Breakdown of magnetism in sub-nanometric Ni clusters embedded in Ag

XRD data of the as-deposited and annealed Ni₆Ag₉₄ films are shown in figure 1 together with a Ag film as a control sample. Due to the preparation method, the films show a strong (111) texture, as observed in similar DC sputtered films [22, 23]. A unique peak is observed, which corresponds to the Ag (111) reflection. Note the clear asymmetry of the (111) peak due to the presence of Cu-K${\alpha }_{1}$ and ${\rm{K}}{\alpha }_{2}$ wavelengths, indicative of a very narrow peak (large crystallite size). A much weaker peak is also observed in the Ag film in the (200) position. Due to the low Ni concentration of the samples and/or small nanoparticle sizes, XRD does not show any trace of the Ni face centered cubic (fcc) lattices, even in the annealed samples.

To determine the lattice parameters of the Ag-rich phase as a function of annealing temperature, the (111) peak has been fitted to a pseudo-Voigt function as implemented in the FullProf software [24]. The results of the fit for the lattice parameters are shown in figure 2 together with an example of the fit. The as-deposited film shows a lattice parameter similar to that of bulk fcc Ag ($a=4.09\;\mathring{\rm A}$ [25]). Annealing provides thermal energy, which allows the system to evolve towards a more ordered and stable structure, as indicated by the monotonous narrowing of the Ag (111) peak with annealing, indicative of a large crystallite size. The lattice parameter, even though it contracts slightly at 100 °C, presumably due to stress relaxation from the fabrication method, at 200 °C recovers a final value ($a\approx 4.085$ Å) that is basically that of the bulk ($a=4.09$ Å).

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The near-edge region of the XAS spectra (XANES) is shown in figure 3 for the as-deposited and annealed Ni₆Ag₉₄ films together with the XANES spectra of Ag and Ni foils, as references. There is a notable change in the shape of the jump at the edge position (E₀) between the samples as-deposited and annealed at 100 °C and the annealed at 200 °C and 400 °C. In the latter two films, both the shape and the edge position resemble those of bulk fcc Ni, but the films as-deposited and annealed at 100 °C are shifted $\approx \;-1\;{\rm{eV}}$ with respect to the bulk. This indicates that electronic changes are taking place due to atomic rearrangements. Furthermore, from inspection of the structure of the XANES signal just above the edge, it is clear that all films retain the fcc structure present in bulk, but it can be readily observed from the position of the minima and maxima that the structure of the as-deposited film and the film annealed at 100 °C resembles the structure of fcc Ag, while annealing above 200 °C promotes the evolution towards the Ni fcc structure. This is indicative of a high number of Ag atoms as nearest neighbors of Ni in the as-deposited film and the film annealed at 100 °C, a sign of a small nanoparticle size with a large surface-to-volume ratio, as will be confirmed later by means of the extended x-ray absorption fine structure (EXAFS) analysis. Another important point deduced from the XANES observation is that there are no Ni oxides, as this would be easily observed by the appearance of a pre-edge peak.

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The structural EXAFS signals were extracted from the absorption spectra using standard procedures for background substraction and data normalization as implemented in the software Athena [26]. Systematic errors were eliminated by using the same procedure for all the data sets. The fine structure extended from 20 to 700eV above the edge was first normalized to the jump of the K-absorption edge and then fitted with the aid of a cubic spline curve to remove the low frequency background oscillations. Finally, it was converted to photon-electron wave vector k-space. The EXAFS signals, $\chi (k),$ obtained in this way are displayed in figure 3(b) for the as-deposited and annealed samples together with the Ag and Ni foils as references. Afterwards, the range $2\lt k\lt 12$ Å⁻¹ of the EXAFS signals was Fourier transformed to radial coordinates, R, in order to gain direct information about the structure around the Ni sites (figure 4(a)). We have selected the first shells contribution (1 Å$\;\leqslant \;R\;\leqslant \;3$ Å) and fitted the back-transformed (filtered) EXAFS signal (figure 4(b)).

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Quantitative information on the local structure around the Ni atoms and its evolution with the annealing temperature was obtained by fitting the filtered EXAFS data to the expression [27]:

$$\begin{eqnarray}&&k\chi (k)=\displaystyle \sum _{j}{S}_{0}^{2}{N}_{j}{f}_{j}(k,\pi )\displaystyle \frac{{e}^{-2{\sigma }_{j}^{2}{k}^{2}}{e}^{-2{{\rm{\Gamma }}}_{j}/k}}{{R}_{j}^{2}}\mathrm{sin}[2{{kR}}_{j}+{\phi }_{j}(k,\pi )].\end{eqnarray} \tag{ 1 }$$

The sum expands over all the species of backscattering atoms at the same distance R_j of the central atom with variance ${\sigma }_{j}^{2}$ (Debye–Waller factor) around the absorber, and N_j is the number of such atoms. The scale factor ${S}_{0}^{2}$ is related to the many body effects and ${e}^{-2{{\rm{\Gamma }}}_{j}/k}$ is the mean free path term that takes into account the inelastic losses of the photoelectron. ${f}_{j}(k,\pi )$ is the magnitude of the effective curved-wave backscattering amplitude for the jth type of atoms and ${\phi }_{j}(k,\pi )$ is the modification in the phase shift of the ejected photoelectron wave function by the potential of the central absorbing and backscattering atoms. In our case, the central atom is Ni and two single scattering paths have been considered: Ni–Ni and Ni–Ag. The corresponding backscattering parameters of both kinds of neighbors, $f(k,\pi )$ and $\phi (k,\pi )$ have been theoretically generated with the FEFF6.0 codes [28].

