Kondo screening of the spin and orbital magnetic moments of Fe impurities in Cu .

L. Joly,1 J.-P. Kappler,2 P. Ohresser,2 Ph. Sainctavit,3 Y. Henry,1 F. Gautier,1 G. Schmerber,1 D. J. Kim,1,* C. Goyhenex,1 H. Bulou,1 O. Bengone,1 J. Kavich,4 P. Gambardella,5 and F. Scheurer1,† 1Université de Strasbourg, CNRS, IPCMS, UMR 7504, F-67000 Strasbourg, France 2Synchrotron-SOLEIL, L’Orme des Merisiers Saint-Aubin, BP 48, F-91192 Gif-sur-Yvette Cedex, France 3Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, UMR 7590 CNRS, UPMC, IRD et MNHN, F-75005 Paris, France 4Catalan Institute of Nanoscience and Nanotechnology (ICN2), UAB Campus, E-08193 Bellaterra, Spain 5Department of Materials, ETH Zürich, Hönggerbergring 64, CH-8093 Zurich, Switzerland (Received 4 June 2016; revised manuscript received 8 December 2016; published 20 January 2017)

The Kondo effect [1] is a consequence of many-body interactions that originates from the hybridization of localized strongly correlated electrons with a continuum of free-electron-like metal states.According to the Anderson impurity model [2] and the related s-d Kondo model [3,4], the spin of an S = 1  2 impurity is effectively screened by the continuum states of the metal host upon the formation of a coherent many-body singlet state, which occurs below the Kondo temperature T K [3,5].At T K , the system exhibits a crossover [6] from a low-temperature local Fermi liquid state [3,5] to a high-temperature regime characterized by a free-spin behavior corrected by logarithmic temperature terms.It was noted early that a realistic description of the Kondo effect should take into account the orbital degrees of freedom in addition to the localized exchange interaction and spin multiplicity of the impurities [7,8].
Despite recent theoretical progress using ab initio methods, keeping track of all the relevant parameters for transition metal impurities in nonmagnetic hosts, such as crystal field or spin-orbit coupling, remains extremely difficult [9][10][11][12][13].For example, theoretical studies of Fe impurities in Au [9,10] propose different low-energy scenarios, namely, the n-channel model [14] and the orbital-dependent Kondo effect [15], to interpret magnetotransport and decoherence experiments.On another hand, studies combining density functional theory (DFT) and quantum Monte Carlo [10,13], as well as the noncrossing approximation [12], reveal the importance of multiorbital effects and the difficulty to determine a reliable T K .For the Cu:Fe dilute alloy, an archetypal Kondo system [3,[16][17][18], the n-channel model with n = 4 and S = 2, has been shown to fit the magnetization data deduced from Mössbauer spectroscopy and specific heat [19].These results suggest, without further theoretical justification, that the ground state of the Fe impurities is both a spin and an orbital singlet.
An intrinsic difficulty for experiments is to probe the spin and orbital magnetic moments in a separate way.Classical magnetometry techniques measure the macroscopic susceptibility and do not provide information at the level of the impurity itself.Local techniques such as Mössbauer spectroscopy and nuclear magnetic resonance (NMR) probe the microscopic susceptibility, but rely on the assumptions that spin and orbital components are proportional to the hyperfine field, and that the orbital component is constant with temperature [17,18,20].Scanning tunneling microscopy has recently provided useful information about the spatial and structural dependence of the Kondo resonance [21][22][23], including Fe on Cu [24], but the details of the magnetic configuration remain unaccessible.X-ray magnetic circular dichroism (XMCD), on the other hand, has the unique capability to separately probe m s and m l in a direct and quantitative way [25,26], besides being sensitive to dilute amounts of transition metal impurities [27][28][29][30].So far, it has, however, not been used to investigate the temperature dependence of the local magnetic moment in a Kondo system.
Here, we investigate the crossover from the paramagnetic limit to the Kondo-screened state of Fe impurities in Cu using XMCD.We provide a separate measurement of the spin and orbital magnetic moments as a function of temperature in a dilute Kondo system.Two main consequences of Kondo correlations are evidenced: (i) a strong reduction of the impurity spin saturation moment compared to a paramagnetic impurity, and (ii) a temperature-independent behavior for m s below the Kondo temperature.Furthermore, m l is constant over the considered temperature range, suggesting that m s and m l are screened differently.
