Magnetotransport and magnetic properties of amorphous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{NdNi}_5$$\end{document}NdNi5 thin films

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{NdNi}_5$$\end{document}NdNi5 is an intermetallic compound with a bulk Curie temperature (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{Curie}}$$\end{document}TCurie) of 6–13 K. While existing studies have focused on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{NdNi}_5$$\end{document}NdNi5 crystals, amorphous thin-films of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{NdNi}_5$$\end{document}NdNi5 are potentially important since they would be magnetically soft without magnetocrystalline anisotropy, meaning that small external magnetic fields could reverse the direction of their magnetization. Here, we report \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{NdNi}_5$$\end{document}NdNi5 thin-films with a thickness in the 5–200 nm range, deposited by DC magnetron sputtering onto Si(100). Films are amorphous with a weak temperature-dependent resistivity with values ranging between 150 and 300 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu \Omega$$\end{document}μΩ cm. By means of noise spectroscopy, by analyzing the time-dependence of fluctuation-induced voltages, it is found that at low temperatures the resistance fluctuations are due to the Kondo effect. Volume magnetometry indicates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{Curie}} = 70$$\end{document}TCurie=70 K with a magnetic coercive field of 30 mT at 5 K for a 125-nm-thick film. The results are promising for the development of Ferromagnet(F)/Superconductor(S)/Ferromagnet(F) pseudo spin-valve devices based on amorphous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{NdNi}_5$$\end{document}NdNi5 thin films.

www.nature.com/scientificreports/ to reverse the direction of magnetization 13 . Ferromagnetic thin films with small values of H c can also be used in electronic applications where small intensity local fields are available to record the logic state, as in the case of magnetic superconducting memories, both Josephson junctions 14,15 and nanowires-based devices 16 . Moreover, due to their disordered structure, amorphous materials are robust against the presence of impurities and then, in general, easier to fabricate, which is another important property for their potential applications. These are some of the reasons why the study of this class of materials has recently encountered an increasing interest in spintronics and other research fields related to it 17 .

Results
Structural properties. NdNi 5 crystallizes in a CaCu 5 -type hexagonal structure (space group P6/mmm) 10 with lattice parameters a = 4.952 Å and c = 3.976 Å 8,10 . X-ray diffraction traces on polycrystalline NdNi 5 show their highest-intensity peaks at 2θ = 31 • for the NdNi 5 (101) diffraction and at 2θ = 42 • for the NdNi 5 (111) diffraction 8 . The thin films investigated in this study are amorphous, as determined through high resolution X-ray diffraction (XRD) measurements performed in grazing incident configuration. Figure 1 shows high-angle XRD data of 45-and 200-nm-thick NdNi 5 films on Si(100). For both films, the only peak detected is the one related to the (400) diffraction planes of Si. The small-intensity peak observed at 2θ = 33 • in the spectrum of the bare substrate is due to the basis-forbidden reflection from the Si(200) planes 18,19 . As reported previously, it may sometimes occur due to multiple diffractions which can be present when X-ray patterns are acquired using a ω − 2θ scan 19 . In supplementary Fig.S1 we show an additional spectrum taken with a different diffractometer on a 200-nm-thick NdNi 5 film deposited on a different substrate, namely Al 2 O 3 (1120) . Again, only diffraction peaks connected to the substrate are present.
