Kondo effect and superconductivity in niobium with iron impurities

Kondo effect is an interesting phenomenon in quantum many-body physics. Niobium (Nb) is a conventional superconductor important for many superconducting device applications. It was long thought that the Kondo effect cannot be observed in Nb because the magnetic moment of a magnetic impurity, e.g. iron (Fe), would have been quenched in Nb. Here we report an observation of the Kondo effect in a Nb thin film structure. We found that by co-annealing Nb films with Fe in Argon gas at above 400 ∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}C for an hour, one can induce a Kondo effect in Nb. The Kondo effect is more pronounced at higher annealing temperature. The temperature dependence of the resistance suggests existence of remnant superconductivity at low temperatures even though the system never becomes superconducting. We find that the Hamann theory for the Kondo resistivity gives a satisfactory fitting to the result. The Hamann analysis gives a Kondo temperature for this Nb–Fe system at ∼\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document} 16 K, well above the superconducting transition onset temperature 9 K of the starting Nb film, suggesting that the screening of the impurity spins is effective to allow Cooper pairs to form at low temperatures. We suggest that the mechanism by which the Fe impurities retain partially their magnetic moment is that they are located at the grain boundaries, not fully dissolved into the bcc lattice of Nb.

electron-phonon interactions. The formation of a phase coherent ground state of many Cooper pairs results in resistance vanishing when the temperature is lowered to below T c 29 . When magnetic impurities are incorporated into the system, the interplay between these two competing ground states has been a subject of great interest 1,[30][31][32][33][34][35] . In superconducting alloys, Kondo effect can change its superconducting properties greatly [36][37][38] . The competition between superconductivity and Kondo effect has been of great interests [39][40][41][42] . In recent years, the Kondo effect has also been studied in many new superconductors materials [31][32][33][34][35] , in 2D topological superconductors and 3D topological insulators 43,44 . Similar resisivity minimum was also observed in high-T c superconductors 45 .
Nb is an important superconducting material for its stability and for having the highest superconducting transition temperature (9.2 K) among the elemental metals. Superconducting properties of Nb have been investigated intensely over the years [46][47][48][49][50][51] and in theories 52,53 . Thin films of Nb are of great interest for model systems 54 and devices 55 . NbSe 2 is a close relative of Nb, a recent experiment 56 revealed that superconductivity and magnetism can coexist in NbSe 2 . Thus it is of great interest to explore if one can create Kondo effect in Nb as well in spite of early studies 3,4,6 that suggested the quenching of Fe magnetic moment in Nb. Here we report transport measurements of sputtered Nb thin films containing low density of Fe impurities that clearly demonstrate the existence of the Kondo effect in a Nb thin film structure.

Results and discussion
The effects of co-annealing with Fe. Figure 1 shows the main findings of this work. Figure 1a shows the temperature dependence of the resistivity of an as-sputtered sample in zero field and at 5 T. The superconducting transition temperature T c is defined as the temperature at which the sample resistivity has dropped to 1/2 of its normal state value (at 10 K). The onset temperature of superconductivity T * c is defined as the data point where the resistivity shows a clear drop. The as-sputtered sample shows T c = 8.875 K in zero magnetic field. At 5 T, the ρ-T is a smooth monotonic function of temperature down to 2.0 K. Figure 1b shows the temperature dependence of the resistivity of the sample annealed at 300 • C, also in zero field and at 5 T. Immediately one notices the normal state resistivity is increased and the superconducting transition T c is reduced. Yet, the ρ-T at 5 T behaves very similar to that of the as-sputtered sample in Fig. 2a. The ρ-T curve at 5 T is also a monotonic function of temperature. Figure 1c-e show the ρ-T curves (at 0 T and 5 T) for the samples annealed at 400 • C, 500 • C, and 600 • C, respectively. Two distinct features are immediately obvious to the eyes: there is a minimum in the ρ-T in zero field and at 5 T, and the sharp zero-field superconducting transition is replaced by a gradual decrease in resistivity. At 5 T, the ρ-T curves show a minimum around 20 K. Between 5 and 20 K, the ρ-T curves show the characteristic logarithmic dependence o temperature often found in Kondo effect systems 7,8 . In Fig. 1f, the data in Fig. 1e are re-plotted in a semi-log plot, with x-axis being logarithmic. The regime of −lnT is marked by a dashed straightline, indicating the logarithmic behavior characteristic of the Kondo effect.