We chose the dilute Cu:Fe alloy system, because of its historical relevance [3,[16][17][18][19]24,31] but mostly because its Kondo temperature (T K ≈ 20-30 K) provides a relatively broad temperature range below and above T K to probe the Fe magnetic moment.We performed XMCD measurements between 2 and 150 K, limited by the decrease of the magnetic signal with temperature in the paramagnetic phase.The fabrication of dilute alloys requires addressing two difficulties.The first is the formation of magnetically coupled Fe pairs, which occurs when the Fe concentration exceeds about 1000 ppm.Since the Kondo temperature of Fe pairs (T pair K ) is much lower than T K for isolated impurities, the paramagnetic pair signal would dominate the impurity moment at temperatures between T pair K and T K [32,33].The second is related to sample oxidation which must be specifically taken into account for the interpretation of the intrinsically surface-sensitive XMCD measurements.Because Cu is not a good barrier against oxygen penetration, Fe oxidation takes place near the sample surface.As shown below, however, the x-ray absorption signal of Fe oxide can be identified and subtracted from the absorption spectra of Fe.Two types of polycrystalline dilute Cu:Fe alloys were prepared: bulk alloys, obtained by a melting preparation technique [32], and thin films obtained by magnetron sputtering in ultrahigh vacuum conditions (base pressure in the low 10 −9 mbar range).The latter method was used successfully in earlier work on the Kondo effect [34].Films of 200-350 nm were deposited on transparent SiC membranes (200 μm thick).They were grown at room temperature by codeposition from a pure Cu target and a mixed Cu:Fe one containing 1 at.% Fe.The evaporation rates (≈1 nm/s) were adjusted to obtain the desired composition.After fabrication, the samples were kept at ≈100 K to avoid atomic diffusion which may lead to clustering of the Fe impurities (i.e., yielding a paramagnetic pair magnetization) [32].In order to verify the presence of a Kondo effect, the electrical resistivity of the samples was measured as a function of temperature using conventional four-point resistance measurements.
The XMCD experiments were performed at the SIM beamline of the Swiss Light Source on the French cryomagnet end station.The x-ray absorption spectra (XAS) were recorded at the L 2,3 edges of Fe in a ±6.5 T magnetic field in the 2-150 K temperature range.The field was parallel to the incident photon beam, and normal to the sample surface.XMCD spectra were obtained by switching both the x-ray helicity and the direction of the magnetic field in order to remove any possible spurious asymmetries and yield reliable dichroic signals.The spectra were recorded using the "on-the-fly mode" [35], the light helicity being switched after a full absorption spectrum.The magnetic field was inverted after acquisition of a set of several spectra.
We checked that the smallest concentration that can be measured within a 1-week beam time was in the order of 500 ppm.At each temperature, about 80 energy scans, representing 6 h of acquisition time, were averaged to obtain the XMCD signal.The bulk samples were analyzed by total electron yield (TEY) and the thin film samples by TEY and transmission.Because of the very small magnetic signal per impurity and low Fe concentration, XMCD was only measured with the largest available field.In order to provide a comparison of the experimental results with the magnetic moment of Fe expected in the absence of Kondo correlation effects, we performed an extensive series of DFT and Ligand field multiplet calculations (LFMs).While DFT provides an accurate description of the bare Fe spin moment at 0 K, LFM allows comparing the spin and orbital moments of Fe ions in a 3d configuration as a function of temperature and magnetic field, for different crystal field symmetries and Slater correlation parameters.
Two samples were investigated: a 2500 ppm bulk sample, and a 500 ppm thin film sample.The first yields a larger Fe signal, but with an important pair interaction, whereas the second provides a negligible pair interaction.The Fe concentrations were estimated by measuring the edge jump intensity at the Fe L 3 edge and agree within ≈10% with the nominal concentrations.The measured Kondo minima of the resistivity are respectively 21 K (500 ppm) and 40 K (2500 ppm), in excellent agreement with earlier measurements [31].In the following we will focus on the 500 ppm thin film sample.The results for the 2500 ppm are discussed in the Supplemental Material [36].
