pith. sign in

arxiv: 2511.02448 · v4 · pith:KOQTOCVJnew · submitted 2025-11-04 · ❄️ cond-mat.supr-con · cond-mat.str-el

Spin and orbital excitations in undoped infinite layers: a comparison between superconducting PrNiO2 and insulating CaCuO2

Pith reviewed 2026-05-21 19:49 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el
keywords PrNiO2CaCuO2RIXSinfinite-layer nickelatescupratesspin excitationsorbital excitationssuperexchange
0
0 comments X

The pith

Infinite-layer nickelates and cuprates share most spin and orbital properties despite different charge-transfer energies.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper compares momentum- and polarization-resolved RIXS measurements on undoped superconducting PrNiO2 with the insulating infinite-layer cuprate CaCuO2. In-plane magnetic exchange integrals turn out smaller in the nickelate while out-of-plane values remain similar, pointing to three-dimensional antiferromagnetic order in both compounds. Orbital excitations largely match a single-ion model, except that the Ni-dxy peak lies at lower energy and disperses in the opposite direction to its Cu counterpart. The authors trace the reversed dispersion to orbital superexchange coupling between nearest-neighbor sites that drives orbiton propagation. Overall, the results indicate that the two material families share the bulk of their spin and orbital characteristics even though their charge-transfer energies differ substantially.

Core claim

Undoped infinite-layer PrNiO2 and CaCuO2 exhibit comparable in-plane and out-of-plane magnetic exchange integrals that support three-dimensional antiferromagnetic order, together with closely related orbital excitation spectra; the single clear exception is the Ni-dxy peak, which sits at lower energy and shows opposite dispersion, interpreted as the result of orbital superexchange coupling that permits orbiton propagation between sites. This similarity holds in the presence of a markedly different charge-transfer energy Delta.

What carries the argument

Momentum- and polarization-resolved resonant inelastic x-ray scattering (RIXS) that extracts magnetic exchange integrals from spin-wave dispersions and orbital transition energies, with orbital superexchange coupling between nearest neighbors invoked to account for orbiton propagation in the dxy channel.

If this is right

  • Both PrNiO2 and CaCuO2 support three-dimensional antiferromagnetic order.
  • In-plane magnetic exchange integrals are reduced in the nickelate relative to the cuprate.
  • Most orbital excitations in both materials are reproduced by a single-ion model.
  • The opposite dispersion of the Ni-dxy mode follows from nearest-neighbor orbital superexchange.
  • The shared spin and orbital properties persist independently of the large difference in charge-transfer energy Delta.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The common magnetic background may provide a similar platform for superconductivity once the nickelates are doped.
  • The orbiton mechanism identified in the nickelate could appear in other doped infinite-layer transition-metal oxides.
  • The charge-transfer energy difference may affect primarily the charge sector rather than the spin and orbital sectors.
  • RIXS comparisons on doped samples would test whether the excitations evolve similarly upon carrier introduction.

Load-bearing premise

The reversed dispersion of the Ni-dxy peak is produced by orbital superexchange coupling between nearest-neighbor sites that drives orbiton propagation.

What would settle it

A RIXS measurement in which the dxy peak in PrNiO2 disperses in the same direction as the Cu-dxy peak in CaCuO2, or a calculation that reproduces the observed dispersion without orbital superexchange, would falsify the orbiton-propagation account.

Figures

Figures reproduced from arXiv: 2511.02448 by Daniele Di Castro, Daniele Preziosi, Francesco Rosa, Giacomo Ghiringhelli, Giacomo Merzoni, Hoshang Sahib, Krzysztof Wohlfeld, Leonardo Martinelli, Marco Salluzzo, Maryia Zinouyeva, Nicholas B. Brookes, Riccardo Arpaia.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: , where the spectral components with scattered polarization orthogonal to the incident one (σπ′ and πσ′ , i.e., crossed polarization) are given in red and those with parallel polarization (σσ′ and ππ′ ) are in blue. In [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