Transport properties. The resistivity, ρ , of the amorphous NdNi 5 (from now on called a-NdNi 5 ) thin films is measured from room temperature down to T = 4.2 K, using a van der Pauw configuration 20 . Previous studies, on single crystals or polycrystalline NdNi 5 samples 8,11 , show pronounced anomalies in the resistivity at T ∼ 7.2 K, close to the magnetic ordering temperature 10 . However, differences in the transport properties originate from the loss of periodic arrangement. While for a crystal ρ is related to electron scattering processes with defects and oscillating ions, the absence of a periodic potential in an amorphous solid generates a diffusive electronic regime, governed by a mean free path, ℓ , of the order of the interatomic distances 21 . In particular, in the case of magnetic amorphous alloys ρ can be strongly affected by magnetic ordering and Kondo effect and can increase below the ordering temperature 22 . At the moment, no information on the transport properties of a-NdNi 5 thin films are available in the literature. However, the amorphousness should determine a dramatic change of the transport properties with respect to the crystalline samples. In particular, according to the Mooij criterion 23 , the temperature coefficient of the resistivity α = (1/ρ)(dρ/dT) of disordered and amorphous metallic systems and alloys containing transition metals is predicted to be almost temperature independent. Furthermore, the decrease in the slope of ρ as a function of T is related to the increase of ρ . For values of ρ ∼ 100-200 µ cm, α is almost zero.
Also negative values of α are observed. However, in the case of magnetic systems this happens in a small range of T, of the order of few Kelvin, close to the magnetic transition 8,11,23 . In the case of magnetic amorphous alloys this behavior, studied by means of electron-transport measurements, is attributed to weak-localization (WL)  www.nature.com/scientificreports/ effects 24-26 rather than to Kondo mechanism, which is related to the presence of localized magnetic impurities in the system 27 . Figure 2 shows the temperature-dependence of the resistivity of a-NdNi 5 films of different thickness. The values of ρ approximately range from 160 to 300 µ cm and they are weakly-dependent on T. These values are similar to those observed in magnetic amorphous alloys containing rare earth elements 22 . The high ρ of the amorphous samples is mainly due to lack of structural order, indicating a small value of ℓ . A rough estimate of ℓ is made on the basis of the Drude model of conduction in metals even if it is not strictly applicable for amorphous systems since in this case the electronic transport is diffusive and not ballistic, meaning that electron-phonon interaction plays a relevant role 28 . Furthermore, in magnetic metallic glasses containing rare earth elements, the resistivity below T Curie is further increased due to the fact that the spin correlation function is spatially coherent only over very short distances 21,22 . In the Drude expression of the mean free path, ℓ = (v F m e )/(n e e 2 ρ) , the Fermi velocity, v F , and the value of the electronic densities at the Fermi level can be estimated as an average of the corresponding quantities of the single elements weighted by their atomic percentage ( n Nd e = 5.60 · 10 22 cm −3 , n Ni e = 1.82 · 10 23 cm −3 , v Nd F = 1.7 · 10 8 cm/s , v Ni F = 3.2 · 10 8 cm/s) 29 . Therefore, using ρ = 230 µ� cm we estimate ℓ ∼ 0.3 nm, a value which is smaller than the interatomic distances of crystalline NdNi 5 . This result indicates that, according to the Ioffe-Regel criterion 30 , the nearly free electron theory of electrical conduction in metals is a poor approximation and other scattering mechanisms should be invoked to describe the conduction in our amorphous films. In this respect, a more detailed analysis is needed to better clarify this point. The slope of the linear part of the curves (approximately from T ∼ 280 K down to T ∼ 80 K) is evaluated for all the samples. The calculated values of α are all extremely small, almost temperature independent (at T = 80 K we find α ∼ 2 × 10 −5 K −1 for the 125-nm-thick film) and even slightly negative for larger values of ρ , in reasonable agreement with the Mooij criterion 23 .
