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Empirical surface treatments, such as low-temperature baking (LTB) in a gaseous atmosphere or in vacuum, are important for the surface preparation of Nb superconducting radio frequency (SRF) cavities. These treatments inhomogeneously dope the first $\sim$50 nm of Nb's subsurface and are expected to impart depth-dependent characteristics to its Meissner response; however, direct evidence supporting this remains elusive, suggesting the effect is subtle. In this work, we revisit the Meissner profile data for several LTB treatments obtained from low-energy muon spin rotation (LE-$\mu$SR) experiments [A. Romanenko et al., Appl. Phys. Lett. 104, 072601 (2014) and R. M. L. McFadden et al., Phys. Rev. Appl. 19, 044018 (2023)], and search for signatures of inhomogeneous field screening. Using a generalized London expression with a recently proposed empirical model for a depth-dependent magnetic penetration depth $\lambda(z)$, we obtain improved fits to the Meissner data, revealing that the presence of a non-superconducting surface "dead layer" $d \geq 25$ nm is a strong indicator of a reduced supercurrent density at shallow subsurface depths. Our analysis supports the notion that vacuum annealing at 120 $^{\circ}$C for 48 h induces a depth-dependent Meissner response, which has consequences for Nb's ability to maintain a magnetic-flux-free state. Evidence of similar behavior from a "nitrogen infusion" treatment is less compelling. Suggestions for further investigation into the matter are provided., Comment: 7 pages, 4 figures, 1 table

We report direct measurements of the magnetic field screening at the limits of the Meissner phase for two superconducting Nb samples. The samples are processed with two different surface treatments that have been developed for superconducting radio-frequency cavity applications -- a "baseline" treatment and an oxygen-doping ("O-doping") treatment. The measurements show: 1) that the screening length is significantly longer in the "O-doping" sample compared to the "baseline" sample; 2) that the screening length near the limits of the Meissner phase increases with applied field; 3) the evolution of the screening profile as the material transitions from the Meissner phase to the mixed phase; and 4) a demonstration of the absence of any screening profile for the highest applied field, indicative of the full flux entering the sample. Measurements are performed utilizing the $\beta$-detected nuclear magnetic resonance ($\beta$-NMR) technique that allows depth resolved studies of the local magnetic field within the first 100 nm of the surface. The study takes advantage of the $\beta$-SRF beamline, a new facility at TRIUMF, Canada, where field levels up to 200 mT are available parallel to the sample surface to replicate radio frequency (RF) fields near the Meissner breakdown limits of Nb.

We report measurements of the first-flux-penetration field in surface-treated and coated Nb samples using muon spin rotation ($\mu$SR). Using thin Ag foils as energy moderators for the implanted muon spin-probes, we "profile" the vortex penetration field $\mu_{0} H_{\mathrm{vp}}$ at sub-surface depths on the order of $\sim 10$ $\mathrm{\mu}$m to $\sim 100$ $\mathrm{\mu}$m. In a coated sample [Nb$_3$Sn(2 $\mathrm{\mu}$m)/Nb], we find that $\mu_{0} H_{\mathrm{vp}}$ is depth-independent with a value of 234.5(35) mT, consistent with Nb's metastable superheating field and suggestive of surface energy barrier for flux penetration. Conversely, in a surface-treated sample [Nb baked in vacuum at 120 $^{\circ}$C for 48 h], vortex penetration onsets close to pure Nb's lower critical field $\mu_{0}H_\mathrm{c1} \approx 170$ mT, but increases with increasing implantation depth, consistent with flux-pinning localized at the surface. The implication of these results for technical applications of superconducting Nb, such as superconducting radio frequency (SRF) cavities, is discussed., Comment: 10 pages, 6 figures

In a recent Letter by Romanenko et al., the authors used low-energy muon spin rotation (LE-$\mu$SR) to measure the Meissner screening profile in cutouts from Nb superconducting radio frequency (SRF) cavities, systematically comparing how different surface treatments affect the screening properties of the elemental type-II superconductor. They reported a "strong" modification to the character of the screening profile upon mild baking at 120 $^{\circ}$C for 48 h, which was interpreted as a depth-dependent carrier mean-free-path resulting from a "gradient in vacancy concentration" near the surface. While this observation led to speculation that this surface treatment yields an "effective" superconducting bilayer, we suggest that its likeness to such is accidental and that the behavior is an artifact from the analysis., Comment: 4 pages, 2 figures

