The non-local spin-valve is pivotal in spintronics, enabling separation of charge and spin currents, disruptive potential applications and the study of pressing problems in the physics of spin injection and relaxation. Primary among these problems is the perplexing non-monotonicity in the temperature-dependent spin accumulation in non-local ferromagnetic/non-magnetic metal structures, where the spin signal decreases at low temperatures. Here we show that this effect is strongly correlated with the ability of the ferromagnetic to form dilute local magnetic moments in the NM. This we achieve by studying a significantly expanded range of ferromagnetic/non-magnetic combinations. We argue that local moments, formed by ferromagnetic/non-magnetic interdiffusion, suppress the injected spin polarization and diffusion length via a manifestation of the Kondo effect, thus explaining all observations. We further show that this suppression can be completely quenched, even at interfaces that are highly susceptible to the effect, by insertion of a thin non-moment-supporting interlayer.
Spintronic devices based on metals and insulators have been remarkably successful, as illustrated by the universal use of spin-valves, and now magnetic tunnel junctions, in hard disk read sensors. The need to scale such devices to extremely small sizes introduces serious impedance matching and noise issues, however, making all-metallic structures (for example, current-perpendicular-to-plane giant magnetoresistance stacks)1 attractive for next-generation devices2. Remarkably, despite the maturity of metallic spintronics, there remain large gaps in our fundamental understanding of spin transport in metals, particularly with injection of spins across ferromagnet (FM)/non-magnetic metal (NM) interfaces, and their subsequent diffusion and relaxation. Unresolved issues include the applicability of the widely employed Elliott-Yafet (E-Y)3 spin relaxation mechanism4,5,6,7,8,9,10, the influence of defects, surfaces and interfaces on spin relaxation at nanoscopic dimensions8,11,12,13,14,15, the importance of magnetic and spin-orbit scattering16,17,18 and the accuracy of existing models19,20,21,22,23.
In the quest to understand such issues, the non-local spin valve (NLSV)24 has a pivotal role as it enables separation of charge and spin currents, providing a direct means to study spin injection, transport and relaxation25. In the NLSV geometry, two nanoscopic FM electrodes separated a distance d are electrically connected via a nanoscopic NM (that is, para- or dia-magnetic) channel. A spin-polarized charge current IQ is injected from one FM (FMinj), and extracted from the far edge of the NM, away from the second FM electrode (FMdet). Ideally, in this geometry, no charge current flows between the two FM contacts. A non-equilibrium spin polarization thus accumulates above FMinj and diffuses, in both directions, along the NM channel, generating a diffusive pure spin current (IS) between FMinj and FMdet. Some fraction of the injected spins reach FMdet, generating a non-local spin-dependent potential difference, VNL (and a non-local resistance, RNL=VNL/IQ) between FMdet and the right edge of the NM. The magnetizations of FMinj and FMdet are then switched between parallel (P) and antiparallel (AP) to determine ΔRNL=RP–RAP, a direct measure of the spin accumulation at FMdet, devoid of complications due to charge currents. ΔRNL(d) can then be used to determine, via an appropriate model19,21,22,25, parameters such as the spin polarization of the injected current (α) and the NM spin diffusion length (λN).
This non-local geometry has enabled significant advances in the understanding of spin transport in metals4,5,6,7,8,9,10,11,12,13,14,15,16,18,22,24,25,26,27,28,29,30,31,32,33,34,35,36,37, but has also highlighted serious discrepancies with theory. The primary example of the latter is the surprising non-monotonicity in the temperature (T) dependence of ΔRNL, and thus the deduced λN, in the transparent interface limit. In the widely investigated Ni80Fe20/Cu, for example, ΔRNL initially increases on cooling but then drops (by 10–40%, dependent on dimensions) below ~40 K (refs 8, 10, 18, 30, 31, 32, 33). This is in stark contrast to expectations from the E-Y mechanism17,38, which posits τs∝τp (where τs is the NM spin lifetime and τp the momentum relaxation time), that is, that spin relaxation occurs with finite probability at each momentum scattering event (~1 × 10−3 for pure Cu38). A monotonic decrease in NM resistivity (ρN) on cooling implies a monotonic increase in τp, and thus a monotonic increase in τs and λN, in direct contradiction with observations. This anomalous behaviour has proven very difficult to explain. Surface spin relaxation10, reduced dimensions9 and surface18/bulk8 (magnetic) impurities have all been advanced, but no consensus has emerged. One issue contributing to this is the focus on only a small set of materials, with Ni80Fe20/Cu and Ni80Fe20/Ag accounting for a major fraction of prior work10,18,28,30,31,32,33,34,35,39.