The x-ray absorption spectra of the Fe L 2,3 edges show a strong oxide contribution.One must therefore first isolate the Fe impurity contribution by subtracting the oxide part in the spectra (see the Supplemental Material [36], Fig. S1). Figure 1 shows oxide-corrected XAS and XMCD spectra at 100 and 2 K.No obvious spectral changes are observed in the XAS when going from the paramagnetic to the Kondo regime.Since the system is metallic, possible modifications due to the Kondo correlations are too faint to be observable.The main qualitative observation is a reduced XMCD intensity at 100 K as compared to the XMCD at 2 K, indicating a smaller spin moment at high temperature.
The projection of the spin (m s ) and orbital (m l ) magnetic moments along the photon beam (parallel to the magnetic field) was determined by applying the XMCD sum rules [25,26,36].Since the samples are polycrystalline and present a local cubic environment, the magnetic dipolar term (T z ) to the spin sum rule can be safely neglected, as it is usual for bulk metal compounds [37].Figure 2 shows the m l /m s ratio as a function of temperature, obtained after subtracting the oxide contribution from the Fe XMCD spectra.This ratio depends only on the relative intensity of the L 3 and L 2 components of the dichroic signal, and can thus be obtained self-consistently  from each XMCD spectrum without the need for a normalization to the total absorption intensity.We note that the way the oxide/background is subtracted affects the values of m s and m l .The data points result from an average of different sets obtained by slightly changing the subtraction parameters.Roughly half of the error arises from the variability introduced by the subtraction procedure.In Fig. 2 one might distinguish a first regime independent of temperature below about 30-50 K, and a temperature-dependent regime at higher temperatures.The error bars are, however, quite large and a χ 2 test gives indeed a rejection confidence of only 75% for a constant m l /m s (T ) ratio hypothesis.The LFM calculations, which neglect Kondo correlations, present a weaker temperature dependence compared to the data (see Fig. 2 and Ref. [36]), but it is not possible to unambiguously conclude on the presence of a Kondo effect on the basis of m l /m s alone.Hence, it is mandatory to analyze m s and m l separately in order to get further information.Note that in the presence of crystal field, the ratio m l /m s is not necessarily constant, as it would be for a paramagnetic impurity in spherical symmetry (Fig. 2 and see also Ref. [36]).
In order to extract absolute values of m s and m l as a function of temperature, the XMCD signal is normalized to the integral of the isotropic cross section, which is proportional to the number of holes in the 3d states, N h .As the latter was found to be temperature independent, we take N h = 3.37 ± 0.15 as calculated by DFT for an Fe impurity embedded in a Cu matrix.Our DFT calculations further predict m s = 2.72 ± 0.16μ B at 0 K for the Fe impurities, a result which is robust against different implementations of the local spin density approximation [36].Figure 3 shows the temperature dependence of m s and m l in a 6.5 T field determined using the XMCD sum rules.orbital magnetic moment per Fe ion as determined from the XMCD sum rules for the 500 ppm sample in a 6.5 T field.The blue lines represent the moments derived from a LFM calculation for the same configuration as in Fig. 2. The Langevin function for a single atom magnetic moment of m s = 2.7μ B in a 6.5 T field is plotted in green.The black lines through the data are guides to the eye.The red dashed line represents n-channel model calculations (S = 2 and n = 4).This curve was obtained from an interpolation of the data of Ref. [19] to our experimental field of 6.5 T to enable comparison.Since these calculations scale with the Mössbauer data of Steiner et al., the red curve thus also holds for Mössbauer data interpolated to 6.5 T.