Superconducting radio frequency (SRF) cavities, which are critical components in many particle accelerators, need to be operated in the Meissner state to avoid strong dissipation from magnetic vortices. For a defect-free superconductor, the maximum attainable magnetic field for operation is set by the superheating field, $B_{\mathrm{sh}}$, which directly depends on the surface current. In heterostructures composed of different superconductors, the current in each layer depends not only on the properties of the individual material, but also on the electromagnetic response of the adjacent layers through boundary conditions at the interfaces. Three prototypical bilayers [$\mathrm{Nb_{1-x}Ti_xN}$(50 nm)/Nb, $\mathrm{Nb_{1-x}Ti_xN}$(80 nm)/Nb, and $\mathrm{Nb_{1-x}Ti_xN}$(160 nm)/Nb] are investigated here by depth-resolved measurements of their Meissner screening profiles using low-energy muon spin rotation (LE-$\mu$SR). From fits to a model based on London theory (with appropriate boundary and continuity conditions), a magnetic penetration depth for the thin $\mathrm{Nb_{1-x}Ti_xN}$ layers of $\lambda_\mathrm{Nb_{1-x}Ti_xN} =$ 182.5(31) nm is found, in good agreement with literature values for the bulk alloy. Using the measured $\lambda_\mathrm{Nb_{1-x}Ti_xN}$, the maximum vortex-free field, $B_{\mathrm{max}}$, of the superconductor-superconductor (SS) bilayer structure was estimated to be 610(40) mT. The strong suppression of the surface current in the $\mathrm{Nb_{1-x}Ti_xN}$ layer suggests an optimal thickness of $\sim 1.4 \lambda_{\mathrm{Nb_{1-x}Ti_xN}} =$ 261(14) nm., Comment: 13 pages and 8 figures

We report $\beta$-detected nuclear magnetic resonance of ultra-dilute $^{8}$Li$^{+}$ implanted in highly oriented pyrolytic graphite (HOPG). The absence of motional narrowing and diffusional spin-lattice relaxation implies Li$^+$ is not appreciably mobile up to 400 K, in sharp contrast to the highly lithiated stage compounds. However, the relaxation is remarkably fast and persists down to cryogenic temperatures. Ruling out extrinsic paramagnetic impurities and intrinsic ferromagnetism, we conclude the relaxation is due to paramagnetic centers correlated with implantation. While the resulting effects are not consistent with a Kondo impurity, they also differ from free paramagnetic centers, and we suggest that a resonant scattering approach may account for much of the observed phenomenology.

We report depth-resolved measurements of the Meissner screening profile in several surface-treated Nb samples using low-energy muon spin rotation (LE-$\mu$SR). In these experiments, implanted positive muons, whose stopping depths below Nb's surface were adjusted between ~10 nm to ~150 nm, reveal the field distribution inside the superconducting element via their spin-precession (communicated through their radioactive decay products). We compare how the field screening is modified by different surface treatments commonly employed to prepare superconducting radio frequency (SRF) cavities used in accelerator beamlines. In contrast to an earlier report [A. Romanenko et al., Appl. Phys. Lett. 104 072601 (2014)], we find no evidence for any "anomalous" modifications to the Meissner profiles, with all data being well-described by a London model. Differences in screening properties between surface treatments can be explained by changes to the carrier mean-free-paths resulting from dopant profiles near the material's surface., Comment: 15 pages, 5 figures, 2 tables

We report measurements of the Meissner screening profile in a Nb(300 nm)/Al$_{2}$O$_{3}$ thin film using $^{8}$Li $\beta$-detected nuclear magnetic resonance ($\beta$-NMR). The NMR probe $^{8}$Li was ion-implanted into the Nb film at energies $\leq$ 20 keV, corresponding to mean stopping depths comparable to Nb's magnetic penetration depth $\lambda$. $^{8}$Li's strong dipole-dipole coupling with the host $^{93}$Nb nuclei provided a "cross-relaxation" channel that dominated in low magnetic fields, which conferred indirect sensitivity to the local magnetic field via the spin-lattice relaxation (SLR) rate $1/T_{1}$. From a fit of the $1/T_{1}$ data to a model accounting for its dependence on temperature, magnetic field, and $^{8}$Li$^{+}$ implantation energy, we obtained a magnetic penetration depth $\lambda_{0}$ = 51.5(22) nm, consistent with a relatively short carrier mean-free-path $\ell$ = 18.7(29) nm typical of similarly prepared Nb films. The results presented here constitute an important step towards using $^{8}$Li $\beta$-NMR to characterize bulk Nb samples with engineered surfaces, which are often used in the fabrication of particle accelerators., Comment: 16 pages, 4 figures, 1 table

