Isotropic Pauli-Limited Superconductivity in the Infinite-Layer Nickelate Nd0.775Sr0.225NiO2 Bai Yang Wang,*1,2 Danfeng Li,2,3 Berit H. Goodge,4 Kyuho Lee,1,2 Motoki Osada2,5, Shannon P. Harvey2,3, Lena F. Kourkoutis,4,6 Malcolm R. Beasley3, and Harold Y. Hwang*2,3 1Department of Physics, Stanford University, Stanford, CA 94305, United States. 2Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, United States. 3Department of Applied Physics, Stanford University, Stanford, CA 94305, United States. 4School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, United States. 5Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, United States. 6Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, NY 14853, United States. *e-mail: [email protected]; [email protected]. ABstract The recent observation of superconductivity in thin film infinite-layer nickelates1–3 offers fresh terrain for investigating superconductivity in layered oxides4. A wide range of perspectives5–10, emphasizing single- or multi-orbital electronic structure, Kondo or Hund’s coupling, and analogies to cuprates, have been theoretically proposed. Clearly further experimental characterization of the superconducting state is needed to develop a foundational understanding of the nickelates. Here we use magnetotransport measurements to probe the superconducting anisotropy in Nd0.775Sr0.225NiO2. We find that the upper critical field is surprisingly isotropic at low temperatures, despite the layered crystal structure. We deduce that under magnetic field, superconductivity is strongly Pauli-limited, such that the paramagnetic effect dominates over orbital de-pairing. Underlying this isotropic response is a substantial anisotropy in the superconducting coherence length, at least four times longer in-plane than out-of-plane. A prominent low-temperature upturn in the upper critical field indicates the likelihood of an unconventional ground state. Main A key characteristic of layered superconductors is an upper critical field Hc2 often exhibiting substantial anisotropy g º Hc2,||/Hc2,^, where Hc2,|| and Hc2,^ indicate magnetic fields in the a-b plane and along the crystal c-direction, respectively. In layered oxides such as cuprates11, ruthenates12, and cobaltates13, the anisotropy reflects the two-dimensional (2D) nature of both the crystal and electronic structure. The case for the recently discovered infinite-layer nickelates is a priori interesting: although it shares the same crystal structure as infinite-layer cuprates, calculations indicate both a quasi-2D hole band and three-dimensional (3D) electron bands are present in the nickelates for a broad range of electron interactions5,6. The relative importance of these bands is a subject of much interest with respect to the superconducting state. More generally, nickelates provide a new system within which to explore longstanding debates on the role of dimensionality for superconductivity. With these motivations, we have studied the superconducting anisotropy through resistive measurements of Hc2 in thin-film Nd0.775Sr0.225NiO2. This composition has the highest crystallinity in our recent investigations, as well as a superconducting transition temperature Tc among the peak values observed across the superconducting dome2. As previously reported, our optimal samples are capped with SrTiO3, and are bounded in thickness to below ~10 nm; above this we observe mixed-phase formation or decomposition. A high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image is shown in Fig. 1a. In good agreement with prior observations, c-axis oriented crystalline coherence is observed throughout the film, together with extended defects primarily based on vertical Ruddlesden-Popper (RP) type faults. Figure 1b, c shows the temperature-dependent resistivity r(T) in the low temperature region, with varying magnetic field applied along the c-axis (H^) and the a-b plane (H||, transverse geometry). While minimal magnetoresistance is observed in the normal state, the superconducting transition is suppressed with increasing magnetic field, allowing us to extract the temperature dependence of Hc2. Figure 2 shows the main result of this study: the magnetic field-temperature phase diagram of Hc2,^ and Hc2,||, down to 0.5 K. Here Tc and Hc2 are identified as the resistive transition reaching 50% of the normal state, as discussed below. Overall, the most striking feature is that Hc2 is largely isotropic at low temperatures (as emphasized in Fig. 2a inset), despite the layered crystal 5,6 structure, the quasi-2D nature of the !"