50 51 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 2 1 / 2 2 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 2 1 / 2 2 Magnetic excitations in infinite-layer nickelates superconductors Related publication: Lu, H., Rossi, M., Nag, A., Osada, M., Li, D. F., Lee, K.,Wang, B. Y., Garcia-Fernandez, M., Agrestini, S., Shen, Z. X., Been, E. M., Moritz, B., Devereaux, T. P., Zaanen, J., Hwang, H. Y., Zhou, K.-J., & Lee,W. S. Magnetic excitations in infinite-layer nickelates. Science 373 , 213–216 (2021). DOI: 10.1126/science.abd7726 Publication keywords: HighTc superconductor; Strongly correlated electronic system; Nickelate; RIXS S ince the 1986 discovery of cuprates (copper oxide materials that are superconducting at high temperatures), scientists have been searching for materials that are superconducting at closer to room temperature. The discovery of infinite-layer nickelate (nickel oxide) superconductors has drawn a lot of attention. An important research focus is to characterise similarities and differences between the nickelates and the high-temperature cuprate superconductors. A key question regards whether the nickelate superconductors are strongly correlated electronic systems, like cuprates. Investigating the structure of magnetic excitations in the nickelate can provide needed clarity to this question. A team of researchers from the SLAC National Accelerator Laboratory, Stanford University and Diamond Light Source recently made the first measurements of magnetic excitations that spread through the newmaterial like ripples in a pond. On Diamond’s Resonant Inelastic X-ray Scattering beamline (I21), they collected data using the Resonant Inelastic X-ray Scattering (RIXS) instrument. RIXS is presently the only instrument that can extract magnetic excitations in themomentum space from thin film samples. The high energy resolution and high photon flux available at I21 also played a vital role in the success of this experiment. In undoped NdNiO 2 , they observed a branch of dispersivemagnetic excitations with a bandwidth of approximately 200meV, suggesting that the spins are strongly antiferromagnetically coupled. These results provide a direct piece of experimental evidence that support the possible exhibition of strong correlations in infinite-layer nickelates. This work reveals the microscopic electronic structures of the nickelate, informing the design and synthesis of new unconventional superconductors. Understanding the richphenomenon inhigh temperature superconducting cuprates is one of the important questions in condensed matter physics. Not only themechanismof the superconductivity, but also unsolved questions such as the origin of the strange metal phase and the implication of intertwined orders have pushed the limits of established theory paradigm. To tackle these challenges, tremendous amount of effort has been spent on synthesising materials with different transition metal ions that mimic the electronic and spin structures of cuprates. This goal, however, proves to be difficult to achieve. The recent discovery of superconductivity in doped mono-valence infinite nickelate is a game-changer 1 . Their crystal structures are very similar to that of cuprates, with NiO 2 planes separated by spacer layers that only contain some rare-earth ions. They were predicted to be isoelectronic to the cuprates: monovalent Ni + characterised by the same 3 d 9 state as Cu 2+ in the cuprates 2,3 . Yet, at this early stage of nickelate superconductivity research, microscopic characterisations from experiments are needed to clarify the similarity and difference between the nickelate and cuprate superconductors 4,5 . A key issue is whether the infinite-layer nickelates also exhibit strong correlation effects arising from a strong on-site Coulomb interaction U, which is known to be a critical ingredient responsible for the rich cuprate phenomenonology. One of the key signatures of a strong U is themanifestation of an intense antiferromagnetic exchange interaction J between neighbouring spins, like those found in cuprates. As for the infinite-layer nickelates, whether a strong U exists is considerably uncertain, as the atomic d-orbitals of monovalent Ni + are more extended than those of divalent Cu 2+ . The difference in the spatial distribution can have a substantial influence on the magnitude of U, which would consequently affect the strength and the sign of J . Indeed, while theories mostly predict an antiferromagnetic coupling between neighbouring spins in the infinite-layer nickelates, the energy scale of J did not reach a consensus: some theories suggest J to be one order of magnitude smaller than in cuprates