A new high field spectrometer has been built to extend the capabilities of the $\beta$-detected nuclear magnetic resonance ($\beta$-NMR) facility at TRIUMF. This new beamline extension allows $\beta$-NMR spectroscopy to be performed with fields up to 200 mT parallel to a sample's surface (perpendicular to the ion beam), allowing depth-resolved studies of local electromagnetic fields with spin polarized probes at a much higher applied magnetic field than previously available in this configuration. The primary motivation and application is to allow studies of superconducting radio frequency (SRF) materials, close to the critical fields of Nb metal, which is extensively used to fabricate SRF cavities. The details of the design considerations and implementation of the ultra-high vacuum (UHV) system, ion optics, beam diagnostics are presented here. Commissioning of the beamline and spectrometer with radioactive ions are also reported here. Future capabilities and applications in other areas are also described., Comment: Co-authors' misspelled names are fixed to conform with their ORCiD. Typho in eq. (1) is fixed

We report on the stability and magnetic state of ion implanted $^8$Li in single crystals of the semiconductor ZnO using $\beta$-detected nuclear magnetic resonance. At ultradilute concentrations, the spectra reveal distinct Li sites from 7.6 to 400 K. Ionized shallow donor interstitial Li is stable across the entire temperature range, confirming its ability to self-compensate the acceptor character of its (Zn) substitutional counterpart. Above 300 K, spin-lattice relaxation indicates the onset of correlated local motion of interacting defects, and the spectra show a site change transition from disordered configurations to substitutional. Like the interstitial, the substitutional shows no resolved hyperfine splitting, indicating it is also fully ionized above 210 K. The electric field gradient at the interstitial $^8$Li exhibits substantial temperature dependence with a power law typical of non-cubic metals., Comment: 15 pages and 11 figures

We report $\beta$-detected nuclear magnetic resonance ($\beta$-NMR) measurements in Bi$_{2}$Se$_{3}$:Ca (BSC) and Bi$_{2}$Te$_{3}$:Mn (BTM) single crystals using $^{8}$Li$^{+}$ implanted to depths on the order of 100 nm. Above $\sim 200$ K, spin-lattice relaxation (SLR) reveals diffusion of $^{8}$Li$^{+}$, with activation energies of $\sim 0.4$ eV ($\sim 0.2$ eV) in BSC (BTM). At lower temperatures, the nuclear magnetic resonance (NMR) properties are those of a heavily doped semiconductor in the metallic limit, with Korringa relaxation and a small, negative, temperature-dependent Knight shift in BSC. From this, we make a detailed comparison with the isostructural tetradymite Bi$_{2}$Te$_{2}$Se (BTS) [McFadden et al., Phys Rev. B 99, 125201 (2019)]. In the magnetic BTM, the effects of the dilute Mn moments predominate, but remarkably the $^{8}$Li signal is not wiped out through the magnetic transition at 13 K, with a prominent critical peak in the SLR that is suppressed in a high applied field. This detailed characterization of the $^{8}$Li NMR response is an important step towards using depth-resolved $\beta$-NMR to study the low-energy properties of the chiral topological surface state (TSS). With the bulk NMR response now established in several Bi$_{2}$Ch$_{3}$ tetradymite topological insulators (TIs), the prospect of directly probing their chiral TSS using the depth resolution afforded by $\beta$-NMR remains strong., Comment: 14 pages, 10 figures

We have studied a mosaic of 1T-CrSe$_2$ single crystals using $\beta$-detected nuclear magnetic resonance of $^{8}$Li from 4 to 300 K. We identify two broad resonances that show no evidence of quadrupolar splitting, indicating two magnetically distinct environments for the implanted ion. We observe stretched exponential spin lattice relaxation and a corresponding rate ($1/T_1$) that increases monotonically above 200 K, consistent with the onset of ionic diffusion. A pronounced maximum in $1/T_1$ is observed at the low temperature magnetic transition near 20 K. Between these limits, $1/T_1$ instead exhibits a broad minimum with a remarkable absence of strong features in the vicinity of structural and magnetic transitions between 150 and 200 K. Together, the results suggest $^{8}$Li$^{+}$ site occupation within the van der Waals gap between CrSe$_2$ trilayers. Possible origins of the two environments are discussed.