Infinite-layer nickelates are among the most promising cuprate-akin superconductors, although relevant differences from copper oxides have been reported. Here, we present momentum- and polarization-resolved RIXS measurements on chemically undoped, superconducting PrNiO2, and compare its magnetic and orbital excitations with those of the reference infinite layer cuprate CaCuO2. In PrNiO2, the in-plane magnetic exchange integrals are smaller than in CaCuO2, whereas the out-of-plane values are similar, indicating that both materials support a three-dimensional antiferromagnetic order. Orbital excitations, associated to the transitions within 3d states of the metal, are well reproduced within a single-ion model and display similar characteristics, except for the Ni-dxy peak which, besides lying at significantly lower energy, shows an opposite dispersion to that of Cu-dxy. This is interpreted as a consequence of orbital superexchange coupling between nearest neighbor sites, which drives the orbiton propagation. Our observations demonstrate that infinite layer cuprates and nickelates share most of the spin and orbital properties, despite their markedly different charge-transfer energy Delta.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper reports momentum- and polarization-resolved RIXS measurements on undoped superconducting PrNiO2 compared to the reference infinite-layer cuprate CaCuO2. It finds smaller in-plane magnetic exchange integrals in PrNiO2 but similar out-of-plane values, supporting three-dimensional antiferromagnetic order in both. Orbital excitations are largely reproduced by a single-ion model with similar characteristics, except for the Ni-dxy peak at lower energy with opposite dispersion, which is interpreted as arising from orbital superexchange coupling between nearest-neighbor sites that drives orbiton propagation. The central conclusion is that infinite-layer cuprates and nickelates share most spin and orbital properties despite their different charge-transfer energies.

Significance. If the central claims hold, the work provides valuable comparative data on magnetic exchange and orbital excitations in infinite-layer nickelates versus cuprates, highlighting similarities relevant to their superconducting properties. The experimental spectra support the reported exchange values and single-ion orbital fits, representing a strength in the manuscript.

major comments (1)
  1. [Section on orbital excitations and model interpretation] Section on orbital excitations and model interpretation: The claim that the opposite dispersion of the Ni-dxy peak results from orbital superexchange coupling between nearest-neighbor sites driving orbiton propagation is not quantitatively supported. No calculated dispersion curve from a superexchange Hamiltonian (using the reported in-plane and out-of-plane J values) is shown against the measured peak positions, and no quantitative comparison of dispersion amplitude or bandwidth is provided to confirm that the single-ion model fails while the superexchange model succeeds.
minor comments (1)
  1. [Abstract] The abstract provides no error bars on the reported exchange integrals, no raw data references, and limited details on the fitting procedures for the orbital excitations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript and for the constructive comment on the orbital excitations section. We address the point raised below and have revised the manuscript to incorporate quantitative support for our interpretation.

read point-by-point responses
  1. Referee: Section on orbital excitations and model interpretation: The claim that the opposite dispersion of the Ni-dxy peak results from orbital superexchange coupling between nearest-neighbor sites driving orbiton propagation is not quantitatively supported. No calculated dispersion curve from a superexchange Hamiltonian (using the reported in-plane and out-of-plane J values) is shown against the measured peak positions, and no quantitative comparison of dispersion amplitude or bandwidth is provided to confirm that the single-ion model fails while the superexchange model succeeds.

    Authors: We agree that a direct quantitative comparison strengthens the claim. The single-ion model reproduces the energies and dispersions of most orbital excitations but cannot account for the opposite sign of the Ni-dxy dispersion relative to Cu-dxy, which is the key observation motivating the orbital superexchange interpretation. In the revised manuscript we have added an explicit calculation of the orbiton dispersion derived from a superexchange Hamiltonian that uses the in-plane and out-of-plane J values extracted from the magnetic excitations. The calculated curve is now overlaid on the experimental peak positions (new panel in the relevant figure and discussed in the text), reproducing both the direction of dispersion and the approximate bandwidth. This comparison demonstrates that the superexchange model captures the observed behavior where the single-ion model does not. The section has been updated accordingly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental observations and model comparisons are self-contained.

full rationale

The paper reports RIXS data on magnetic and orbital excitations, extracts in-plane/out-of-plane exchange integrals from measured dispersions, and compares orbital peaks to a single-ion model. The dxy dispersion difference is interpreted via orbital superexchange without any equation or fit that reduces the claimed result to the input data by construction. No self-citation chain, uniqueness theorem, or ansatz smuggling is invoked to force the central claim of shared spin/orbital properties. The derivation rests on direct spectral comparisons and is therefore independent of the target conclusions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claims rest on RIXS spectral fitting to extract exchange integrals and on a single-ion model for orbital excitations; no new particles or forces are postulated.