In the inset of Fig. 2 we have plotted the resistivity at room temperature, ρ 300 , as a function of the thickness, d, of the a-NdNi 5 films. ρ 300 does not show any definite trend over the entire thickness range investigated, as expected for amorphous films. Due to the high resistivity of the samples (one order of magnitude larger than for polycrystals of NdNi 5 ) 11 related to the absence of lattice ordering, the contribution to the resistivity connected to the scattering of electrons at the interfaces of the film with both the substrate and the vacuum is negligible. For this reason, the Fuchs-Sondheimer behavior 31 which, in the case of thin metallic films, predicts an increase of ρ when d is reduced, it is not reproduced. Figure 3 shows on an enlarged scale the low-temperature part of the ρ(T) curve of the 200-nm-thick film, chosen as a representative sample (in the inset we show the ρ(T) curve over the full temperature range). The slope of the linear part of the curve (from T ∼ 280 K down to T ∼ 80 K) is evaluated and at T = 170 K it is α ∼ 10 −4 K −1 . The presence of a minimum and an upturn in the temperature dependence of the resistivity is analyzed in terms of a Kondo-like mechanism or a strong electron-electron (e-e) interaction. The data are fitted using both models, as shown in Fig. 3. Kondo model and e-e interaction describe different physical mechanisms. The former relates the modification of resistivity to the electron scattering with magnetic impurities and gives a logarithmic www.nature.com/scientificreports/ type dependence of ρ on the temperature 27 To reproduce the minimum in the ρ versus T curve, A has to be positive. On the other hand, in highly inhomogeneous samples, where weak-localization phenomena are the main factor affecting the transport properties, e-e interactions are the predominant mechanism in determining the conduction of the system 32 . In this case ρ(T) ∼ C/ √ T + D T n . The exponent n in both models is equal to 2, when the temperature dependence of the resistivity is due to e-e scattering, or to 5 in the case of lattice resistance 28 . In the case of inhomogeneous and disordered material different values of n are possible. In the case of granular aluminum oxide films the value n = 1 has been obtained 33,34 . The experimental data are reproduced for both the models with good accuracy, see green and red lines in Fig. 3, and realistic fitting parameters ( A = 0.63 ± 0.03 µ cm, B = 0.046 ± 0.002 µ cmK −1 and n = 1.02 ± 0.03 for the Kondo model, C = 12.1 ± 0.6 µ� · cm K 1/2 , D = 0.046 ± 0.002 µ cm K −1 , and n = 1.03 ± 0.05 in the case of weak-localization). Moreover, the statistical parameters associated to the fitting to the experimental data are very similar. In particular, the reduced χ 2 is equal to 5.2 × 10 −3 for the Kondo model and to 14.7 × 10 −3 in the case of weak-localization. The coefficient of correlation is r 2 = 0.998 for both the models. This makes impossible, based only on the electric transport characterization, to identify the physical mechanism responsible of the upturn in the temperature dependence of the resistivity in our samples. As we will show in detail later on, noise spectroscopy measurements help to shed light on this important issue.
Magnetic properties. Magnetization loops are measured at different temperatures on several samples of different thickness, as reported for example in Fig. 4a where the magnetic moment, m(H), at low fields is shown for the 125-nm-thick film. In the inset of the same figure, the high-field magnetization data at the same representative temperatures are presented. It is evident that the magnetic moment does not show a full saturation up to 1.0 T. This result confirms what already measured on polycrystalline samples where this effect is connected to the magnetic anisotropy of the material 7,8,11 . The low-field data allow to estimate the value of the coercive field, H c , at different temperatures. In Fig. 4b H   Electric noise spectroscopy. The direct-current (DC) transport measurements show evidence for the existence of scattering mechanisms occurring at temperatures below 70 K, where a sign of magnetic activity is observed. In this low-temperature regime, the possible coexistence of electron-electron type interaction and magnetic Kondo effect cannot be excluded. Moreover, in determining the electrical transport of a-NdNi 5 thin films, the magnetic behavior observed near 20 K could also play a role. A powerful experimental technique, which is able to evidence subtle effects on charge motion, is given by noise spectroscopy, which analyzes the time dependence of fluctuation-induced voltages. Noise spectroscopy gives a detailed insight into the basic electrical conduction mechanisms and can be a very informative methodology to understand the kinetic processes and the dynamic behaviors of the charge carriers in the investigated systems, as already demonstrated in a large variety of materials 39 and devices 40,41 . For all the investigated samples, having different thickness [45 nm, Fig. 5a and 200 nm, Fig. 5b] the voltage-spectral density S V shows two different frequency (f) components in the whole temperature range: a 1/f-type noise in the low-frequency region and a "white" frequency-independent noise at higher frequencies.
