The antiferromagnetic layer of FeMn exchange biases the top layer of Py (Ni₈₀Fe₂₀), ensuring a stable AP-state (Fig. 1a). The Cu between the Nb and Py improves interface quality by limiting magnetic dead layers^39–41, and also increases the magnitude of magnetoresistance³⁸. As Cu contact layers are used, the section under measurement is not exclusively the nanopillar device, but includes part of the patterned structure from which the nanopillar was milled, which is 4 μm wide and 20 μm long (illustration available in Supplementary Methods). This section of heterostructure, referred to as the ‘contact leads’, contributes to the measured resistance and so we refer to the measurement as ‘quasi’ four-point. One important impact of this contact lead resistance is that R(T) measurements can appear to contain two distinct superconducting transitions (Fig. 2a, d). The higher temperature transition (‘contact transition’) corresponds to the Nb in the contact leads, whereas the lower temperature transition (‘device transition’) corresponds to the nanopillar device. We define the onset temperature of the latter as T_device, and T_c as the temperature at 50% of the resistance change below T_device (Supplementary Note 4). Finally, in CPP measurements, since the cross-sectional areas (A) of the CPP spin-valves vary, ΔR is normalized by multiplying by A (i.e. AΔR)⁵.Fig. 2

The two different device responses observed. a Resistance (R) vs. temperature (T) curve for a device with Nb thickness d_Nb = 25 nm, in both the parallel (black) and antiparallel (blue) states. b, c Minor R(H) loops (μ₀: magnetic permeability in a vacuum, H: in-plane magnetic field) from the same device as (a), in the normal state, (b), showing giant magnetoresistance, and the superconducting (c) state, which has greater resistance in the parallel state. dR(T) curve for a device with d_Nb = 28.5 nm, in both the parallel (black) and antiparallel (blue) states. e, f Minor R(H) loops from the same device as (d), in the normal state, (e), showing giant magnetoresistance, and the superconducting (f) state. In the superconducting state, the antiparallel state has higher resistance, similar to the normal state. For the R(H) loops, light data represent sweeps from positive to negative H, starting at high positive values. The dark data in each loop is for the return sweep. In these minor loops, only the free permalloy layer undergoes switching, illustrated by the black arrows, which show the relative magnetic moment orientation of the permalloy layers. Arrows in a, d indicate the temperature of the corresponding R(H) loops. Supplementary Fig. 1 features b, f with different axes, and Supplementary Fig. 2 features similar plots for two additional devices.

R(T) and R(H) measurements of two devices are shown in Fig. 2. Whilst the normal state R(H) loops (Fig. 2b, e) indicate GMR behaviour as expected, the superconducting state loops (Fig. 2c, f) reveal that two distinct behaviours appear in our devices, which is supported by the device transitions in Fig. 2a, d; for the device with higher d_Nb = 28.5 nm, T_c(AP) < T_c(P) and ΔR > 0, consistent with the results of Gu et al.³⁸, suggesting GMR moderated by quasiparticles (QP GMR). For the device with lower d_Nb = 25 nm ΔR is negative (Fig. 2c), and T_c(P) < T_c(AP). These results are those expected for superconducting spin-valve effect behaviour observed in CIP devices. The resistance increase with increasing field visible in Fig. 2c occurs for all superconducting spin-valve effect devices, which all have low H_c2 values (being mid-transition at measurement temperatures), and therefore exhibit visible resistance increases within an applied magnetic field.

In Fig. 3 we show the absolute value A∣ΔR∣ versus d_Nb, with data points and y-error representing the mean of multiple devices from a single substrate and their standard deviation respectively. Grey data are from devices in their normal state (measured at < 10 K) and coloured data are from devices in the superconducting state at T/T_device = 0.3. Blue points are devices demonstrating the superconducting spin valve effect. By fitting a simple decaying exponential, exp(−dNb/lsf)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\exp (-{d}_{{{{{{{{\rm{Nb}}}}}}}}}/{l}_{{{{{{{{\rm{sf}}}}}}}}})$$\end{document}⁴², a reasonable approximation where the thickness of the ferromagnet (15 nm) is much greater than the spin-flip length in the ferromagnet (5.5 nm⁴³), we estimate spin-diffusion lengths from the GMR data in both the normal and superconducting states: lsfN=25±3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{N}}}}}}}}}=25\pm 3$$\end{document} nm, and lsfS=12±4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{S}}}}}}}}}=12\pm 4$$\end{document} nm. The decay length for QP GMR (in the superconducting state) is shorter than the normal state decay length, as found previously³⁸. Normalised values of ΔR_norm = [R^AP(H = 0) − R^P(0)]/R^P(0) range from ΔR_norm = 0.00024–0.0045 in the normal state, from ΔR_norm = 0.00032–0.0054 for QP GMR devices, and from ΔR_norm = −0.011 to −0.053 for devices demonstrating the superconducting spin valve effect.Fig. 3

A∣ΔR∣ (device area A, magnetoresistance ΔR) vs. Nb thickness (d_Nb) in current perpendicular-to-plane spin valves for both the normal state (below 10 K, grey) and superconducting state (T/T_device = 0.3, red/blue, where T is temperature and T_device is the onset temperature of the device transition). Red circles are devices showing quasiparticle giant magnetoresistance, whereas blue circles show the superconducting spin valve effect. For clarity, points are the mean value from multiple devices on a single substrate; vertical error bars are the standard deviation in AΔR of these devices and horizontal error bars the uncertainty in d_Nb. Supplementary Fig. 3 features this plot with devices plotted as individual points. Fits are a simple exponential decay considering each device individually, as described in the Normal state spin decay section.