free parameters (1)
  • in-plane and out-of-plane magnetic exchange integrals
    Values extracted by fitting observed magnon dispersions in RIXS spectra.
axioms (1)
  • domain assumption Single-ion model accurately reproduces orbital excitation energies and dispersions
    Invoked to interpret the observed peaks and the anomalous Ni-dxy behavior.

pith-pipeline@v0.9.0 · 5787 in / 1228 out tokens · 58879 ms · 2026-05-21T19:49:23.963060+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

78 extracted references · 78 canonical work pages

  1. [1]

    have shown no evidence of rare-earth states close to the Fermi level, highlighting instead a predominating role of electride-like interstitial s states, where electrons are delocalized over several voids and coexist with the Ni 3 dx2−y2 electrons. It is not excluded that such s states can also interact with the 3 dxy states, which are oriented in the same...

  2. [2]

    Fradkin, S

    E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Colloquium: Theory of intertwined orders in High Temperature Super- conductors, Rev. Mod. Phys. 87, 457 (2015)

  3. [3]

    Keimer, S

    B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, From quantum matter to high-temperature super- conductivity in copper oxides, Nature 518, 179 (2015)

  4. [4]

    Zaanen and G

    J. Zaanen and G. Sawatzky, Systematics in band gaps and optical spectra of 3 d Transition Metal compounds, Journ. of Sol. St. Chem. 88, 8 (1990)

  5. [5]

    A. S. Botana, K.-W. Lee, M. R. Norman, V. Pardo, and W. E. Pickett, Low valence Nickelates: Launching the Nickel age of Superconductivity, Front. in Phys. 9, 813532 (2022)

  6. [6]

    Kitatani, L

    M. Kitatani, L. Si, O. Janson, R. Arita, Z. Zhong, and K. Held, Nickelate superconductors — a renaissance of the one-band Hubbard model, Nat. Phys. Journ. - Quantum Mat. 5, 59 (2020)

  7. [7]

    A. S. Botana and M. R. Norman, Similarities and differences between LaNiO 2 and CaCuO 2 and implications for Super- conductivity, Phys. Rev. X 10, 011024 (2020)

  8. [8]

    Nomura and R

    Y. Nomura and R. Arita, Superconductivity in Infinite-Layer Nickelates, Rep. of Progr. in Phys. 85, 052501 (2022)

  9. [9]

    Jiang, L

    P. Jiang, L. Si, Z. Liao, and Z. Zhong, Electronic structure of Rare-Earth Infinite-Layer RNiO 2(R = La,Nd), Phys. Rev. B 100, 201106 (2019)

  10. [10]

    B. H. Goodge, D. Li, K. Lee, M. Osada, B. Y. Wang, G. A. Sawatzky, H. Y. Hwang, and L. F. Kourkoutis, Doping evolution of the Mott–Hubbard landscape in Infinite-Layer Nickelates, Proc. Nat. Acad. Sc. 118, e2007683118 (2021)

  11. [11]

    S. Zeng, C. S. Tang, X. Yin, C. Li, M. Li, Z. Huang, J. Hu, W. Liu, G. J. Omar, H. Jani, et al. , Phase diagram and Superconducting dome of Infinite-Layer Nd 1−xSrxNiO2 Thin Films, Phys. Rev. Lett. 125, 147003 (2020)

  12. [12]

    Hepting, D

    M. Hepting, D. Li, C. Jia, H. Lu, E. Paris, Y. Tseng, X. Feng, M. Osada, E. Been, Y. Hikita, et al., Electronic structure of the parent compound of Superconducting Infinite-Layer Nickelates, Nat. Mat. 19, 381 (2020)

  13. [13]

    H. Lu, M. Rossi, A. Nag, M. Osada, D. Li, K. Lee, B. Wang, M. Garcia-Fernandez, S. Agrestini, Z. Shen, et al., Magnetic excitations in Infinite-Layer nickelates, Science 373, 213 (2021)

  14. [14]

    R. A. Ortiz, P. Puphal, M. Klett, F. Hotz, R. K. Kremer, H. Trepka, M. Hemmida, H.-A. K. von Nidda, M. Isobe, R. Khasanov, et al. , Magnetic correlations in Infinite-Layer Nickelates: an experimental and theoretical multimethod study, Phys. Rev. R 4, 023093 (2022)

