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The superconducting infinite-layer nickelate family has risen as a promising platform for revealing the mechanism of high-temperature superconductivity. However, its challenging material synthesis has obscured effort in understanding the nature of its ground state and low-lying excitations, which is a prerequisite for identifying the origin of the Cooper pairing in high-temperature superconductors. In particular, the superconducting gap symmetry of nickelates has hardly been investigated and remains controversial. Here, we report the pairing symmetry of the infinite-layer nickelates determined by London penetration depth measurements in neodymium-based (Nd,Sr)NiO$_2$ and lanthanide-based (La,Ca)NiO$_2$ thin films of high crystallinity. A rare-earth-specific order parameter is observed. While the lanthanide nickelates follow dirty line-node behaviour, the neodymium-counterpart exhibits nodeless order parameters such as the $(d+is)$ wave. In contrast to the cuprates, our results suggest that the superconducting order parameter in nickelates is beyond a single $d_(x^2-y^2 )$-wave gap. Furthermore, the superfluid density shows a long tail near the superconducting transition temperature which is consistent with the emergence of a two-dimensional to three-dimensional crossover in the superconducting state. These observations challenge the early theoretical framework and propel further experimental and theoretical interests in the pairing nature of the infinite-layer nickelate family., Main manuscript: 26 pages, 3 figures; Supplementary file: 11 pages, 3 figures

Superconductivity can be destroyed by a magnetic field with an upper bound known as the Pauli-limit in spin-singlet superconductors. Almost all the discovered superconductors are spin-singlet, with the highest transition temperature $T_c$ at ambient pressure achieved in the cuprate family. The closest cuprate analogue is the recently discovered infinite-layer nickelate, which hosts substantial structural and electronic similarity to the cuprate. A previous magnetotransport study on Nd$_{0.775}$Sr$_{0.225}$NiO$_2$ has observed an isotropic Pauli-limited upper critical field. Here, we report a large violation (>2 times) of Pauli-limit in every crystallographic directions in La$_{1-x}$(Ca/Sr)$_x$NiO$_2$ regardless of the doping $x$. Such a large violation of the Pauli-limit in all directions in La$_{1-x}$(Ca/Sr)$_x$NiO$_2$ is unexpected and unlikely accounted by a Fulde Ferrell-Larkin-Ovchinnikov (FFLO)-state, strong spin-orbit-coupling, strong-coupling or a large pseudogap. On the other hand, in agreement with the previous report, we observe a Pauli-limiting critical field in Nd$_{1-x}$Sr$_x$NiO$_2$ and the superconducting anisotropy decreases as doping increases, suggesting a spin-singlet pairing. Therefore, superconductivity in La$_{1-x}$(Ca/Sr)$_x$NiO$_2$ could be driven by a non-spin-singlet Cooper pairing mechanism with an attractive high-$T_c$ at 10 K, an order of magnitude higher than the known spin triplet superconductors, favourably extending the application of spin-triplet superconductivity in topological matter, non-dissipative spintronics, and quantum computing., 21 pages, 4 main figures, 2 extended data

Nickel-based complex oxides have served as a playground for decades in the quest for a copper-oxide analog of the high-temperature superconductivity. They may provide clues towards understanding the mechanism and an alternative route for high-temperature superconductors. The recent discovery of superconductivity in the infinite-layer nickelate thin films has fulfilled this pursuit. However, material synthesis remains challenging, direct demonstration of perfect diamagnetism is still missing, and understanding of the role of the interface and bulk to the superconducting properties is still lacking. Here, we show high-quality Nd0.8Sr0.2NiO2 thin films with different thicknesses and demonstrate the interface and strain effects on the electrical, magnetic and optical properties. Perfect diamagnetism is achieved, confirming the occurrence of superconductivity in the films. Unlike the thick films in which the normal-state Hall-coefficient changes signs as the temperature decreases, the Hall-coefficient of films thinner than 5.5 nm remains negative, suggesting a thickness-driven band structure modification. Moreover, X-ray absorption spectroscopy reveals the Ni-O hybridization nature in doped infinite-layer nickelates, and the hybridization is enhanced as the thickness decreases. Consistent with band structure calculations on the nickelate/SrTiO3 heterostructure, the interface and strain effect induce a dominating electron-like band in the ultrathin film, thus causing the sign-change of the Hall-coefficient., 24 pages, 3 main figures, 6 supplementary figures

Among various magnetic thin film heterostructures in solid state Physics, two contrasting mechanisms of the hump-shaped Hall Effects remain ambiguous and debated, namely the overlap of two opposite-signed Karplus-Luttinger Hall-loops associated with inhomogeneous collinear magnetic bubbles with perpendicular anisotropy, or the Topological/geometrical Hall Effect associated with magnetic skyrmions. Their similarity in topology imposes difficulty in discrimination via magnetic imaging. Here, this ambiguity is overcome by the divergence exponent of angle-dependent hump peak fields via magnetic field rotation characterization on several heterostructures. Their difference in sensitivity to in-plane fields reveals that the former mechanism involves higher uniaxial anisotropy than the latter, departing from the pure skyrmion regime described by Ginzburg-Landau framework of triple-q spin-wave superposition. Various materials can be collapsed into a single curve of divergence exponent versus domain wall energy, bridging the crossover of the two aforementioned mechanisms., Comment: 6 Pages and 4 figures in the main text, 9 pages and 5 figures in the supplementary information