In this work, via systematic studies significantly expanding the range of FM and NM materials investigated (encompassing Ni80Fe20, Ni, Fe, Co, Cu and Al), we show that in devices where the FM and NM are synthesized in a single deposition sequence, the low T downturn in ΔRNL is not a property of an individual NM but rather of the FM/NM pair. NM materials that do not support local magnetic moments when a given FM is diluted in them are found to show no low T anomalies, exemplified by Al. For the FM/NM pairs that do exhibit the anomalous non-monotonicity, we provide strong evidence that FM/NM interdiffusion leads to the formation of local moments which suppress α, and to a lesser extent λN, via a manifestation of the Kondo effect. We further show that this suppression can be quenched by ultra-thin non-moment-supporting interlayers (ILs). We argue that these concepts provide a coherent explanation of all major features of the available data, with implications even for room temperature spin transport.
Field dependence of the non-local resistance
A schematic of the NLSV geometry employed in our work is shown in Fig. 1a; a typical (d=250 nm) NLSV device is shown in the scanning electron microscope image of Fig. 1b. The FM electrodes have widths wFM,inj and wFM,det, and thickness tFM, whereas the NM channel has width wN and thickness tN. Unless otherwise noted, devices in this work have tFM=16 nm and tN=200 nm. In Fig. 1c,d, we first illustrate the basic response of RNL to in-plane and perpendicular-to-plane magnetic fields (H|| and H⊥, Fig. 1a). Figure 1c shows RNL(H||) for a d=250 nm Ni80Fe20/Al device at T=50 K, the labels showing the magnetization orientation of FMinj and FMdet. As is typical26, a small field-independent background (16 μΩ here) has been subtracted. Complete and abrupt switching between P and AP is observed, enabling determination of ΔRNL, the T and d dependence of which allow for extraction of α(T) and λN(T). Figure 1d shows the dependence of RP and RAP on H⊥, for a d=2 μm Fe/Cu device at T=50 K. The gradually damped oscillations derive from the Hanle effect12,23,25,29,36,37,39 (because of the precession of the diffusing spins about H⊥), RP and RAP merging at high H⊥ when FMinj and FMdet are driven out of plane (see schematics, Fig. 1d). Such data enable extraction of τs, and thus (where D is the electron diffusivity), complementary to that from ΔRNL(d).
Varying FM/NM material combinations
Before detailed analysis of α(T), λN(T) and τs(T), we first present a central observation of this work, arrived at by studying ΔRNL(T) in a large set of materials (Fig. 2). The data are from NLSVs with d=250 nm, and a logarithmic T axis is chosen to illustrate the low T behaviour. Figure 2a focuses on Cu channels with Fe, Ni80Fe20, Co and Ni, Fig. 2b on Cu channels with Ni100-xFex (x=0, 20 and 100), and Fig. 2c on Al with Fe, Ni80Fe20 and Co. Beginning with Fig. 2a, we first note the ΔRNL(T) for Ni80Fe20/Cu, which indeed shows the anomalous decrease below ~40 K (refs 8, 10, 18, 30, 31, 32, 33). Considering Co, Fe and Ni, however, it can be seen that the low T downturn in ΔRNL(T) is obviously not a property of the NM alone, but is strongly influenced by the FM. Specifically, Fe/Cu shows the strongest downturn (onset temperature of 60 K), followed by Ni80Fe20/Cu (40 K onset), and then Co/Cu, where the effect is weak but occurs below ~130 K. In Ni/Cu on the other hand, we find no evidence for a low T downturn in ΔRNL(T). The Ni100−xFex/Cu case is particularly interesting and is highlighted in Fig. 2b, where data for Ni, Ni80Fe20 and Fe are shown normalized to the maximum ΔRNL. A clear progression is apparent. One interpretation, which we return to below, is that the low T downturn in ΔRNL(T) only occurs in Ni80Fe20/Cu because of the presence of Fe. Additional important information is obtained by extending the T range down to ~1 K. As shown in the inset to Fig. 2b (for Fe/Cu), the suppression of ΔRNL in fact saturates at low T, below ~5 K in this case. Finally, turning to Fig. 2c, we find radically different behaviour with Al channels. In Al devices, no significant low T suppression is observed for any FM, ΔRNL(T) monotonically increasing on cooling, qualitatively consistent with the E-Y mechanism. A number of other trends are also apparent in Fig. 2, such as the influence of the FM on the high T behaviour. The T dependence in this region strengthens as the FM is varied from Ni80Fe20→Ni→Fe→Co, which we ascribe to the influence of Curie temperature (TC) and magneto-crystalline anisotropy on α(T). FMs such as Co, with high TC and relatively large anisotropy, are expected to present weak α(T), whereas FMs such as Ni80Fe20 and Ni, with lower TC and anisotropy, should have stronger α(T)40. A second observation is the large variation in ΔRNL(T=0), which spans 30–2,500 μΩ. Although a number of factors contribute, particularly the resistivities of the FM and NM (ρFM and ρN), α(T=0) is a dominant parameter. It accounts in particular for the low ΔRNL in Ni, where α is significantly smaller than in Co, Ni80Fe20 and Fe (refs 41, 42).