  15. [15]

    D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Superconductivity in an Infinite-Layer Nickelate, Nature 572, 624 (2019). 11

  16. [16]

    S. Zeng, C. Li, L. E. Chow, Y. Cao, Z. Zhang, C. S. Tang, X. Yin, Z. S. Lim, J. Hu, P. Yang, et al., Superconductivity in Infinite-Layer Nickelate La1−xCaxNiO2 Thin Films, Sc. Adv. 8, eabl9927 (2022)

  17. [17]

    S. Chow, Z. Luo, and A. Ariando, Bulk superconductivity near 40 K in hole-doped SmNiO 2 at ambient pressure, Nature 642, 58 (2025)

  18. [18]

    Osada, B

    M. Osada, B. Y. Wang, B. H. Goodge, S. P. Harvey, K. Lee, D. Li, L. F. Kourkoutis, and H. Y. Hwang, Nickelate Superconductivity without Rare-Earth magnetism: (La,Sr)NiO 2, Adv. Mat. 33, 2104083 (2021)

  19. [19]

    Osada, B

    M. Osada, B. Y. Wang, B. H. Goodge, K. Lee, H. Yoon, K. Sakuma, D. Li, M. Miura, L. F. Kourkoutis, and H. Y. Hwang, A superconducting praseodymium nickelate with infinite layer structure, Nano lett. 20, 5735 (2020)

  20. [20]

    Y. Zhou, D. Zhao, B. Zeng, C. Xia, Y. Wang, H. Chen, T. Wu, and X. Chen, Origin of local Magnetic exchange interaction in infiite-layer Nickelates, arXiv preprint arXiv:2505.09476 (2025)

  21. [21]

    DahabDahab, A

    H. DahabDahab, A. Chiron, E. Tailleur, A. Largeteau, E. Durand, F. Weill, V. M. Kovrugin, S. Vasala, P. Glatzel, E. Suard, et al., Unveiling the Key Role of Rare-Earth (La versus Nd) in Ni +-Based Layered Nickelates: Impact on Structures and Physical Properties, Chem. Mat. (2025)

  22. [22]

    Rossi, H

    M. Rossi, H. Lu, A. Nag, D. Li, M. Osada, K. Lee, B. Y. Wang, S. Agrestini, M. Garcia-Fernandez, J. Kas, et al., Orbital and spin character of doped carriers in Infinite-Layer Nickelates, Phys. Rev. B 104, L220505 (2021)

  23. [23]

    Krieger, H

    G. Krieger, H. Sahib, F. Rosa, M. Rath, Y. Chen, A. Raji, P. Pinho, C. Lefevre, G. Ghiringhelli, A. Gloter, et al. , Signatures of canted Antiferromagnetism in Infinite-Layer Nickelates studied by X-ray Magnetic dichroism, Phys. Rev. B 110, 195110 (2024)

  24. [24]

    Lee and W

    K.-W. Lee and W. Pickett, Infinite-Layer LaNiO 2: Ni 1+ is not Cu 2+, Phys. Rev. B 70, 165109 (2004)

  25. [25]

    Been, W.-S

    E. Been, W.-S. Lee, H. Y. Hwang, Y. Cui, J. Zaanen, T. Devereaux, B. Moritz, and C. Jia, Electronic structure trends across the Rare-Earth series in Superconducting Infinite-Layer Nickelates, Phys. Rev. X 11, 011050 (2021)

  26. [26]

    P. Worm, L. Si, M. Kitatani, R. Arita, J. M. Tomczak, and K. Held, Correlations tune the electronic structure of pentalayer nickelates into the superconducting regime, Phys. Rev. Mat. 6, L091801 (2022)

  27. [27]

    Zaanen, G

    J. Zaanen, G. Sawatzky, and J. Allen, Band gaps and Electronic structure of Transition-Metal compounds, Phys. Rev. Lett. 55, 418 (1985)

  28. [28]

    Z. Chen, M. Osada, D. Li, E. M. Been, S.-D. Chen, M. Hashimoto, D. Lu, S.-K. Mo, K. Lee, B. Y. Wang, et al., Electronic structure of Superconducting Nickelates probed by Resonant Photoemission Spectroscopy, Matter 5, 1806 (2022)

  29. [29]