We demonstrate the application of implanted-ion $\beta$-detected NMR as a probe of ionic liquid molecular dynamics through the measurement of $^8$Li spin-lattice relaxation (SLR) and resonance in 1-ethyl-3-methylimidazolium acetate. The motional narrowing of the resonance, and the local maxima in the SLR rate, $1/T_1$, imply a sensitivity to sub-nanosecond Li$^+$ solvation dynamics. From an analysis of $1/T_1$, we extract an activation energy ${E_A = 74.8 \pm 1.5}$ meV and Vogel-Fulcher-Tammann constant ${T_{\mathrm{VFT}} = 165.8 \pm 0.9}$ K, in agreement with the dynamic viscosity of the bulk solvent. Near the melting point, the lineshape is broad and intense, and the form of the relaxation is non-exponential, reflective of our sensitivity to heterogeneous dynamics near the glass transition. The depth resolution of this technique may later provide a unique means of studying nanoscale phenomena in ionic liquids.

We report $\beta$-detected NMR of ion-implanted $^{8}$Li in a single crystal and thin film of the strongly correlated metal LaNiO$_{3}$. In both samples, spin-lattice relaxation measurements reveal two distinct local metallic environments, as is evident from $T$-linear Korringa $1/T_{1}$ below 200 K with slopes comparable to other metals. A small, approximately temperature independent Knight shift of $\sim 74$ ppm is observed, yielding a normalized Korringa product characteristic of substantial antiferromagnetic correlations, but, we find no evidence for a magnetic transition from 4 to 310 K. Two distinct, equally abundant $^{8}$Li sites is inconsistent with the widely accepted rhombohedral structure of LaNiO$_{3}$, but cannot be simply explained by either of the common alternative orthorhombic or monoclinic distortions., Comment: 10 pages, 8 figures

We report measurements on the high temperature ionic and low temperature electronic properties of the 3D topological insulator Bi$_2$Te$_2$Se using ion-implanted $^8$Li $\beta$-detected nuclear magnetic relaxation and resonance. With implantation energies in the range 5-28 keV, the probes penetrate beyond the expected range of the topological surface state, but are still within 250 nm of the surface. At temperatures above ~150 K, spin-lattice relaxation measurements reveal isolated $^8$Li$^{+}$ diffusion with an activation energy $E_{A} = 0.185(8)$ eV and attempt frequency $\tau_{0}^{-1} = 8(3) \times 10^{11}$ s$^{-1}$ for atomic site-to-site hopping. At lower temperature, we find a linear Korringa-like relaxation mechanism with a field dependent slope and intercept, which is accompanied by an anomalous field dependence to the resonance shift. We suggest that these may be related to a strong contribution from orbital currents or the magnetic freezeout of charge carriers in this heavily compensated semiconductor, but that conventional theories are unable to account for the extent of the field dependence. Conventional NMR of the stable host nuclei may help elucidate their origin., Comment: 17 pages, 12 figures, submitted to Phys. Rev. B

We report measurements of the dynamics of isolated $^{8}$Li$^{+}$ in single crystal rutile TiO$_{2}$ using $\beta$-detected NMR. From spin-lattice relaxation and motional narrowing, we find two sets of thermally activated dynamics: one below 100 K; and one at higher temperatures. At low temperature, the activation barrier is $26.8(6)$ meV with prefactor $1.23(5) \times 10^{10}$ s$^{-1}$. We suggest this is unrelated to Li$^{+}$ motion, and rather is a consequence of electron polarons in the vicinity of the implanted $^{8}$Li$^{+}$ that are known to become mobile in this temperature range. Above 100 K, Li$^{+}$ undergoes long-range diffusion as an isolated uncomplexed cation, characterized by an activation energy and prefactor of $0.32(2)$ eV and $1.0(5) \times 10^{16}$ s$^{-1}$, in agreement with macroscopic diffusion measurements. These results in the dilute limit from a microscopic probe indicate that Li$^{+}$ concentration does not limit the diffusivity even up to high concentrations, but that some key ingredient is missing in the calculations of the migration barrier. The anomalous prefactors provide further insight into both Li$^{+}$ and polaron motion., Comment: 14 pages, 9 figures