Fitting ΔRNL(d) and the Hanle effect
To further investigate such issues, particularly the low T decrease in ΔRNL, α(T) and λN(T) were extracted from ΔRNL(d,T), focusing on Fe/Cu (with the strongest downturn) and Fe/Al (no downturn). Such data are shown in Fig. 3a,b, where ΔRNL(d) is plotted at various T. The solid lines are fits using an analytical solution20,21 to the NLSV spin diffusion problem in 1-D:
where α=I↑−I↓/I↑+I↓ is the current polarization of the FM, λFM is the spin diffusion length in the FM, and RN=ρNλN/wNtN and RFM=ρFMλFM/wFMwN are the N and FM spin resistances. This expression applies in the transparent interface limit, that is, interface resistance <RN, RFM, which we verify to be the case here (see Supplementary Figs 1 and 2 and Supplementary Notes 1 and 2). All geometrical parameters in equation (1) were measured for each device, as were ρN(T) and ρFM(T) (see Supplementary Fig. 2 and Supplementary Note 2). This nevertheless leaves α(T), λFM(T) and λN(T) as free parameters, resulting in poorly constrained fitting. Specifically, although λN(T) determines the d dependence of ΔRNL, and can be independently extracted (particularly in the d>λN limit where an exponential fall-off is recovered), α(T) and λFM(T) control the magnitude of ΔRNL and are inseparable, entering through λFM/(1−α2). Constraints on one of λFM or α are thus required. As a starting point, we simply hold λFe constant at 4 nm, a value determined from the measured ρFe(T=5 K) via the observed scaling between λFM and ρFM43. The resulting λN(T) is shown in Fig. 3g,h, labelled as ‘Cu, NLSV’ and ‘Al, NLSV’, while α(T) is shown in Fig. 3i,j. In the Fe/Al case, both α and λN increase monotonically on cooling. However, Fe/Cu is more complex. As shown in Fig. 3g, λN(T) increases down to 50 K, below which it appears to undergo a slight decrease. This decrease is barely above experimental uncertainty, however, amounting to 6±6% based on our best error estimates. In contrast, a clear and statistically significant decrease in α is found as T is lowered below 50 K (Fig. 3i). As ΔRNL at d=250 nm is more sensitive to α than λN (from equation (1), see Supplementary Fig. 3 and Supplementary Note 3), this 15% decrease in α corresponds to a 28% decrease in ΔRNL, the majority of the observed suppression. We thus conclude that the low T downturn in ΔRNL in our NLSVs, although containing some contribution from enhanced spin relaxation, is dominated by d-independent suppression of the spin injection/detection efficiency. Exhaustive fitting, with a multitude of parameter constraints (see Supplementary Fig. 3 and Supplementary Note 3), confirms this.