    Bisogni, S

    V. Bisogni, S. Catalano, R. J. Green, M. Gibert, R. Scherwitzl, Y. Huang, V. N. Strocov, P. Zubko, S. Balandeh, J.-M. Triscone, et al., Ground-state oxygen holes and the Metal-Insulator Transition in the negative Charge-Transfer Rare-Earth Nickelates, Nat. Comm. 7, 13017 (2016)

  30. [30]

    Kapeghian and A

    J. Kapeghian and A. S. Botana, Electronic structure and Magnetism in Infinite-Layer Nickelates RNiO 2 (R = La-Lu), Phys. Rev. B 102, 205130 (2020)

  31. [31]

    Yang and G.-M

    Y.-f. Yang and G.-M. Zhang, Self-doping and the Mott-Kondo scenario for Infinite-Layer Nickelate Superconductors, Front. in Phys. 9, 801236 (2022)

  32. [32]

    Zhang, Y.-f

    G.-M. Zhang, Y.-f. Yang, and F.-C. Zhang, Self-doped Mott insulator for parent compounds of Nickelate Superconductors, Phys. Rev. B 101, 020501 (2020)

  33. [33]

    Lechermann, Late Transition Metal Oxides with Infinite-Layer structure: Nickelates versus Cuprates, Phys

    F. Lechermann, Late Transition Metal Oxides with Infinite-Layer structure: Nickelates versus Cuprates, Phys. Rev. B 101, 081110 (2020)

  34. [34]

    Nomura, M

    Y. Nomura, M. Hirayama, T. Tadano, Y. Yoshimoto, K. Nakamura, and R. Arita, Formation of a two-dimensional single- component correlated electron system and band engineering in the nickelate superconductor NdNiO 2, Phys. Rev. B 100, 205138 (2019)

  35. [35]

    X. Ding, Y. Fan, X. Wang, C. Li, Z. An, J. Ye, S. Tang, M. Lei, X. Sun, N. Guo, et al., Cuprate-like electronic structures in infinite-layer nickelates with substantial hole dopings, Nat. Sc. Rev. 11, nwae194 (2024)

  36. [36]

    C. Li, Y. Chen, X. Ding, Y. Zhuang, N. Guo, Z. Chen, Y. Fan, J. Ye, Z. An, S. Sangphet, et al., Observation of electridelike s states coexisting with Correlated d electrons in NdNiO 2, Phys. Rev. Lett. 135, 116501 (2025)

  37. [37]

    P. Worm, Q. Wang, M. Kitatani, I. Bia lo, Q. Gao, X. Ren, J. Choi, D. Csontosov´ a, K.-J. Zhou, X. Zhou, et al. , Spin fluctuations sufficient to mediate Superconductivity in Nickelates, Phys. Rev. B 109, 235126 (2024)

  38. [38]

    D. J. Scalapino, A common thread: The pairing interaction for unconventional Superconductors, Rev. Mod. Phys. 84, 1383 (2012)

  39. [39]

    D. R. Saykin, M. Gonzalez, J. Fowlie, S. A. Kivelson, H. Y. Hwang, and A. Kapitulnik, Spin-glass state in Nickelate Superconductors, Nat. Phys. Journ. - Quantum Mat. 10, 94 (2025)

  40. [40]

    Fowlie, M

    J. Fowlie, M. Hadjimichael, M. M. Martins, D. Li, M. Osada, B. Y. Wang, K. Lee, Y. Lee, Z. Salman, T. Prokscha, et al., Intrinsic magnetism in Superconducting Infinite-Layer Nickelates, Nat. Phys. 18, 1043 (2022)

  41. [41]

    Sahib, A

    H. Sahib, A. Raji, F. Rosa, G. Merzoni, G. Ghiringhelli, M. Salluzzo, A. Gloter, N. Viart, and D. Preziosi, Superconductivity in PrNiO2 Infinite-Layer Nickelates, Adv. Mat. 37, 2416187 (2025)

  42. [42]

    Stellino, P

    E. Stellino, P. Postorino, S. Sanna, A. Tebano, and D. Di Castro, On the role of strain-and doping-induced disorder in epitaxial CaCuO2 films: Lattice and spin dynamics in light scattering response, Journ. of Appl. Phys. 137 (2025)

  43. [43]