Understanding the "normal" behavior. In Fig. 1a,b, the temperature dependence of the resistivity in a magnetic field of 5 T, when the superconductivity in the system is suppressed, behave as expected for "pure" Nb films. With decreasing temperature, the resistivity decreases monotonically towards a constant value. We made an attempt to fit these two data sets to the normal metal resistivity formula 57 ρ(T) = ρ 0 + aT 2 + bT 5 that contains the residual resistivity (constant ρ 0 ), the Fermi liquid contribution (electron-electron scattering, ∼ T 2 ), and the electron-phonon interaction ( ∼ T 5 ). The fitting (not shown) is reasonably well considering the fact that it did not consider the effects of grain boundary scattering 58 and surface scattering 59 . In the early study of the normal state resistivity of Nb 48 , it was argued that there should be a T 3 term in the ρ-T due to the inter-band scattering (Nb conduction band consists of a mixture of s-d bands 53 ), in addition to the three terms discussed above. We found that by adding a T 3 term can indeed improve on the data fitting to almost perfection, however, the fitting parameters for the coefficients for the Fermi liquid T 2 and the electron-phonon T 5 terms become negative, i.e. nonphysical. Thus we believe the standard three terms are adequate description of the normal state resistivity in our as-sputtered and 300 • C annealed Nb films. Figure 1b deserves some special attention. After co-annealing at 300 • C, the T c of the Nb film is reduced slightly, by 1.4 K, yet there is no Kondo effect even at 5 T magnetic field when the superconductivity is fully suppressed. We believe this T c reduction is the formation of NbO due to the substrate SiO 2 , as also found previously 60 . NbO is a metal which becomes superconducting at 1.2 K 61 . Thus it is likely the layer of Nb that is in intimate contact with SiO 2 layer is converted to NbO which then reduces the T c of the top layer of Nb by the proximity effect 62 . It should be noted that NbO is itself an interesting quantum material 63,64 . Ruling out localization. In disordered metals, in addition to the Kondo effect, there is another mechanism that can give rise to an anomalous increase in resistance as a function of decreasing temperature, namely the weak localization (for a review , see 65 ). At very low temperatures, the quantum interference between the elastic scattering paths in a disordered metal can cause additional resistance. This resistance decreases with increasing temperature, before the eventual rise again in resistance due to the electron-phonon scattering. This weak localization effect can also lead to a resistance minimum without any magnetic impurities. We believe this is not what happens in our samples. For weak localization, adding magnetic field will suppress the quantum interference effects, resulting in a negative magneto-resistance 66 . Here, as shown in Fig. 2, the magneto-resistance below 30 K is positive for all samples.
As shown in Fig. 2, the R vs. T curves at different magnetic fields are shown, for the samples annealed at (a) 400 • C; (b) 500 • C; (c) 600 • C. They all clearly show a resistance minimum around a T min ∼ 10-20 K. We also tried annealing in shorter time, 30 min., the effects are equivalent to that at lower temperatures for a longer time. For samples annealed at 400 • C, 500 • C and 600 • C, the resistance minima T min appear at ∼ 14 K, 16  www.nature.com/scientificreports/ K, respectively. In Kondo's model 8 , with decreasing temperature, the resistance minimum is where the scattering from the magnetic impurities start to dominate in the electron transport (we should point out that the charge carriers are hole-like in Nb due to the anisotropic shape of its band structure 67 ). Below T min , in zero magnetic field, the resistance increases with decreasing temperature, then reaches a maximum and starts to decrease again. For the 400 • C-annealed sample, the resistance drops to zero near 2 K, while for 500 • C and 600 • C-annealed samples, the resistance remains at a large value down to 2 K. Nevertheless, we attribute the low-T decrease in resistance to the onset of superconductivity in the sample, or more precisely small regions of the sample becoming superconducting, even though the system as a whole does not have a percolating path of superconducting regions. This picture is confirmed when we apply magnetic field. As shown in Fig. 2a-c, at field larger than 3 T, the resistance increases with decreasing temperature to approach a saturation. The superconductivity is completely destroyed.