As discussed above, RNL(H⊥), via the Hanle effect, provides access to τs, and an independent check of λN(T). In Fig. 3c,d, we thus plot ΔRNL (H⊥)=[RP(H⊥)−RAP(H⊥)]/[RP (0)−RAP (0)], at various T, for Fe/Cu and Fe/Al at d=2 μm. (This was recorded for positive and negative H⊥, but we plot here only the symmetric component.) Such large d is used to enable fitting with analytical expressions for spin diffusion-precession (see Methods), with no need to account for back-diffusion of injected spins23. The width and amplitude of the oscillations in Fig. 3c,d are controlled solely by τs and D, and the fits (solid lines) use D(T) determined from the measured ρN(T), resulting in the τs(T) shown in Fig. 3e,f. For both Fe/Cu and Fe/Al, τs is remarkably flat above 70 K, a dramatic illustration of the dominance of defects (for example, non-magnetic point-defects, grain boundaries) in spin relaxation. In accord with the E-Y mechanism, T-independent momentum relaxation processes associated with such defects result in T-independent spin relaxation. For Fe/Cu only (Fig. 3e), the situation is markedly different below 70 K, where τs drops from 12 to 7 ps, clearly correlated with ΔRNL(T). Despite this substantial decrease in τs, the corresponding drop in (Fig. 3g, ‘Cu, Hanle’) is small due to the increase in D (from 1/ρN) on cooling. The overall agreement between λN determined from ΔRNL(d) and from the Hanle effect is excellent (Fig. 3g,h), and the form of λN(T) for Fe/Cu is confirmed.
The observation that the downturn in ΔRNL(T) in our devices is dominated by α(T) (with only a secondary contribution from λN(T)), and is highly sensitive to the FM/NM pairing, is inconsistent with ‘channel only’ explanations, such as surface spin relaxation. This is underscored by the additional observation (for example, in Ni80Fe20/Cu, Supplementary Fig. 4 and Supplementary Note 4) that the ΔRNL suppression is tN independent8. Rather, the dominance of α(T) and sensitivity to FM/NM pairing point to explanations based on low T suppression of spin injection/detection efficiency at the interfaces. One general possibility for such is the formation of non-trivial interfacial magnetic states at low T because of FM/NM interdiffusion, such as spin-glass-like interfaces (potentially depolarizing the injected spin current), or non-collinear states (preventing full polarization). To investigate such possibilities, we undertook detailed T-dependent polarized neutron and X-ray reflectivity measurements on Ni80Fe20/Cu and Co/Cu bilayers deposited under identical conditions to our NLSVs. The data (Supplementary Figs 5 and 6 and Supplementary Notes 5 and 6) reveal remarkably T-independent magnetic depth profiles, however, ruling out even minor changes in the interfacial magnetic structure at low T. In Ni80Fe20/Cu, for example, the magnetic interface width is only 0.6 nm, with no apparent T dependence.
Local moments and the Kondo effect in spin transport
This confinement of strong FM/NM intermixing to a thin region close to the interface does not, however, rule out explanations based on low densities of FM impurities in the NM, whether from interdiffusion, residual FM vapour pressure during NM deposition, contamination of the NM source material8 or other sources18. Table 1, which compares the ability of Cu and Al to host local magnetic moments when the FMs used in this work are added as dilute impurities, reveals some striking correlations in this context. 3d elements form local moments only when diluted in certain NMs44,45,46, a fact that can be understood within the Anderson virtual bound state model44,45, where the local moment is dictated by the relative magnitudes of the NM Fermi energy (EF), s-d hybridization potential and FM intra-atomic d-d Coulomb repulsion. In Al, for example, the high EF locates both up-spin and down-spin virtual bound states below the Fermi surface, quenching local moments44,45,46. Considering Table 1, the correlation between local moment formation and the occurrence of a low T downturn in ΔRNL(T) in a given FM/NM pair is in fact striking, the only apparent anomaly being Ni/Cu, as discussed below.