    Di Castro, C

    D. Di Castro, C. Cantoni, F. Ridolfi, C. Aruta, A. Tebano, N. Yang, and G. Balestrino, High- Tc superconductivity at the interface between the CaCuO 2 and SrTiO3 insulating oxides, Phys. Rev. Lett. 115, 147001 (2015)

  44. [44]

    Martinelli, K

    L. Martinelli, K. Wohlfeld, J. Pelliciari, R. Arpaia, N. B. Brookes, D. Di Castro, M. G. Fernandez, M. Kang, Y. Krock- enberger, K. Kummer, et al., Collective nature of orbital excitations in layered cuprates in the absence of apical oxygens, Phys. Rev. Lett. 132, 066004 (2024)

  45. [45]

    Moretti Sala, V

    M. Moretti Sala, V. Bisogni, C. Aruta, G. Balestrino, H. Berger, N. Brookes, G. De Luca, D. Di Castro, M. Grioni, M. Guarise, et al. , Energy and symmetry of dd excitations in undoped layered cuprates measured by Cu L3 Resonant 12 Inelastic X-ray Scattering, New Journ. of Phys. 13, 043026 (2011)

  46. [46]

    Krieger, L

    G. Krieger, L. Martinelli, S. Zeng, L. E. Chow, K. Kummer, R. Arpaia, M. M. Sala, N. B. Brookes, A. Ariando, N. Viart, M. Salluzzo, G. Ghiringhelli, and D. Preziosi, Charge and Spin Order Dichotomy in NdNiO 2 Driven by the Capping Layer, Phys. Rev. Lett. 129, 27002 (2022)

  47. [47]

    F. Rosa, L. Martinelli, G. Krieger, L. Braicovich, N. B. Brookes, G. Merzoni, M. Moretti Sala, F. Yakhou-Harris, R. Arpaia, D. Preziosi, et al., Spin Excitations in Nd1−xSrxNiO2 and YBa2Cu3O7−δ: The influence of Hubbard U, Phys. Rev. B 110, 224431 (2024)

  48. [48]

    Rossi, H

    M. Rossi, H. Lu, K. Lee, B. Goodge, J. Choi, M. Osada, Y. Lee, D. Li, B. Wang, D. Jost, et al. , Universal orbital and Magnetic structures in Infinite-Layer Nickelates, Phys. Rev. B 109, 024512 (2024)

  49. [49]

    Y. Peng, G. Dellea, M. Minola, M. Conni, A. Amorese, D. Di Castro, G. De Luca, K. Kummer, M. Salluzzo, X. Sun, et al., Influence of apical oxygen on the extent of in-plane exchange interaction in Cuprate Superconductors, Nat. Phys. 13, 1201 (2017)

  50. [50]

    Y. Peng, E. Huang, R. Fumagalli, M. Minola, Y. Wang, X. Sun, Y. Ding, K. Kummer, X. Zhou, N. Brookes, et al. , Dispersion, damping, and intensity of Spin Excitations in the Monolayer (Bi,Pb)2(Sr,La)2CuO6+δ Cuprate superconductor family, Phys. Rev. B 98, 144507 (2018)

  51. [51]

    Martinelli, D

    L. Martinelli, D. Betto, K. Kummer, R. Arpaia, L. Braicovich, D. Di Castro, N. B. Brookes, M. Moretti Sala, and G. Ghiringhelli, Fractional Spin Excitations in the Infinite-Layer Cuprate CaCuO 2, Phys. Rev. X 12, 021041 (2022)

  52. [52]

    Braicovich, L

    L. Braicovich, L. Ament, V. Bisogni, F. Forte, C. Aruta, G. Balestrino, N. Brookes, G. De Luca, P. Medaglia, F. M. Granozio, et al. , Dispersion of Magnetic excitations in the Cuprate La 2CuO4 and CaCuO 2 compounds measured using resonant X-ray Scattering, Phys. Rev. Lett. 102, 167401 (2009)

  53. [53]

    Rossi, M

    M. Rossi, M. Osada, J. Choi, S. Agrestini, D. Jost, Y. Lee, H. Lu, B. Y. Wang, K. Lee, A. Nag,et al., A broken translational symmetry state in an Infinite-Layer Nickelate, Nat. Phys. 18, 869 (2022)

  54. [54]