In order to improve the reliability of the fits, the four films have been fitted simultaneously as implemented in the IFeffit and Artemis softwares [26, 29]. The parameters ${S}_{0}^{2}$ and ${\rm{\Delta }}E$ for each path Ni–Ni and Ni–Ag were left free in the fitting procedure but were common for all the samples. An additional constraint was made as a result of the XANES inspection: the number of first nearest neighbors has been fixed to 12 (${N}_{\mathrm{Ni}-\mathrm{Ni}}+{N}_{\mathrm{Ni}-\mathrm{Ag}}=12$) as corresponds to a fcc ordering. Results have been checked with the additional XAFS software Viper [30]. Fits in the direct $R-$ and back-Fourier (filtered) $k-$ spaces are shown in figure 4 and the results of the fit are represented in figure 5.

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As shown in figure 5(a), the Ni–Ni coordination number for the as-deposited film is ${N}_{\mathrm{Ni}-\mathrm{Ni}}=3.9(4),$ well below the bulk value (12). This indicates that, on average, every Ni atom is surrounded by only four Ni atoms, the other eight being Ag atoms. This suggests that the film is composed of very small clusters with a high surface-to-volume ratio. Annealing at 100 °C increases ${N}_{\mathrm{Ni}-\mathrm{Ni}}$ to $5.4(3),$ an indication of the thermal treatment promoting the segregation of Ni and consequently a reduction of the number of surface atoms (an increment of the cluster size). An estimation of the cluster size can be gathered from the average number of Ni nearest neighbors (${N}_{\mathrm{Ni}-\mathrm{Ni}}$). As shown from theoretical calculations [1, 31], for compact shapes retaining an fcc ordering the mean number of nearest neighbors increases rapidly with the cluster size. In our case, a coordination value of ${N}_{\mathrm{Ni}-\mathrm{Ni}}\approx 4$ obtained for the as-deposited film would imply having a cluster size of $m\approx 6$ atoms, increasing to $m\approx 10$ atoms for the film annealed at 100 °C (${N}_{\mathrm{Ni}-\mathrm{Ni}}=5.4(3)$), in which all atoms count at least 1 Ag atom as nearest neighbor. A similar result for the cluster size can be obtained from the phenomenological expression published in [32] that relates ${N}_{\mathrm{Ni}-\mathrm{Ni}}$ with the cluster size D (see the Supplementary Information (SI)).

Above 200 °C the contribution of the Ni–Ag path becomes negligible and ${N}_{\mathrm{Ni}-\mathrm{Ni}}$ equals the bulk value (12), a sign of the Ni particles becoming larger than $\approx 4\;{\rm{nm}}$ [32].

The segregation process promoted by the thermal treatment is also reflected in the evolution of the Ni–Ni interatomic distances (${R}_{\mathrm{Ni}-\mathrm{Ni}}$), see figure 5(b). In this respect, the Ni–Ni interatomic distances are slightly contracted with respect to the Ni fcc bulk and expand with the thermal treatment, until they reach the Ni bulk value (2.482 Å) at 200 °C. The Ni–Ag interatomic distances (${R}_{\mathrm{Ni}-\mathrm{Ag}}$) of the as-deposited film and the annealed at 100 °C remain practically unchanged at 2.81–2.82 Å, also slightly smaller than the Ag–Ag distance in an fcc Ag lattice (2.89 Å) [25].

Regarding the Debye–Waller factors, they provide a measure of the structural disorder around the Ni atoms. The disorder can be dynamic, due to thermal agitation, or static, due to lattice distortions. In this case, because all measurements were performed at 80 K, the changes in the Debye–Waller factor from one film to another reflect uniquely the static disorder. As shown in figure 5(c), the Debye–Waller factor of the Ni–Ni path decreases with the annealing due to the structural ordering induced by the thermal treatment, and the Ni–Ag path displays a slightly larger Debye–Waller factor than the Ni–Ni path, as corresponds to the more disordered environment of surface atoms.

As shown in figure 6, 5 K hysteresis loops ($M(H)$) and zero-field cooling–field cooling (ZFC–FC) measurements of the as-deposited NiAg thin film display a paramagnetic-like behavior down to 5 K. The fact that blocking is not observed is a consequence of either the low magnetocrystalline anisotropy of Ni or the presence of a small magnetic moment per particle (small volume), or both.