More information on the fluctuation mechanisms and, consequently, on the electric transport can be extracted by studying the bias current dependencies of the noise amplitude components. In particular: (I) resistance fluctuations are usually characterized by a quadratic current dependence of the 1/f noise 39 , (II) nonequilibrium universal conductance fluctuations produce a linear bias dependence of the 1/f noise 42,43 , (III) fluctuation-induced tunneling processes show an unusual quadratic current dependence of the "white" noise 44 . In the case of our samples, this last mechanism is ruled out, as the frequency-independent part of the experimental does not depend on the current bias and therefore is attributed to the thermal Johnson noise added to the instrumental background noise. In order to investigate the other two fluctuation processes, an analysis of the 1/f component is done as a function of the current and is shown in Fig. 5c, d at temperatures between 9 and 300 K. The noise where the constant term a 0 represents the value of the bias-independent "white" noise amplitude. The good agreement of the simple expression of Equation 1 to the data is testified by the red solid lines in Fig. 5c, d. This makes possible a precise evaluation of the noise parameters a 2 and a 1 , whose temperature dependence is shown in Fig. 6. The most evident fingerprint of Fig. 6 is the very similar behavior of a 2 and a 1 coefficients, both for the thinner film [(panel (a)] and for the thicker one [(panel (b)]. It can be also observed that, above the temperature where the resistivity has the minimum, T min , the quadratic current coefficient a 2 is dominant. Therefore, resistance fluctuations are the noise source, as usually observed in a metallic regime in many materials. Between T min and T ∼ 27 K, the linear current coefficient a 1 becomes significant, indicating that in this case non-equilibrium universal conductance fluctuations are the noise source, as usually observed in a weak-localization regime. Below T ∼ 27 K, the quadratic current coefficient a 2 increases, indicating that resistance fluctuations become relevant again although the a 1 parameter does not vanish, as in the metallic regime. Here, it is important to note that being a 2 and a 1 the quadratic and the linear current term, they affect differently the amplitude of the noise spectral density, depending on the value of the bias current.
The nature of these observed fluctuation processes can be understood by studying the magnetic field dependence of the noise components, as shown in Fig. 6, panels (c) and (d). These plots indicate that at high temperatures, above and around T min , no magnetic effect is visible. This is expected, for the applied values of the magnetic field (0-0.15 T), in the case of standard resistance fluctuations, characteristic of a metallic regime, and in the case of nonequilibrium universal conductance fluctuations, characteristic of a weak-localization regime. In the lowtemperature region below 27 K, instead, the effect of a relatively weak magnetic field on the resistance fluctuations is clearly observed. The type of fluctuation detected cannot be attributed to the growth of ferromagnetic domains which is typically associated with a Barkhausen magnetic noise, whose frequency dependence is completely different from the observed one [45][46][47] . Moreover, as evident in Fig. 6, a reduction of the 1/f noise amplitude (i.e., a 2 coefficient) is measured by increasing the value of the applied magnetic field, and this effect is enhanced by lowering the temperature. This experimental finding, reported also for granular aluminum oxide thin films 33,34 , gives a further indication in favour of the occurrence of magnetic noise fluctuations to be ascribed to the presence of magnetic impurities found in a Kondo-like regime, as also observed in disordered amorphous alloys 22 .