First, we find that at low temperature m s is much smaller (≈10 times) than the value expected for a paramagnetic Fe atom.This very weak m s is spectacularly different from what is observed for isolated atoms on surfaces [27,29,30], including Fe on Cu(111) [38], which show magnetic moments of several Bohr magnetons at these temperatures.Such a reduction, on the other hand, is expected for Kondo screening.For comparison, a Langevin function [39] (green line) assuming a spin moment of 2.7μ B per atom (as obtained by DFT for Fe in Cu) is plotted together with the spin moment obtained by LFM calculations (blue line) for a paramagnetic Fe ion in a cuboctahedral crystal field (Kondo correlations are not included in LFM calculations).Although several crystal field models were tested, none reproduces the experimental behavior of m s [36].In addition, we observe that m s exhibits a crossover from a nearly-temperature-independent regime, identified as the Kondo regime, to a paramagnetic behavior for T T K .A χ 2 on m s (T ) yields a rejection confidence of 99% for a constant m s hypothesis.Although our values for m s are smaller, this behavior is qualitatively similar to the evolution of the Fe magnetization as determined by Mössbauer spectroscopy [17].The red dashed curve in Fig. 3 represents n-channel model calculations [19], describing the evolution of the impurity magnetization as a function of temperature in a given magnetic field (see the caption for details) and which also reproduce the Mössbauer data of Steiner et al. on dilute Cu:Fe alloys [17].
The 2500 ppm sample yields both a similar temperature evolution and spin moment per isolated Fe atom.The analysis is, however, more complicated in this case, since it requires removal of a paramagnetic Fe pair contribution [36].
The temperature dependence of the orbital moment is in strong contrast with that of the spin moment.Our data reveal a finite m l value of (0.04 ± 0.01)μ B per atom, which is almost constant with temperature (a χ 2 test indicates that only the constant hypothesis must be retained) and much smaller than the value of (0.66 ± 0.04)μ B reported for Fe impurities on a Cu(111) surface at low temperature [38].Although a nearly quenched m l relative to the free-atom value is expected based on the cubic crystal field symmetry and the strong Fe-Cu hybridization [28], such a weak temperature dependence is unexpected.An explanation for this behavior requires taking into account both the on-site correlation within the impurity, as in a ionic model, as well as its many-body interactions with the host.
The above results are now compared to those of an ionic model of Fe impurities in Cu [40].Consistently with DFT and the best fit of m s (T ) in the paramagnetic regime, we assign a spin S = 3  2 to the Fe impurities, corresponding to a monovalent Fe + (3d 7 ) electron configuration, the one also suggested for the ground state of Fe impurities in simple metal hosts [27], for Fe atoms on a Cu(111) surface [38], and by early Mössbauer and NMR experiments [17,40].According to the Hund's rules, the lowest-energy atomic term is then the 4 F state with total orbital moment L = 3.The cubic crystal field at the Fe sites splits this state into a lower orbital singlet ( 4 A 2g ) and two upper orbital triplets ( 4 T 2g , 4 T 1g ).When the spin-orbit interaction is included as a perturbation, the mixing of the higher-energy orbitally degenerate states with the 4 A 2g ground state results in a finite orbital moment, of the order of (8λ/10Dq)μ B [41].Taking the spin-orbit constant of the 4 F Fe term λ ≈ 15 meV and 10Dq = 0.25 eV for the cubic crystal field splitting, as suggested by our LFM calculations and the NMR data [40], one obtains m l ≈ 0.5μ B , which we may consider as an upper limit of m l in the absence of s-d hybridization and Kondo screening effects.Such a perturbative contribution to the orbital moment, however, besides being too large, is also temperature dependent, in contrast with the behavior reported in Fig. 3. LFM calculations, which provide an exact treatment of spin-orbit-induced mixing of the ground state with higher-energy levels, also yield too large values of m l at low temperature, unless the on-site electron correlation is reduced to an unusually low level (see Fig. S3 in Ref. [36]).On the other hand, there exists also a smaller, temperature-independent contribution to the orbital moment, which arises from the second-order Zeeman effect.This contribution, which has been discussed but is yet to be quantified in the interpretation of early Mössbauer and NMR studies [17,18], is of the order of 2μ B B/10Dq, where B is the applied magnetic field [40].In our case, this term may account for about one tenth of the experimental m l , and is thus too small to provide a satisfactory explanation for the weak temperature dependence of the Fe orbital moment.
This analysis, together with the results of our LFM calculations, indicates that the finite and nearly-temperatureindependent m l cannot be associated with single-ion properties, as determined by the interplay of crystal field, spin-orbit coupling, and Zeeman interactions only.A correct description must consider, for both m s and m l , the Kondo effect resulting from the d-d correlation effects and the hybridization between the d orbitals of the impurity and conduction electrons [7,8,42].Following this hypothesis, our results suggest that Kondo screening of the Fe orbital moment starts to occur at a much higher temperature than for the spin moment, beyond the range probed in the present study.
