpal Singh Awana, National Physical Laboratory (CSIR), India
Reviewed by:Atsushi Fujimori, The University of Tokyo, Japan
Kenji Ishii, National Institutes for Quantum Science and Technology, Japan
Copyright © 2021 Hepting, Dean and Lee. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Matthias Hepting, firstname.lastname@example.org