Choosing theoretical framework for data analysis: the Hamann formula. To analyze the R-T curves in Fig. 2, we need a theoretical framework for the data analysis. In the original Kondo model 8 , the resistivity has a logarithmic dependence on temperature, or −ln(T/T K ), where T K is the Kondo temperature. In Fig. 2  www.nature.com/scientificreports/ we plot the resistance vs. log(T). There is indeed a region below T min that the R(T) curves have a logarithmic dependence on temperature. Upon further decrease in temperature, however, the resistance levels off. This feature was not explained by Kondo 8 . It was later understood that the logarithmic divergence as T approaches absolute zero in Kondo's model is avoided by a screening effect of the impurity spin by a cloud of antiparallel spins from the conduction electrons, due to their antiferromagnetic exchange interactions 9,11,68 . This occurs below T K . The screening of the impurity spin by the Kondo cloud 69 leads to a levelling off in the scattering rate (hence resistivity) as T approaches absolute zero. For analyzing experimental results on temperature-dependent resistivity, however, researchers need an analytical formula. The resistivity formula given by Hamann 11 was the closest in describing experimental results 15 . In early experiments people adopted an empirical approach to mimic theoretical results of complex forms 13,17 . Recently, using empirical approach for the numerical renormalization group (NRG) result has gained wide popularity [70][71][72][73][74] . We also attempted to use this empirical NRG approach to fit our data in Fig. 2. However, we found that there is an underlying inconsistency in the analysis: the extracted T K is much larger than T min , where the resistance clearly deviates from the normal metallic behavior (Drude + Fermi liquid + electron-phonon scattering).
Thus we decide to follow a recent study of the Kondo effect in VSe 2 75 and adopt the resistivity formula derived by Hamann 11 using the theoretical approach proposed by Nagaoka 10 ,  www.nature.com/scientificreports/ where R 0 (Drude), q (Fermi liquid), p (electron-phonon), R 1 (Hamann's unitarity limit), T K (Kondo) are fitting parameters. The fitting curves using Eq. 1 are shown in Fig. 2 overlaying on top of the experimental data points. The agreement is striking. We found that if we set the impurity spin S = 1/2 or larger, the fitting routine cannot converge. This was known to the field 16,22 for quite sometime, and perhaps the main motivation for the empirical approaches 13,17,22,70 . Thus we also kept S as a fitting parameter. We find that the extracted S = 0.1-0.17, the extracted Kondo temperature T K = 15-24 K, for magnetic field = 0-8.5 T.
Kondo temperature T K and T min . In Fig. 3, we compare the Kondo temperature with the resistance minimum temperature T min . The extracted Kondo temperatures T K are consistent with the physical picture of Kondo 8 that the spin-flip scattering starts to dominate at temperatures around the resistance minimum. In comparison, the Kondo temperatures T K extracted using the empirical NRG approach are much larger than T min . In comparison, the remnant superconductivity sets in at T * c = 3 K. This is consistent with the expectations that the localized spin on Fe is sufficiently screened that the electron-phonon interaction is strong enough to create localized, non-coherent, superconducting regions.
Coherence length vs. mean free path. To gain some insights into the nature of the electronic states in the as-sputtered and 300 • C annealed Nb films, i.e. the "normal" films, we measured the H c2 -T phase diagrams near T c for these two samples, as shown in Fig. 4. The H c2 (T) curves show linear temperature dependence near T c , in agreement with the Ginzburg-Landau (GL) theory 62 . From the slopes of the H c2 (T) curves, using the GL theory we estimate ξ to be about 12.9 nm for the as-sputtered sample, and 6.2 nm for the annealed at 300 • C sample. We also estimated the Drude mean free paths l = k F /ne 2 ρ xx using their 10 K resistivities, l ∼ 18.5 nm for the as-sputtered, and 7.2 nm for the annealed at 300 • C samples, respectively. These results suggest that the  www.nature.com/scientificreports/ coherence length is of the same order of magnitude as the mean free paths. Since 1/ξ = 1/ξ 0 + 1/l , where ξ 0 is the intrinsic coherence length, l is the mean free path, we conclude that the superconducting coherence length in our Nb films is determined by the electronic mean free paths. In Table 1, we summarize some of the key parameters of the five samples discussed in Fig. 1.

Why is the magnetic moment of Fe not quenched in Nb thin films?