Importantly, in the cases where local moments do form, the Kondo effect44,45,46,47,48,49 is anticipated. Essentially, delocalized electrons in the NM are expected to screen the local moments from dilute FM impurities around some characteristic T scale, TK (refs 45, 46). Table 1 shows not only that the downturn in ΔRNL(T) correlates with the formation of local moments, but moreover, that the observed downturn temperature (Tmax) correlates with TK. For Ni in Cu, for example, although dilute moments form, the extremely high TK (>1,000 K) precludes observation of Kondo physics at T≤300 K, consistent with observations. For Fe in Cu on the other hand, TK=30 K (ref. 44), comparing reasonably to Tmax=60 K for Fe/Cu and Tmax=40 K for Ni80Fe20/Cu. Note that in the latter case, because of the prohibitively high TK for Ni in Cu, only Fe impurities contribute to the changes of ΔRNL(T) over the measured T range, consistent with the larger downturn in Fe than Ni80Fe20 (Fig. 2b). For Co in Cu, we observe only a weak downturn, with Tmax=130 K. The limited solubility in this case limits the strength of Kondo effects, whereas the 130 K Tmax is consistent with the 23 K<TK<500 K bound from known limits for surface and bulk Co impurities in Cu (refs 44, 47). This Kondo-suppressed spin accumulation picture is also consistent with literature observations in the heavily studied Ni80Fe20/Ag system5,29,35,36, including the existence of a downturn (because of local Fe moments in Ag), the relatively weak decrease in ΔRNL (7%, because of low miscibility) and the approximate correspondence between Tmax (<20 K) and TK (~5 K for Fe/Ag). Taken as a whole, the correlations between moment formation, TK, and the magnitude and onset temperature of the downturn in ΔRNL are thus remarkably strong across a wide variety of materials, revealing a simple pattern to the apparently complexity in Fig. 2.
Given these strong correlations with moment formation, miscibility and TK, we propose a scenario where dilute quantities of FM impurities in the near-interface region of the NM lead to a novel manifestation of the Kondo effect. We suggest that the disordered local moments (and the accompanying conduction electron screening) depolarize the injected spin current at temperatures around TK, reducing the polarization injected into the bulk of the channel (see Supplementary Fig. 7 and Supplementary Note 7). Although such physics has not been previously discussed in NLSVs, the reciprocal role of spin injection on the Kondo effect in charge transport has been explored48, and some precedent for related effects exists in magnetic tunnel junctions50. Critically, we believe that this picture provides qualitative explanations for all observed phenomena. The absence of a downturn in Al-based devices, the miscibility-related magnitude in FM/Cu and the correlation between Tmax and TK are all straightforwardly understood. Regarding the latter it should be noted that in this picture Tmax will be determined by the competition between the Kondo suppression of the spin accumulation and the usual α(T), λ(T) and ρ(T), meaning that the correlation between TK and Tmax is expected to be only approximate, as is the case. Our model also explains the saturation of the downturn in ΔRNL(T) at very low T in Fe/Cu (Fig. 2b, inset), as the Kondo suppression of α should saturate at T<<TK, because of inter-moment d–d interactions and entry into the unitary scattering limit44,45,46. Note that the fact that we observe no conventional Kondo effect in direct four-terminal ρN(T) measurements on our devices (see Supplementary Figs 2 and 4 and Supplementary Notes 2 and 4) in no way contradicts this picture. The charge current in such measurements will be dominated by the highest conductivity central regions of the NM channel, the near-interface regions relatively rich in FM impurities having little influence on ρN(T). This would be expected to change if interdiffusion were promoted to the extent that the bulk of the NM channel reached FM concentrations >O(1 p.p.m.), where the Kondo effect emerges. To demonstrate this directly, we thermally annealed a d=250 nm Fe/Cu device for 2 h under high vacuum at 500 °C, resulting in the ρN(T) shown in the inset of Fig. 4a, where a clear Kondo minimum occurs. The ρN(T) curve can in fact be fit to an empirical relation51 for the Kondo effect (purple solid line, see Methods) with TK=30 K, yielding a Kondo resistivity, ρK=0.06 μΩcm, and a resistivity minimum at 20.5 K. The latter is consistent with an average Fe concentration of 100–200 p.p.m. (ref. 52). Most importantly, examining ΔRNL(T) for such a device (Fig. 4a), we find a substantial enhancement of the downturn, ΔRNL being reduced by ~50% below a Tmax that now exceeds 100 K. These results prove that Kondo physics is active in charge transport in our devices and that the anomaly in ΔRNL(T) is indeed enhanced as the charge Kondo effect is promoted, as expected.
A final point to emphasize regarding the Kondo suppression of ΔRNL(T) is that while in our case the role of α(T) is dominant over λN(T), this balance could vary with synthesis conditions. Deposition of the FM and NM in separate systems10, contamination of the NM source with FM impurities53 and transfer of FM impurities to the NM channel from resists18 will change the balance between FM/NM interface and bulk channel magnetic impurity contributions, altering the relative contributions of α(T) and λN(T) to the downturn in ΔRNL.