owing to a large charge transfer energy, whereas some others argue differently. Thus, it is important to directly probe the magnetic structure to clarify this important issue. The main result of this work is the direct observation of magnetic excitations in infinite-layer nickelates Nd 1-x Sr x NiO 2 . Raw RIXS intensity map taken on an undoped NdNiO 2 film (Fig. 1) clearly reveals a branch of magnetic excitations, which exhibit a significant dispersion in the energy-momentum space. The dispersion emanates from the zone centre and reaches maxima at (0.5, 0) and (0.25, 0.25). In addition, the spectral intensity is suppressed near (0.5, 0). Note that the magnetic excitations do not exhibit obvious dispersion along the c-axis, indicating that they are quasi-two-dimensional. The gross features of the dispersion and spectral weight bear a striking resemblance to spin-1/2 Antiferromagnet (AFM) magnons on a 2D square lattice, lending a strong support that the spin exchange interaction in the NdNiO 2 is indeed antiferromagnetic. Importantly, the energy scale of the band width is approximately 0.2 eV, which is comparable to that found in the parent cuprates (~ 0.3 – 0.4 eV) and notably higher than other nickelates. By fitting the dispersion to a linear spin wave theory, we obtain the nearest-neighbour coupling J1 = 63.6 ± 3.3 meV, and a sizable next-nearest-neighbor coupling J2 = -10.3 ± 2.3 meV. The authors also measured doping evolution of the magnetic excitations in Nd 1-x Sr x NiO 2 from x = 0 to 0.225, across the superconducting phase boundary. Upon doping, the mode energy (Fig. 2A) mildly softens and the spectral weight (Fig. 2B) slightly reduces, accompanied with significant broadened spectrum suggesting that the mode becomes overdamped. These behaviours are in fact consistent with spin dilution as expected in a doped Mott insulator as some spins are replaced by holes, indicating the potential relevance of Mott-physics in sculpting the electronic structures of the infinite-layer nickelates. Overall, while the gross feature of the magnetic excitations in nickelate superconductors are similar to those in cuprates, subtle but important differences are observed. First, undoped cuprates are insulators, and the magnetic excitations are sharply defined due to the existence of a long- ranged antiferromagnetic order. In contrast, the undoped nickelate NdNiO 2 is metallic due to the involvement of the Nd 5 d states, which significantly damp the magnetic excitations. In addition, whether an AFM order exists in the undoped compound remains an important open question. The authors note that the doping dependence of the magnetic excitations is also different from the paramagnon in cuprates, which they attribute this difference to a possibly less active longer-range charge dynamics in the nickelates. they anticipate that these observations can further constrain the theories. Importantly, the results establish that the nickelate superconductor possesses a strong antiferromagnetic interaction, placing the material in the strong U regime. This implies that strong correlation effects should be also at play in the nickelate superconductors, laying a foundation for future studies. References: 1. Li, D. et al. Superconductivity in an infinite-layer nickelate. Nature 572 , 624–627 (2019). DOI: 10.1038/s41586-019-1496-5 2. Anisimov, V. I. et al. Electronic structure of possible nickelate analogs to the cuprates. Physical Review B 59 , 7901–7906 (1999). DOI: 10.1103/ PhysRevB.59.7901 3. Lee, K.-W. et al. Infinite-layer LaNiO 2 : Ni 1+ is not Cu 2+ . Physical Review B 70 , 165109 (2004). DOI: 10.1103/PhysRevB.70.165109 4. Mitchell, J. F. A nickelate renaissance. Frontiers in Physics 9 (2021). DOI : 10.3389/fphy.2021.813483 5. Botana, A. S. et al. Low valence nickelates: Launching the nickel age of superconductivity. Frontiers in Physics , 9 . (2022). DOI: 10.3389/ fphy.2021.813532 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. We acknowledge the Gordon and Betty Moore Foundation’s Emergent Phenomena in Quantum Systems Initiative through grant number GBMF4415 for synthesis equipment. Corresponding author: Dr. Wei-Sheng Lee, SLAC National Accelerator Lab,
[email protected] MagneticMaterials Group Beamline I21 Figure 1:RIXS intensity maps versus energy loss and projected in-plane momentum transfer along three high-symmetry directions, as indicated by red arrows in the insets which show a Brillouin zone with the first AFM zone shaded. Measurements were taken at 20 K. The red circles indicate peak positions of the magnetic excitation spectra. Figure 2: Summary of (A) mode energy and (B)spectral weight for three different doping concentrations.