In conclusion, the XMCD measurements of dilute Cu:Fe alloys reported in this Rapid Communication provide a separate determination of the spin and orbital moments of a Kondo system above and below T K .The crossover from the free-atom-like paramagnetic regime to the Kondo-screened regime is clearly identified for the spin magnetic moment, which shows Curie-Weiss behavior for T > T K and saturates at m s ≈ 0.35μ B for T < T K in a magnetic field of 6.5 T, a value much smaller than the "bare" Fe spin magnetic moment of 2.7μ B calculated by DFT.In contrast with the spin moment, we find the orbital magnetic moment to be nearly temperature independent, remaining close to m l = 0.04 ± 0.01μ B between 2 and 150 K.In order to understand theoretically such a behavior, and to investigate a possible spin and orbital decoupling, it would be necessary to solve the multiorbital Kondo problem by taking into account not only the Hund's rule coupling and the crystal field effect but also the spin-orbit coupling, which is a very challenging problem.

Application of the XMCD sum rules at finite temperature
The XMCD magneto-optical sum rules were initially developed in an atomic model [1][2][3], then for extended systems in the independent electron approximation [4,5].However, it has been shown shortly after that these sum rules are generally valid at T = 0 for strongly correlated systems [6] (see also Refs .5 and 7 for a review).They can be easily extended for T = 0 [5] as discussed in the following.Sum rules at 0 K follow from the fact that the integrated x-ray spectra at given absorption edges, here L 2,3 , are proportional to linear combinations (LC) of the ground state |g quantum average g| nh m,σ |g of the number of holes operator nh m,σ in the m, σ th spin orbital; the coefficients of these LC are the angular part of the transition probability 2p j,mj → 3d m,σ and they depend only on the polarization and on the quantum numbers characterizing the absorption edges.For the considered temperature range, the x-ray transition energies are much larger than the thermal energy k B T , and the x-ray absorption by a sample in equilibrium at a temperature T is the thermal average of the absorption spectra from excited states |m whose expressions are the same as those for T = 0 replacing |g by |m .Therefore, the charge, spin and orbital sum rules for T = 0 derived from the integrated intensities of the fundamental spectra are expressed as for T = 0, by replacing the number of holes, spin and orbital moments at T = 0 with their thermal average value at T = 0.

Oxide correction of the spectra
Figure S1 shows the x-ray absorption spectra (XAS) and XMCD of Fe in the (a, b) TEY and (c, d) transmission modes.The TEY spectra are characteristic of the surface and are of pure oxide character.The absorption features of these spectra originate from Fe atoms in an inhomogeneous environment and small crystal fields, as expected for cuboctahedral or tetrahedral symmetries.They are not comparable to those of conventional bulk Fe oxides [8,9].Conversely, the transmission spectra are characteristic of the whole sample, including a surface contribution, and contain features from both unoxidized and oxidized Fe atoms.The oxide contribution to the transmitted XMCD signal can be removed by subtracting the TEY signal measured on the same sample, after proper normalization.Such procedure to separate different contributions has already been applied successfully to other systems [10,11].

Ligand field multiplet calculations
Ligand field multiplet (LFM) theory [12] allows calculating spin and orbital moments of an ion in an arbitrary crystal field at finite temperature.Here, we compare the experimental XMCD data to LFM calculations for different crystal field symmetries (octahedral, tetrahedral) and strength (10Dq), as well as for different values of the Slater integral reduction parameter (κ).The magnetic field is set equal to µ 0 H = 6.5 T, as in the experiments.These calculations do not take into account Kondo correlations.