Quenching local moments and restoring ΔRNL(T)
Having identified the Kondo effect at FM/NM interfaces as the key factor in the low T downturn in ΔRNL, it is natural to consider whether this effect, which is deleterious in terms of maximizing spin signals, can be mitigated. Although it is clear that pure Al channels provide one means to do so, a more general approach, compatible with any channel material, would be preferable. To this end, we pursued insertion of thin Al ILs between FM and NM, the low solubility of transition metal FMs in Al minimizing interdiffusion, whereas the properties of Al eliminate local moment formation and Kondo effects. Fe/Cu NLSVs were thus fabricated with a ~5-nm thick IL between the Fe and Cu (see Methods, and the schematic in Fig. 4b). Simple calculations establish that contributions to the spin transport from the IL in comparison to the bulk of the Cu channel can safely be neglected (Supplementary Fig. 8 and Supplementary Note 8). Figure 4b compares ΔRNL at d=250 nm for Fe/Cu and Fe/Al IL/Cu devices. The data are scaled to overlap at high T (>150 K), in order to easily assess the impact of the Al IL on the low T ΔRNL. Remarkably, the low T Kondo suppression of the spin accumulation is almost completely removed by an IL of only 5 nm. Defining δRNL as the difference between the high-T-scaled ΔRNL(T) for Fe/Al IL/Cu and Fe/Cu devices (Fig. 4b), we plot in Fig. 4cδRNL(T), normalized to its 5 K value, for several d. Not only do the data collapse to a single universal curve, but also, as demonstrated by the fit, the behaviour around TK is well described by logarithmic scaling. Specifically, the solid line is a fit to δRNL=a[1–b log(T/TK)] with TK=30 K, the accepted value for Fe in Cu. Such a logarithmic form around TK, with expected negative and positive deviations below and above TK, respectively, is a commonly used phenomenological description of Kondo physics44,50, and can be rationalized from equation (1) assuming δα ∝ [1–A log(T/TK)], that is, a Kondo-related suppression of α. An understanding beyond simple phenomenology will require an approach sophisticated enough to capture the T-dependent influence of local moments and their associated conduction electron screening, as was achieved in the normal Kondo effect via higher-order perturbation theory. That the effect we see here is certainly dominated by α, however, is emphasized in Fig. 4d, where α(T), scaled to its maximum value, is plotted for Fe/Al, Fe/Cu and Fe/Al IL/Cu. These data result from a large set of ΔRNL(T,d) data (Supplementary Fig. 8 and Supplementary Note 8). The 5-nm thick IL in the Fe/Al IL/Cu device almost completely restores α(T) to the monotonic form found in Fe/Al. We note that tunnel barriers between the FM and NM5,13,14,25,36,50 could have a similar role, provided they prevent even minor NM/FM contamination.
In summary, we have proposed a solution to the long-standing puzzle of the non-monotonicity of the T-dependence of the spin accumulation signal in metallic NLSV devices, the essential concept being a novel manifestation of the Kondo effect. In essence, we propose that in FM/NM combinations where the FM forms local moments when diluted in the NM, Kondo screening of the spin-disordered local moments leads to suppression of the injection/detection efficiency, and to some extent the NM spin diffusion length, around the Kondo temperature. We have further demonstrated a simple means to mitigate this effect, via insertion of a thin non-moment-supporting layer between the FM and NM. In addition to providing a solution to this immediate problem, and posing a significant challenge for future theoretical work, we propose that this work also highlights a number of potential new directions at the interface between spintronics and Kondo physics54,55. We imagine future research to more fully explore the impact of Kondo physics on spin transport in metallic hetero- and nano-structures, as well as the reciprocal effects of spin injection and relaxation on Kondo systems. Significantly, the potential relevance of these ideas to room temperature spin transport should also be explored. Common systems such as Ni/Cu, Co/Cu and Co/Au possess very high Kondo temperatures, raising the possibility that physics of the type elucidated here could be suppressing spin accumulation even at room temperature.