It is well-known that the magnetic moment of Fe impurities will be quenched when the Fe atoms are dissolved in Nb 3,4,6 . In those systems, mixing of Fe into Nb was done at 1200 • C for a time period of a week. It is expected that Fe atoms are well incorporated into the bcc lattice of Nb, even though their exact locations are unknown. Here, given the highest temperature we used, 600 • C, the Fe atoms are expected to be adsorbed between the crystalline grains, i.e. not fully dissolved into the bcc lattice of the Nb crystalline grains. The fact that the extracted spin parameter S ∼ 0.10-0.17 is small is consistent with Anderson's theory 5 on local magnetic moment formation in metals.
The sign of magneto-resistance. The sign of the magneto-resistance of the Kondo effect contribution should be negative since the magnetic field tends to destablize the virtual bound state between the localized moment and the conduction electrons. As shown in Fig. 2, the sign of magneto-resistance here is positive, the resistance increases with magnetic field. In the Au-Fe system 76 , the raw data of magneto-resistance was also positive, only after subtracting out the non-Kondo part can one see the negative magneto-resistance. Unfortunately, such a subtraction procedure cannot be carried out for the Nb-Fe system here due to the residual superconductivity in the system. As shown in Supplementary Fig. SI-2 (in Supplementary Information), we re-plot the data in Fig. 2c as a function of magnetic field for the Nb sample annealed at 600 • C. In Supplementary Fig. SI-2a, below 10 K, there is a large positive magneto-resistance effect due to the destruction of the Cooper pairs with increasing field. Above 10 K, shown in Supplementary Fig. SI-2b, the magneto-resistance effect is small, but still positive. This is the well known "classical" magneto-resistance of metals due to grain boundaries and Fermi surface anisotropy as discussed by Giordano 76 . However, due to the presence of the residual superconductivity in the Nb-Fe system here, the subtraction procedure of Giordano 76 cannot be applied. Thus we rely on the curve fitting using Hamann's theory 11 .

Conclusions
We report a resistance anomaly of sputtered Nb films after co-annealing with Fe in inert gas at different temperatures up to 600 • C. We found that with an increase of annealing temperature from 300 to 600 • C, the superconducting transition temperature ( T c ) of Nb film changes sharply from 8.9 K to below 2 K, even though there are hints of superconductivity remaining below 3 K for samples annealed at 600 • C for 60 min. Moreover, for films annealed at above 400 • C, a R-T resistance minimum is observed which persists under different magnetic field up to 8.5 T. This resistance minimum can be well fitted with the Hamann resistivity formula. We suggest that the survival of the magnetic moment of Fe impurities in Nb is due to their not being fully dissolved into the bcc structure of Nb. In spite of the strong agreement with the Hamann theory we found in this report, a few words of caution are warranted. First, we do not have direct evidence that the Fe impurity atoms retain their magnetic moments, a direct test (e.g. using spin-polarized STM) would be highly desirable. Second, the formation of the Kondo bound states may be detectable in the change of effective mass of the charge carriers.

Methods
The five samples used in this paper are from the same Nb thin film wafer. Our Nb film has a thickness of 120 nm, deposited on SiO 2 /Si substrates by DC magnetron sputtering, as reported previously 77,78 . The SEM micrographs show that the films are granular in nature, with average grain size around 20 nm in as-sputtered sample and the grain sizes increase with annealing temperature, up to about 40 nm at 600 • C, as shown in Supplementary  Fig. SI-1 in the Supplementary Information. The Nb films were patterned into 4-probe devices, using standard photo lithography and ion beam etching. The sample region is a micro-bridge of sizes 1 mm × 10 µ m. The sample was annealed in the thermal annealing chamber filled with flowing argon gas (purity: 99.99% , pressure: 50 Pa, flow rate: 20 sccm) at different temperatures (300 • C, 400 • C, 500 • C and 600 • C) and for different duration (30 min and 60 min). During the annealing, the Nb film chip was held using an iron clip. Even though the annealing temperature is far below the melting point (1538 • C) for Fe, the bombardment by argon gas molecules was enough to transport a minute amount of Fe into the Nb film sample. This "co-annealing" method of introducing Table 1. Summary of the parameters measured from the as-sputtered Nb film and the annealed samples.