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Additionally, the blocking not being observed down to 5 K suggests that magnetic interactions between nanoparticles are negligible [33]. This is also supported by the ${MvsH}$ purely linear behavior occurring at temperatures above 40 K (see inset of figure 6(a).

On the contrary, the $M(H)$ curves of the films annealed at 200 °C and 400 °C are saturated and display coercivity and remanence (figure 6), and the ZFC–FC curves are slowly variable and irreversible (see the SI). This indicates that Ni has segregated in the form of large ferromagnetic particles, in accordance with the EXAFS results. The saturation magnetization (M_s) at 200 °C is only slightly lower than at 400 °C, indicating that annealing at 200 °C promotes an almost full segregation of Ni. The saturation value at 400 °C (17.4 emu/cc) corresponds to a Ni atomic content of 5.2% assuming an fcc Ni bulk value of 512 emu/cc. This confirms the value obtained from EDX ($6(1)$%).

Additional magnetic and structural information can be put forward from the analysis of the paramagnetic response of the as-deposited film by a fit to the Langevin law [34]:

$$\begin{eqnarray}&&M={M}_{0}{\mathcal{L}}(a),\qquad {\rm{where}}\;{\rm{}}{\mathcal{L}}(a)=\mathrm{coth}a-\displaystyle \frac{1}{a},\end{eqnarray} \tag{ 2 }$$

M₀ being the saturation magnetization and $a=\mu {\mu }_{0}H/{{\rm{k}}}_{{\rm{B}}}(T+{T}^{*}).\;$μ is the magnetic moment of the magnetic clusters given by $\mu ={M}_{s}^{{\rm{fccNi}}}\cdot (\pi {D}^{3}/6)$, where $\pi {D}^{3}/6$ is the volume of the nanoparticles, assumed spheres with diameter D, and ${M}_{s}^{{\rm{fccNi}}}$ = 512 emu/cc is the saturation magnetization of bulk fcc Ni [34]. ${T}^{*}$ is a term that accounts for the strength of the magnetic interactions [35]. In order to take into account the different sizes of the Ni clusters we have introduced a log-normal size distribution function $f(D),$ which is defined as follows:

$$\begin{eqnarray}&&f(D)=\displaystyle \frac{1}{\sqrt{2\pi }D\beta }\mathrm{exp}\left(-\displaystyle \frac{{\mathrm{ln}}^{2}(D/\alpha )}{2{\beta }^{2}}\right),\end{eqnarray} \tag{ 3 }$$

and depends on two parameters, α and β. The mean particle diameter ($\bar{D}$) and the standard deviation (σ) are given by

$$\begin{eqnarray}&&\bar{D}=\alpha {e}^{{\beta }^{2}/2};\qquad {\rm{}}\;{\rm{}}{\sigma }^{2}={\bar{D}}^{2}\left(\displaystyle \frac{{\bar{D}}^{2}}{{\alpha }^{2}}-1\right).\end{eqnarray} \tag{ 4 }$$

In sum, the evolution of the magnetization of an array of Ni nanoparticles with a size distribution given by equation (3) is given by:

$$\begin{eqnarray}&&M={M}_{0}{\displaystyle \int }_{0}^{\infty }f(D){\mathcal{L}}(a){\rm{d}}D.\end{eqnarray} \tag{ 5 }$$

To reduce correlations between parameters and corresponding fitting errors, the $M(H)$ curve at 5 K and the ZFC curves measured at $H=0.5,$ 2 and 10 kOe have been fitted simultaneously to equation (5), the four data sets sharing common M₀, α, β and ${T}^{*}.$ The fitted curves (continuous line) with the experimental data (open dots) are shown in figure 6.

Results of the fits give ${M}_{0}=7.6(8)$ emu/cc, which, compared to the magnetization of bulk Ni (512 emu/cc), corresponds to a Ni atomic content of $2.3(2)$%, significantly lower than the $6(1)$% value obtained by EDX. This is a phenomenal sign of a drastic 62% reduction of the magnetic signal with respect to the bulk value. The mean cluster diameter (assuming each Ni atom contributes with a maximum of 0.6 ${\mu }_{B}$ as in bulk [34]) is $\bar{D}=0.70(2)$ nm with a narrow size-distribution function of $\sigma =0.16(2)$ nm, corresponding to a mean cluster size of $m\approx 19$ atoms, considerably larger than the average size obtained from EXAFS ($m\approx 6$ atoms). The distributions of the magnetic cluster size and the number of atoms per cluster (m) are shown in figure 7. Finally, the term accounting for the strength of the magnetic interactions between clusters results in a very small value (${T}^{*}=0.9(3)$ K), an additional sign of the negligible interactions among clusters.

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As supported by DFT calculations below and further discussed in section 4, the observed drastic reduction of the magnetic signal (62%) and the larger mean magnetic cluster size ($m\approx 19$ atoms) compared to the mean cluster size obtained from a purely structural technique such as EXAFS ($m\approx 6$ atoms) suggest that there is a significant number of small clusters with a non-magnetic response that are not being detected in the magnetic analysis.