NLSV devices were fabricated on Si/Si-N(2,000 Å) substrates using a Vistec EBPG5000+ electron beam lithography tool with a PMGI/PMMA bilayer resist stack. Clean, transparent FM/NM interfaces were achieved by multi-angle deposition7,37, without breaking vacuum, with the FM deposited at an angle of 49° and the NM at normal incidence. That the transparent interface limit20,21,22 was achieved was explicitly verified by FM/NM contact resistance, Hanle effect and ΔRNL(d) measurements (see Supplementary Figs 1 and 2). All materials were deposited in the same vacuum system (base pressure O(10−10 Torr)), using electron beam (for Al, Co, Cu, Fe, Ni, Ni80Fe20) or thermal (for Cu) evaporation. Deposition rates for NM and FM materials were 1.0 and 0.5 Å s−1, respectively, with growth pressures from 8 × 10−10 to 1 × 10−8 Torr. Nominal purities for the FM and NM materials were 99.95% and 99.999%, respectively. Film thicknesses were calibrated using ex situ grazing incidence X-ray reflectivity and monitored during deposition using a quartz crystal monitor. Patterned wire widths and separations were directly measured via scanning electron microscopy (wN=150–200 nm, wFM,inj=150 nm and wFM,det=100 nm). A domain wall nucleation pad was incorporated into FMinj to reduce its coercivity and enable the AP state to be reliably obtained.
Transport measurements and fitting
Transport measurements were performed with 13 Hz AC excitation, at bias currents from 100 μA to 1 mA. At low T, careful checks for self-heating were carried out. Measured ΔRNL values were corrected for small (<10%) sample-to-sample variations in ρ and wN using the scaling expected from equation 1. For Hanle measurements, data were acquired in both the P and AP states (as shown in Fig. 1d). The difference between these two signals (Fig. 3c,d) removes any background associated with FM rotation and leaves only the spin precession component37. Note that the data presented in Fig. 3c,d are averages from positive and negative H⊥ sweeps. These data were fit to a solution of the spin-precession-diffusion equation, taking into account finite contact size and rotation of the magnetization of the FM electrodes:
where ωL is the Larmor frequency (ωL=γB, with γ the gyromagnetic ratio and B the magnetic flux density), t is the spin transit time, S0 is a scaling term to account for the zero-field spin signal and xdet(xinj) accounts for integration of the signal over the finite detector (injector) contact width. Note that this model does not take into account the effect of back-diffusion of spins into the FMs (that is, spin sinking). However, by d-dependent Hanle measurements, we have verified that the large separations reported here (d=2 μm) are in the NM-channel-dominated regime, where spin sinking is negligible23. For fitting, D(T) is determined from the experimental ρN(T) using a form of the Einstein relation, ρN(T)−1=e2N(EF)D(T), where N(EF) is the density-of-states at the Fermi level. Note that the displayed curves (Fig. 3c,d) use a slightly suppressed Ms to phenomenologically account for in-plane rotation and demagnetization of the FM electrodes. The fitting results are quite insensitive to this value of Ms, however, and, although the fit quality suffers, using standard literature values for Ms does give quantitatively similar results for τs.
The Fe/Cu devices for which data are shown in Fig. 4a were annealed in high vacuum (base pressure 10−7 Torr). The low T resistivity was fit using a phenomenological model for the Kondo contribution to the resistivity51:
with . ρ0 describes the impurity scattering contribution to ρ, whereas A and B account for electron–electron and electron–phonon scattering. We fix s=0.225 and TK=30 K from literature values to obtain the Kondo resistivity ρK.
IL device fabrication
For the devices with an IL, a ~5-nm thick Al layer was grown after FM deposition. To ensure appropriate coverage of the FM/NM interface region (that is, a layer width>wN, see inset to Fig. 4a), this was done in discrete steps between −3° and +3° from normal incidence. Al was chosen as the IL material for several reasons: Fe atoms that diffuse into Al will not form local moments; the diffusivity of Fe in Al is substantially lower than it is in Cu and the use of a thin (t<<λN), low ρN material such as Al should not otherwise alter the magnitude or T-dependence of the spin accumulation.
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This project was funded by the NSF MRSEC under award DMR-0819885 and a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme (project no. 299376). Research at the ORNL Spallation Neutron Source ORNL was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. ORNL is managed by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy. Parts of this work were carried out in the Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program. Parts of this work were carried out in the Minnesota Nano Center, which receives partial support from the NSF through the NNIN program.
The authors declare no competing financial interests.
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O'Brien, L., Erickson, M., Spivak, D. et al. Kondo physics in non-local metallic spin transport devices. Nat Commun 5, 3927 (2014). https://doi.org/10.1038/ncomms4927
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