Discussion
We investigate amorphous NdNi 5 thin films deposited by DC magnetron sputtering. The thickness of a-NdNi 5 is varied between 5 and 200 nm with a resistivity of the order 250 µ cm , which is weakly temperature dependent. The upturn observed in the DC resistivity at low temperatures is interpreted as being due to a Kondo-like mechanism or strong electron-electron interactions, is analyzed using electronic noise spectroscopy. We find for temperatures below 100 K a linear current dependence of the 1/f noise amplitude, which is indicative of non-equilibrium universal conductance fluctuations characteristic of a weak-localization regime. For T < 25 K Kondo effect contributes to the resistance fluctuation processes. The presence of these two different temperature regimes is also observed when measuring the temperature dependence of the magnetic moment of these samples which indicate a T Curie = 70 K in the 125-nm-thick sample. Interestingly, this study reveals the coexistence of Kondo effect and ferromagnetic ordering as already reported in different classes of crystalline materials, such as for instance ternary intermetallic Ce-and Np-based compounds 37,48,49 . Although unusual, this occurrence is not unexpected in amorphous ferromagnets, where structural and compositional disorder may produce a distribution of internal effective exchange field 50,51 , which could result in the increase in T Curie observed in our amorphous films with respect to crystalline specimens 13 . Further experimental investigation, such as specific heat and magnetoresistance measurements as well as a deeper structural characterization, may help in gaining insight into this system 37,52 . Finally, it is important to underline that the values obtained for H c and M s are smaller than those for bulk and polycrystalline samples, and are very promising for the development of superconducting spin valves based on a-NdNi 5 films.

Methods
Thin films of a-NdNi 5 in the thickness range of 5-200 nm are deposited in an ultra-high vacuum DC diode magnetron sputtering system on Si(100) substrates. Control films are sputtered on Al 2 O 3 (1120) to investigate the role of the substrate on the growth mechanism. By depositing the samples in different conditions, including the Ar pressure, P Ar , in the 10 −3 mbar range, the substrate temperature, T Sub , and the sputtering power, P, no substantial differences are detected. The films investigated are grown at P Ar = 6.4 · 10 −3 mbar, T Sub = 200 • C , and P = 250 W, while the base pressure inside the sputtering chamber is in the low ∼ 10 −8 mbar range. Typical deposition rates are 0.11 nm s −1 monitored by a quartz crystal monitor previously calibrated by measuring, with a 3D optical profilometer, the thickness of a deliberately deposited film. XRD measurements are performed in grazing incident configuration by using a Rigaku Smartlab diffractometer. The primary arm is equipped with a double-bounce channel cut Ge(220) monochromator and an incident slit of 0.1 mm, which provide a monochromatic CuKα1 ( = 1.5406 Å) radiation. X-ray diffraction data reported in Supplementary Information are acquired by a Bruker D2 diffractometer in a specular Bragg-Brentano www.nature.com/scientificreports/ geometry. The system operates with a source of CuKα ( = 1.54184 Å) and CuKβ ( = 1.39222 Å) radiation at 30 kV and 10 mA. The resistivity of the films is measured using a 4-probe van der Pauw configuration with Ag contacts realized at the four corners of unpatterned films. The high-resitivity value of the Si substrate, ρ = 1.3 � cm at room temperature, ensures that no role is played by the substrate in the measurement of the electron transport properties of the films.
The magnetic characterization is performed using a vibrating sample magnetometer. In all the reported measurements the magnetic field is applied parallel to the sample surface.
The noise characterization is carried out in a closed-cycle refrigerator at temperatures between 8 and 300 K with a temperature stabilization of ± 0.1 K. Low-noise DC and AC electronic bias and readout are used 53,54 . A Signal Recovery 5113 amplified the AC signal, which is acquired by a dynamic signal analyzer type HP35670A controlled with LabVIEW software. The peaks visible in the voltage-noise spectra are due to external spurious sources and, therefore, are not considered in the analysis, being the relevant information in the background curves. The external magnetic field, used for noise measurements, is generated with a dipole electromagnet, type 3470 from GMW Associates. The maximum value, obtained with an operating current of 3.5 A, is 1500 Gauss.