46 47 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 1 9 / 2 0 D I A M O N D L I G H T S O U R C E A N N U A L R E V I E W 2 0 1 9 / 2 0 Revealing the electronic structures of nickelate superconductors Related publication: Hepting M., Li D., Jia C. J., Lu H., Paris E., Tseng Y., Feng X., Osada M., Been E., Hikita Y., Chuang Y.-D., Hussain Z., Zhou K. J., Nag A., Garcia-Fernandez M., Rossi M., Huang H. Y., Huang D. J., Shen Z. X., Schmitt T., Hwang H. Y., Moritz B., Zaanen J., Devereaux T. P. & Lee W. S. Electronic structure of the parent compound of superconducting infinite-layer nickelates. Nature Mater. 19 , 381-385 (2020). DOI: 10.1038/s41563-019-0585-z Publication keywords: High Tc superconductor; Strongly correlated electronic system; Nickelate; XAS; RIXS S ince the 1986 discovery of high-temperature superconducting copper oxides (cuprates), researchers have been trying to engineer nickelate oxides (nickelates) to produce another high-temperature superconductor. With the recent discovery of the first nickelate superconductor, there is a renewed push to uncover the electronic structures of the nickelate. Revealing the electronic structure allows us to characterise its similarities and differences to cuprates. This information is crucial to understand the mechanism of superconductivity in nickelates and cuprates. It is also useful to synthesise other unconventional high- temperature superconductors. Researcherssetouttodeterminetheelectronicstructureofnickelates,usingtheoreticalcalculationsanddatatakenatseveralsynchrotrons. TheyusedtheResonantInelasticX-rayScattering(RIXS)beamline(I21)atDiamondLightSource.BothRIXSandX-rayAbsorptionSpectroscopy (XAS) can uncover how the electrons of constituent ions hybridise to form the low energy electronic states from which superconductivity emerges. In particular, the RIXS beamline at I21 possesses the high resolution and high efficiency required for this work. Their results showed that the rare-earth layers in the nickelate provide a 3Dmetallic state which couples with the electrons in the 2D nickel oxide planes. This is very different from the case of cuprates, in which the rare-earth layer is insulating, and not actively involved in the low energy electronic states. The microscopic electronic structures of the nickelate can now be used to in the design and synthesis of new unconventional superconductors. Since the discovery of high temperature superconducting copper oxide (cuprates), search for another transition metal oxide superconductor has debuted. In particular, nickel oxides have been proposed to be a material that could be engineered to mimic the electronic structures of cuprates 1-3 . Recently, the first nickelate superconductor has finally been discovered 4 . It is a Sr-doped infinite-layer NdNiO 2 , which is produced by removing the apical oxygen atoms from the perovskite nickelate NdNiO 3 using a metal hydride-based soft chemistry reduction process. The undoped infinite nickelates appears to be a close sibling of cuprates, it is isostructural to the infinite-layer cuprates with monovalent Ni 1+ cations and possesses the same 3 d 9 electron count as that of Cu 2+ cations in undoped cuprates. Yet, as discovered in this work, the electronic structure of the undoped RNiO 2 (R = La and Nd) remains distinct from the Mott, or charge-transfer, compounds of undoped cuprates, and even other nickelates. To uncover the electronic structure of the infinite-layer cuprates, X-ray absorption spectroscopy (XAS) and Resonant Inelastic X-ray Scattering (RIXS) across oxygen (O) K-edge and nickel (Ni) L-edges were conducted.The O K-edge XAS of infinite-layer nickelates has first uncovered a major difference from cupratesandothernickelates. Inthe lattersystems,suchasNiOandRNiO 3 ,apre- edge peak exists in the oxygen K-edge XAS, a signature of strong hybridisation between oxygen 2 p ligand states and the Ni(Cu) 3 d states, making them the so-called charge-transfer compounds (Fig. 1a). Interestingly, such pre-peak in O K-edge XAS is absent in the infinite nickelates (Fig. 1a), indicating that the oxygen 2 p ligands states are much less involved in the low energy electronic structures. Therefore, its electronic structure is different from that of charge transfer compounds, including cuprates and other nickelates. MagneticMaterials Group Beamline I21 The XAS and RIXS across the Ni L-edge has further revealed the electronic structures of the Ni cation in the RNiO 2 . As shown in the black curve of Fig. 1b, the XAS for infinite-layer nickelates shows one main absorption peak (denoted A), which is distinct from those of NiO and RNiO 3 , but closely resembles the single peak associated with the 2 p 6 3 d 9 –2 p 5 3 d 10 transition in cuprates. Further information about the electronic states of Ni cation is revealed by RIXS. In Fig. 1b, RIXS intensity map as a function of energy loss and incident energy across the Ni L-edge were shown. The ~1 eV and ~1.8 eV features resemble the dd excitations seen in LaNiO 3 and NdNiO 3 except that they are broader and exhibit a