#$%# hole band and the thin film geometry. Does this reflect a rather isotropic electronic structure, and superconducting coherence length, as unusually 14 found in (K,Ba)FeAs2 (ref. )? Or does it have a different fundamental origin? Our aim is to address this central question. As we argue below, Hc2 is dominated by the isotropic spin response, rather than orbital effects, over much of the phase diagram. Such strongly Pauli-limited superconductivity in nickelates appears unique among the layered oxides. We start by examining the magnetoresistive transition observed in Fig. 1b, c. The visible broadening can have contributions from static compositional inhomogeneity, superconducting fluctuations, and vortex motion in this type-II superconductor1,9. In terms of inhomogeneity, the RP-type faults likely give rise to a spread in Tc. Regarding superconducting fluctuations, we fit the onset of superconductivity following the 2D Aslamazov-Larkin (AL) formulism15,16, with AL representative fits shown in the insets of Fig. 1b, c. From this we obtain a corresponding Tc , above which superconducting fluctuations significantly impact the resistive transition. We note that this regime also includes effects arising from static inhomogeneities. As for vorteX motion, we investigate its contribution in scaled Arrhenius plots, as shown in Fig. 3a, b. Between the normal state and the measurement noise floor, exponentially decreasing resistivity is seen for both orientations across several orders of magnitude. This is well described 17 by thermally-activated vorteX motion : r(T,H) = r0(H) exp(U0/kBT) where r0 is the resistivity prefactor, U0 is the activation energy and kB is Boltzmann’s constant. Figure 3c shows U0 17,18 extracted using this form. Similar to cuprates , U0 for H^ and H|| exhibits regions of power- law dependence on magnetic field. Note that the success of this fitting implies that vortex motion is relevant for H||, and the large difference in U0 values between H^ and H|| indicates substantial VM vorteX-motion anisotropy. We define Tc as the temperature above which resistivity deviates VM from thermally-activated behavior, and attribute the resistive transition below Tc predominantly to vortex motion. Summarizing the onset of fluctuations and vortex motion, we construct the phase diagrams in Fig. VM AL 4a, b. In addition to Hc (T) and Hc (T), we plot representative candidate proxies for Hc2: 90% 50% 1% Hc (T), Hc (T) and Hc (T), corresponding to the resistivity reaching 90%, 50%, and 1% of VM AL the normal state. Between Hc (T) and Hc (T) (extrapolating to 27% and 80% of the resistive transition for H = 0 T) there is a regime where the magnetoresistance can serve as a reliable indicator of Hc2, free from vorteX creep or superconducting fluctuations which tend to 19 50% under/over-estimate Hc2, as well as distort its functional form . Hence, we use Hc to measure Hc2; our conclusions are robust to variations within this regime aside from specific numerical values. We next focus on magnetotransport near Tc, taking advantage of the simplification in the critical regime arising from diverging length scales. Here the central observation is a T-linear 1/2 dependence of Hc2,^ and a T dependence of Hc2,|| (Fig. 4c). We first consider purely orbital de- pairing (superconductivity suppressed by the energy cost of the field-induced supercurrent), with 1/2 the characteristic T dependence of Hc2,|| arising from 2D confinement. This is commonly observed for superconductors thinner than the Ginzburg-Landau (GL) coherence length20,21, and is a reasonable possibility here, given the thickness limits for stabilizing Nd0.775Sr0.225NiO2. In 22 such geometries, Hc2 is well described by the linearized GL form (generalized to an anisotropic, c-axis thickness-limited superconductor) as 01 - &'(,* (-) = ( 81 − ;, (1) 23456(0) -' > √1201 - ( &'(,∥(-) = 81 − ; , (2) 23456(0)! -' where f0 is the flux quantum, xab(0) is the in-plane zero-temperature coherence length, and d is the superconducting thickness. Using these forms, we extract xab(0) = 42.6 ± 0.1 Å and d = 225 ± 7 Å. In previous studies on other material systems, d derived from such analysis was in good quantitative agreement with the physical thickness of the film20,23, except for cases with dominant spin-orbit scattering24,25, for which the thickness is underestimated. Here we deduce a thickness that is 2.3 – 3 times larger than the observed thickness of the film (Table S1, Supplementary Information), which we take to be an unphysical discrepancy. Furthermore, this analysis presumes confinement preventing vortex entry for H||, inconsistent with evident vortex motion in this orientation (Fig. 3c). Finally, 2D confinement of an orbital-limited superconductor usually leads to a dramatic enhancement of Hc2,|| over Hc2,^ that