We suppose an Fe atom with a 3d 7 electronic configuration (close to the one determined by DFT) in a cubic crystal field.Its intensity (called 10Dq) is given by the energy difference between the two-fold and the three-fold degenerate states: 10Dq = E(t 2 ) − E(e) or 10Dq = E(t 2g ) − E(e g ) when the local point group is centro-symmetric.A positive 10Dq corresponds to a cuboctahedral site surrounded by 12 negatively charged ions, and a negative one to a cuboctahedral site surrounded by 12 positively charged ions.For energetical reasons, the substitutional site for Fe is preferred in Cu:Fe dilute alloys, hence Fe is in a cuboctahedral environment.Due to a very weak net charge on the Cu atoms in the neighborhood of the Fe atom, DFT does not allow to univocally determine the sign of the crystal field.On another hand, the Slater integrals can be varied from the atomic value (κ = 1) to a vanishing value (κ = 0.01), whereas the standard value in solid state systems is κ = 0.8. Figure S2 shows the experimental m l /m s ratio compared to results of LFM calculations with different 10Dq parameters.For positive values one obtains a weakly temperature dependent ratio, with a value comparable to the experimental one at low temperature.Conversely, for negative values of 10Dq the ratio is much larger and shows a stronger temperature dependence.Only a strong unreasonable reduction of the Slater integrals down to 1% with respect to the atomic value (κ = 0.01) leads to a temperature dependence of m l /m s in qualitative agreement with the experiment at low temperature.However, such a reduction of the Slater integrals is much larger than the one used to describe metallic systems (κ = 0.5) [13].As low κ values are associated with a reduction of on-site correlation effects, the better agreement between experimental data and LFM calculations in this limit suggests the presence of significant hybridization between the Fe 3d-states and the Cu conduction electrons, as required for Kondo screening of the local moments.
Figure S3 shows the experimental spin moment compared to the one calculated in the LFM framework.Since m s is only weakly dependent on 10Dq we just show m s for 10Dq = ±0.25 eV, for two Slater integral reduction parameters (κ = 0.8 and 0.01).The global behavior fundamentally differs from the one of the experimental data, independently of the set of parameters used in the LFM calculations.In particular, the low temperature experimental m s is much smaller than the calculated values, consistently with the effect of Kondo screening.Similarly, the experimental behavior of m l is not reproduced by the LFM calculations (Fig. S4).

Density Functional Theory calculations
DFT calculations are performed in order to determine the Fe spin magnetic moment at 0 K in an f cc Cu host matrix in the absence of Kondo correlations.These calculations also provide an estimate of the number of holes in the Fe 3d shell, N h , which is required to extract absolute moment from the analysis of the XMCD spectra.Spin-polarized calculations were performed with three different codes: SIESTA [14], Quantum Espresso [15] and a tight-binding linear muffin-tin orbital (TB-LMTO) code [17].The SIESTA code uses local orbital basis sets describing the valence states, whereas the Quantum Espresso code uses plane waves.SIESTA and Quantum Espresso are operated within the Kohn-Sham self-consistent DFT using the generalized gradient approximation with a Perdew-Burke-Ernzerhof parametrized exchange-correlation functional [16].The TB-LMTO code uses an exchange correlation potential described within the local spin density approximation as parametrized by Vosko-Nosair [18].The number of d holes and the spin moment for Fe are calculated for bulk Fe serving as a reference and compared to Cu:Fe periodic dilute alloys containing from 0.5 to 5% Fe atoms.All codes yield similar results, and show that there is no difference for N h (within 0.5%) between bulk Fe and the dilute alloys.We find average values of N h = 3.37 ± 0.15 and m s = 2.72 ± 0.16.This calculated magnetic moment is in good agreement with earlier experimental results [19][20][21][22] and the most recent electronic calculations [23][24][25][26].