dispersion with incident photon energy. This suggests that the Ni 3 d states in NdNiO 2 are mixed with delocalised states. Interestingly, an additional 0.6 eV feature appears, which is absent in the RNiO 3 (R = La, Nd) compounds (Fig. 1c). Using exact diagonalisation calculation, we reproduce the general features from XAS and RIXS, including the 0.6 eV features, which highlights the hybridisation between the Ni 3 d x 2 - y 2 and R 5 d orbitals. Thus, in configuration interaction, the Ni state can be expressed as a combination of |3 d 9 > and |3 d 8 R > where R denotes a charge transfer to the rare-earth cation. Note that as also shown in the paper, the RIXS map of LaNiO 2 is qualitatively similar to that shown in NdNiO 2 , except that the resonant energy for the 0.6 eV peak shifts to lower energy. To further analyse the electronic structure, we turn to LDA+ U calculations. It is found that oxygen 2 p bands lie significantly further away from the Fermi energy, signalling reduced oxidation and implying a charge-transfer energy that exceeds U . As shown in Fig. 2, the density of states near Fermi energy is dominated by the half-filled Ni 3 d x 2 - y 2 states, which appear isolated from the occupied Ni 3 d bands and exhibit a single-band Hubbardmodel-like separation, all but confirming that the Ni cation should be in a nearly monovalent 3 d 9 state, consistent with the Ni L-edge XAS and RIXS (Fig. 1). Furthermore, the density of states at Fermi energy is actually finite, but small. Near the zone point, a Fermi surface pocket forms of mainly La 5 d character; it is quite extended and three- dimensional (3D). This contrasts with the two-dimensional (2D) nature of the correlated 3 d x 2 - y 2 Ni states. In other words, the electronic structure of the infinite layer nickelate consists of a low density 3D metallic rare-earth band coupled to a 2D Mott system. This electronic structure resembles the Anderson- lattice (or Kondo-lattice) model for the rare-earth intermetallics, but with the notable addition of a weakly hybridised single- band Hubbard-like model for the Ni layer, rather than strongly interacting 4f states (or localised spin moments). In this work, an effective model Hamiltonian is derived via downfolding the aforementioned LDA+ U calculation, severing as a starting point to further theoretically investigate emergent phenomena in infinite-layer nickelate system. The results reported in this work provide a glimpse into the remarkable electronic structure of the parent compound of the infinite-layer nickelates, urging for further theoretical and experimental investigations, particularly about the Fermi surface and elementary excitations, such as spin, charge, and phonon excitations. References: 1. AnisimovV. I. et al. Electronic structure of possible nickelate analogy to the cuprates. Phys. Rev. B 59 , 7901 (1999). DOI: 10.1103/PhysRevB.59.7901 2. Lee K.-W. et al. Infinite-layer LaNiO 2 : Ni 1+ is not Cu 2+ . Phys. Rev. B 70 , 165109 (2004). DOI:10.1103/PhysRevB.70.165109 3. Hansmann P. et al. Turning a Nickelate Fermi Surface into a Cuprate-like One through Heterostructuring. Phys. Rev. Lett. 103 , 016401 (2009). DOI: 10.1103/PhysRevLett.103.016401 4. Li D. et al. Superconductivity in an infinite-layer nickelate. Nature 572 , 624 (2019). DOI: 10.1038/s41586-019-1496-5 5. BisogniV. et al. Ground-state oxygen holes and the metal-insulator transition in the negative charge-transfer rare-earth nickelates. Nat. Commun. 7 , 13017 (2016). DOI: 10.1038/ncomms13017 Funding acknowledgement: This work is supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515. X. F. and D. L. acknowledge partial support from the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4415. Part of the synchrotron experiments have been performed at the ADRESS beamline of the Swiss Light Source (SLS) at the Paul Scherrer Institut (PSI).The work at PSI is supported by the Swiss National Science Foundation through the NCCR MARVEL (Research Grant 51NF40_141828) and the Sinergia network Mott Physics Beyond the Heisenberg Model - MPBH (Research Grant CRSII2_160765/1). Part of research was conducted at the Advanced Light Source, which is a DOE Office of Science User Facility under contract DE-AC02- 05CH11231. Corresponding author: DrWei-Sheng Lee, SLAC National Accelerator Lab.,
[email protected] Figure 1: Representative XAS and RIXS Data (a) O K-edge XAS for nickelates. The red arrows indicate the pre-edge peak, which is a signature of oxygen ligand hybridisation. This pre-edge peak is absent in NdNiO 2 . (b) RIXS map of NdNiO 2 across the Ni L-edge. The XAS is superimposed as black curve. The dashed box indicates the 0.6 eV feature attributed to the hybridisation of rare-earth 5d states and Ni 3d state. (c) RIXS spectrum at a fixed incident photon energy to highlight the 0.6 eV feature in La- and Nd-NiO 2 . Such feature is absent in the LaNiO 3 . Figure 2: LDA + U calculation for LaNiO 2 . The orbital-projected density of states is shown in the right panel. The band structure for NdNiO 2 is qualitative the same as those of LaNiO 2 .