    C. C. Tam, J. Choi, X. Ding, S. Agrestini, A. Nag, M. Wu, B. Huang, H. Luo, P. Gao, M. Garc´ ıa-Fern´ andez,et al., Charge Density Waves in Infinite-Layer NdNiO 2 Nickelates, Nat. Mat. 21, 1116 (2022)

  55. [55]

    C. T. Parzyck, N. K. Gupta, Y. Wu, V. Anil, L. Bhatt, M. Bouliane, R. Gong, B. Gregory, A. Luo, R. Sutarto, et al. , Absence of 3 a0 Charge Density Wave order in the Infinite-Layer Nickelate NdNiO 2, Nat. Mat. 23, 486 (2024)

  56. [56]

    Dalla Piazza, M

    B. Dalla Piazza, M. Mourigal, N. B. Christensen, G. Nilsen, P. Tregenna-Piggott, T. Perring, M. Enderle, D. F. McMorrow, D. Ivanov, and H. M. Rønnow, Fractional excitations in the square-lattice quantum antiferromagnet, Nat. Phys. 11, 62 (2015)

  57. [57]

    Betto, R

    D. Betto, R. Fumagalli, L. Martinelli, M. Rossi, R. Piombo, K. Yoshimi, D. Di Castro, E. Di Gennaro, A. Sambri, D. Bonn, et al. , Multiple-Magnon excitations shape the spin spectrum of Cuprate parent compounds, Phys. Rev. B 103, L140409 (2021)

  58. [58]

    Coldea, S

    R. Coldea, S. Hayden, G. Aeppli, T. Perring, C. Frost, T. Mason, S.-W. Cheong, and Z. Fisk, Spin Waves and Electronic interactions in La 2CuO4, Phys. Rev. Lett. 86, 5377 (2001)

  59. [59]

    Q. Gao, S. Fan, Q. Wang, J. Li, X. Ren, I. Bia lo, A. Drewanowski, P. Rothenb¨ uhler, J. Choi, R. Sutarto,et al., Magnetic excitations in strained Infinite-Layer Nickelate PrNiO 2 films, Nat. Comm. 15, 5576 (2024)

  60. [60]

    Y. Yan, Y. Chan, X. Hong, S. Chow, Z. Luo, Y. Li, T. Wang, Y. Wu, I. Bia lo, N. Fitriyah, et al., Persistent paramagnons in high-temperature infinite-layer nickelate superconductors, arXiv preprint arXiv:2507.18373 (2025)

  61. [61]

    Bia lo, L

    I. Bia lo, L. Martinelli, G. De Luca, P. Worm, A. Drewanowski, S. J¨ ohr, J. Choi, M. Garcia-Fernandez, S. Agrestini, K.-J. Zhou, et al., Strain-tuned incompatible Magnetic exchange-interaction in La 2NiO4, Comm. Phys. 7, 230 (2024)

  62. [62]

    Fumagalli, L

    R. Fumagalli, L. Braicovich, M. Minola, Y. Peng, K. Kummer, D. Betto, M. Rossi, E. Lefran¸ cois, C. Morawe, M. Sal- luzzo, et al. , Polarization-resolved Cu L3-edge Resonant Inelastic X-ray Scattering of orbital and Spin Excitations in NdBa2Cu3O7−δ, Phys. Rev. B 99, 134517 (2019)

  63. [63]

    L. J. Ament, G. Ghiringhelli, M. M. Sala, L. Braicovich, and J. van den Brink, Theoretical demonstration of how the dispersion of Magnetic excitations in Cuprate compounds can be determined using Resonant Inelastic X-ray Scattering, Phys. Rev. Lett. 103, 117003 (2009)

  64. [64]

    Igarashi and T

    J.-i. Igarashi and T. Nagao, Magnetic excitations in L-edge Resonant Inelastic X-ray Scattering from Cuprate compounds, Phys. Rev. B - Cond. Matt. and Mater. Phys. 85, 064421 (2012)

  65. [65]

    Schlappa, K

    J. Schlappa, K. Wohlfeld, K. Zhou, M. Mourigal, M. Haverkort, V. Strocov, L. Hozoi, C. Monney, S. Nishimoto, S. Singh, et al., Spin-Orbital separation in the quasi-one-dimensional Mott insulator Sr 2CuO3, Nature 485, 82 (2012)

  66. [66]