ppm sample
For the 2500 ppm bulk sample, due to several spurious contributions, the extraction of the impurity spin moment is more difficult.As for the 500 ppm sample, we have to deal with oxidation, but also with a non negligible interacting pair proportion.On this bulk sample, the oxide contribution could be strongly reduced by scraping with a diamond file and Ar + ion sputtering, but not fully eliminated.Since no reference oxide signal of the same sample is available, as was the case for the 500 ppm sample, it is not possible to separate directly the different contributions in the XAS and XMCD intensities.By comparing the XAS to a clean reference Fe spectrum, we estimate that the oxide part represents about 20% of the total Fe signal, which is then corrected accordingly.The resulting spin moment after this oxide correction is represented in Fig. S5 as open circles.One notices that the magnetic moment is about three times larger than the one measured for the 500 ppm sample, but still four times smaller than the one expected for a free Fe atom with 2.7 µ B magnetic moment.This larger value is due to the ferromagnetically interacting pairs.The measured spin moment (open circles) is therefore the weighted average of the single impurity and pair magnetic moment.The Kondo temperature of the pairs is very low so that the pair behave as a paramagnetic entity in the temperature range considered [19].Taking the pair magnetic moment as defined by a Langevin function for pairs with moment m pair = 2 × 2.7 µ B , one can extract the single impurity magnetic moment (open squares).A good agreement with the 500 ppm data (dots) is obtained if we assume a pair contribution of 24%.This value is in good agreement with earlier work [19,27], which give a pair contribution between 70c and 130c, where c is the Fe concentration (here c = 0.25).Thus, the two experiments done with different types of samples and different experimental procedures yield coherent results.

FIG. 1 .
FIG.1.Oxide-subtracted XAS (top) and XMCD (bottom) transmission spectra of a 500 ppm Cu:Fe sample deposited on a SiC membrane for 100 and 2 K, with an applied magnetic field of ±6.5 T. The spectra have been offset for clarity.

FIG. 2 .
FIG.2.Orbital to spin moment ratio m l /m s as a function of temperature for the 500 ppm sample in a 6.5 T field, as determined by sum rules.The thin (black) line is a guide to the eye.The thick (blue) solid line is a LFM calculation for an Fe ion in a 3d 7 configuration in cuboctahedral symmetry with 10Dq = 0.25 eV and a reduction of the atomic Slater integral parameters of κ = 0.8.Inset: Low-temperature resistivity as a function of T for the 500 ppm sample on a semilogarithmic scale.Note the characteristic ln(T ) Kondo behavior of the resistivity at low temperature.

FIG. 3 .
FIG. 3. (a)Spin and (b) orbital magnetic moment per Fe ion as determined from the XMCD sum rules for the 500 ppm sample in a 6.5 T field.The blue lines represent the moments derived from a LFM calculation for the same configuration as in Fig.2.The Langevin function for a single atom magnetic moment of m s = 2.7μ B in a 6.5 T field is plotted in green.The black lines through the data are guides to the eye.The red dashed line represents n-channel model calculations (S = 2 and n = 4).This curve was obtained from an interpolation of the data of Ref.[19]  to our experimental field of 6.5 T to enable comparison.Since these calculations scale with the Mössbauer data of Steiner et al., the red curve thus also holds for Mössbauer data interpolated to 6.5 T.
FIG. S1. (Color online) XAS and XMCD spectra of a 500 ppm Cu:Fe sample deposited on a SiC membrane.(a) XAS in TEY mode; (b) XMCD in TEY mode; (c) XAS in transmission; (d) XMCD in transmission before (red) and after (black) subtraction of the oxide contribution.The vertical dashed line identifies the position of the main oxide feature.The spectra are recorded in a ±6.5 T field at T = 10 K.
FIG. S2.LFM calculations of m l /ms compared to experimental results (black dots) for the 500 ppm sample in a 6.5 T field, as determined by the XMCD sum rules.The thin black line is a guide to the eye.The colored lines are results of LFM calculations for different crystal field (10Dq) and Slater integral (κ) parameters in a 3d 7 electronic configuration.κ = 0.8 if not specified.
FIG. S3.Spin moment as deduced by the XMCD sum rules assuming N h = 3.37 (dots) and by LFM calculations (solid lines) for the same parameters as in Fig.S2.
FIG.S4.Orbital moment as deduced by the XMCD sum rules assuming N h = 3.37 (squares) and LFM calculations (solid lines) for the same parameters as in Fig.S2.
FIG.S5.d-spin moments in a 6.5 T field as determined by sum rules as a function of temperature for the 500 ppm (filled dots) and 2500 ppm samples (open circles).The blue and green lines represent respectively the paramagnetic moment for a single atom magnetic moment (Langevin function with ms = 2.7 µB) and for pairs (Langevin function with 2 × ms) in a 6.5 T field.The open squares represent the contribution of the single impurity moment in the signal of the 2500 ppm sample, assuming a pair proportion of 24%.Note that the y-scale is linear in this figure.