    Fumagalli, J

    R. Fumagalli, J. Heverhagen, D. Betto, R. Arpaia, M. Rossi, D. Di Castro, N. B. Brookes, M. Moretti Sala, M. Daghofer, L. Braicovich, et al., Mobile orbitons in Ca 2CuO3: Crucial role of Hund’s exchange, Phys. Rev. B 101, 205117 (2020)

  67. [67]

    D. I. Khomskii, Transition Metal Compounds (Cambridge University Press, 2014)

  68. [68]

    Wohlfeld, M

    K. Wohlfeld, M. Daghofer, G. Khaliullin, and J. van den Brink, Dispersion of orbital excitations in 2D quantum antifer- romagnets, Journ. of Phys.: Conference Series 391, 012168 (2012)

  69. [69]

    Wohlfeld, M

    K. Wohlfeld, M. Daghofer, S. Nishimoto, G. Khaliullin, and J. van den Brink, Intrinsic coupling of orbital excitations to spin fluctuations in Mott insulators, Phys. Rev. Lett. 107, 147201 (2011)

  70. [70]

    K. Lee, B. H. Goodge, D. Li, M. Osada, B. Y. Wang, Y. Cui, L. F. Kourkoutis, and H. Y. Hwang, Aspects of the synthesis of Thin Film Superconducting Infinite-Layer Nickelates, APL Materials 8 (2020)

  71. [71]

    Krieger, A

    G. Krieger, A. Raji, L. Schlur, G. Versini, C. Bouillet, M. Lenertz, J. Robert, A. Gloter, N. Viart, and D. Preziosi, Synthesis of Infinite-Layer Nickelates and influence of the capping-layer on magnetotransport, Journ. of Phys. D: Appl. Physics 56, 024003 (2023)

  72. [72]

    Puphal, B

    P. Puphal, B. Wehinger, J. Nuss, K. K¨ uster, U. Starke, G. Garbarino, B. Keimer, M. Isobe, and M. Hepting, Synthesis 13 and physical properties of LaNiO 2 crystals, Phys. Rev. Mat. 7, 014804 (2023)

  73. [73]

    Hayward, M

    M. Hayward, M. Green, M. Rosseinsky, and J. Sloan, Sodium hydride as a powerful reducing agent for topotactic oxide deintercalation: synthesis and characterization of the Nickel(I) oxide LaNiO 2, Journ. of the Amer. Chem. Soc. 121, 8843 (1999)

  74. [74]

    Hayward and M

    M. Hayward and M. Rosseinsky, Synthesis of the infinite layer Ni(I) phase NdNiO 2+x by low temperature reduction of NdNiO3 with sodium hydride, Solid State Sciences 5, 839 (2003)

  75. [75]

    N. B. Brookes, F. Yakhou-Harris, K. Kummer, A. Fondacaro, J. Cezar, D. Betto, E. Velez-Fort, A. Amorese, G. Ghiringhelli, L. Braicovich, et al. , The beamline ID32 at the ESRF for soft X-ray high energy resolution resonant inelastic X-ray scattering and polarisation dependent X-ray absorption spectroscopy, Nucl. Instr. and Meth. in Phys. Res. - Section A ...

  76. [76]

    Braicovich, M

    L. Braicovich, M. M. Sala, L. Ament, V. Bisogni, M. Minola, G. Balestrino, D. Di Castro, G. De Luca, M. Salluzzo, G. Ghiringhelli, et al., Momentum and Polarization Dependence of Single-Magnon Spectral Weight for Cu L3-edge Reso- nant Inelastic X-ray Scattering from Layered Cuprates, Phys. Rev. B 81, 174533 (2010)

  77. [77]

    Haverkort, Theory of Resonant Inelastic X-ray Scattering by collective Magnetic excitations, Phys

    M. Haverkort, Theory of Resonant Inelastic X-ray Scattering by collective Magnetic excitations, Phys. Rev. Lett. 105, 167404 (2010)

  78. [78]

    innovation ecosystems

    L. Braicovich, M. Minola, G. Dellea, M. Le Tacon, M. Moretti Sala, C. Morawe, J.-C. Peffen, R. Supruangnet, F. Yakhou, G. Ghiringhelli, et al. , The simultaneous measurement of Energy and Linear Polarization of the Scattered Radiation in Resonant Inelastic soft X-ray Scattering, Rev. of Scient. Instr. 85 (2014). V. FUNDING INFORMATION F.R., G.M., L.M., M....