We now detail the main results of this article. To the best of our knowledge, the superconducting spin-valve effect has not been previously observed in CPP superconducting spin valves, and so we investigate the factors that determine the appearance of this effect.

In Fig. 4 we plot AΔR at T/T_device = 0.3 versus d_Nb, which shows a systematic dependence of AΔR on d_Nb, with a crossover from positive to negative AΔR occurring at d_Nb = 26 nm. The inset shows the equivalent trend of ΔT_cversus d_Nb. For d_Nb = 21 nm, the superconducting spin valve effect reaches a positive ΔT_c up to 299 mK (Supplementary Note 1: Supplementary Fig. 2a), which is large for transition metal F/S/F spin-valves where values are usually of the order tens of mK^{9–18,22–30}. However, we note that these large values of ΔT_c are linked to inflation of AΔR (Supplementary Note 2); devices showing the superconducting spin-valve effect have suppressed and broadened device transitions (transition width > 1 K in Fig. 2a), meaning even these large ΔT_c values will not allow infinite magnetoresistance (complete switching between superconducting or normal states at a constant temperature). By considering the impact of superconductivity rather than just d_Nb, using T_device as the independent parameter, the outlier points at d_Nb = 31 nm were shown to agree far better with the overall trend in the data (Supplementary Note 1: Supplementary Fig. 4a and Supplementary Fig. 5). This led to consideration of the value d_Nb/ξ_S,d, where ξ_S,d is the dirty limit coherence length in the superconductor, calculated usingξS,d=ℏD1.764kBTdevice,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\xi }_{S,d}=\sqrt{\frac{\hslash D}{1.764{k}_{{{{{{{{\rm{B}}}}}}}}}{T}_{{{{{{{{\rm{device}}}}}}}}}}},$$\end{document}where D = 1.4 × 10⁻⁴ m²s^-1 is the electron diffusivity, calculated from a coherence length measurement of an isolated 30 nm Nb film, and k_B is Boltzmann’s constant. Using this normalised d_Nb, we account for both thickness and processing effects which may affect the superconductivity in the devices. Figure 5 shows AΔR at T/T_device = 0.3 and (Inset) ΔT_c vs. d_Nb/ξ_S,d, which shows that the crossover between the two behaviours occurs at around d_Nb = 2ξ_S,d.Fig. 4

AΔR (device area A, magnetoresistance ΔR) at T/T_device = 0.3 vs. Nb thickness d_Nb, where T is temperature and T_device is the onset temperature of the device transition. The inset is the difference between superconducting critical temperatures in the parallel and antiparallel states, ΔT_c, vs. d_Nb. Red points show quasiparticle giant magnetoresistance dominated behaviour, blue the superconducting spin valve effect dominated behavior. Points represent individual spin-valve devices. Vertical error bars are the measurement uncertainty in AΔR for each device and horizontal error bars the uncertainty in d_Nb. Curves are fits as described in the Phenomenological model section; grey curves fit with all parameters free, black with more limited parameters. The crossover point is d_Nb = 26 nm.

Both Figs. 4 and 5 show the same overall trend: with decreasing d_Nb, QP GMR (red) increases as expected, but then peaks and decreases rapidly, devices crossing over into superconducting spin-valve effect dominated behaviour, which rapidly increases in magnitude with decreasing d_Nb. The peak then fall shape of the trend indicates that rather than being a sudden switch from QP GMR to superconducting spin-valve effect behaviour, these are two separate effects which compete within the devices.

The crossover between positive and negative values of AΔR is clear and the magnitude is significant, ruling out minor background effects. Scatter of the data does not account for the crossover behaviour, as indicated by a plot of ΔR at T/T_device = 0.3 normalised by ΔR in the normal state (Supplementary Note 1: Supplementary Fig. 4b).

The ‘double’ transition visible within these devices highlights the contribution of the ‘contact leads’ to the measured resistance in these devices. It also highlights that the lower transition - the device transition - tends to be more suppressed in devices demonstrating the superconducting spin-valve effect compared to those demonstrating QP GMR (compare Fig. 2a, d, which feature device transitions around 2 K apart, whereas the ‘contact’ transitions differ by less than 1 K). This observation suggests not only d_Nb, but also the strength of superconducting order within the devices affect the appearance of the superconducting spin-valve effect.

Below their superconducting transition, the contact leads are superconducting and do not contribute to the measured R(H) response, as shown in the inset to Fig. 6a, which was measured on the contact leads only. The exception to this is the substrate with thinnest d_Nb = 21 nm: even at the lowest temperatures, the contact leads demonstrate an R(H) response which also shows the superconducting spin valve effect (Fig. 6a), which may contribute to the large magnitude of the measured effect for that device.Fig. 6

a Major resistance (R) vs. in-plane magnetic field (H) loop measured on the contact leads at 0.3 K for the device with Nb thickness d_Nb = 21 nm (μ₀ is the magnetic permeability in a vacuum). For this device only, there is a negative (parallel state is higher resistance) magnetoresistance response in the contact leads at the measurement temperature. Inset: for all other devices, the leads are superconducting below the contact lead transition, and show no magnetoresistance response at T/T_device = 0.3, where T is temperature and T_device is the onset temperature of the device transition. bR(T) curves from two devices on the same substrate d_Nb = 57 nm, normalised by their normal state resistance for comparison. The difference between the temperature of contact and device transitions varies in an unknown manner, and can be small enough that the two transitions are indistinguishable. Inset: T_device vs. nanopillar area, for a device showing the superconducting spin valve effect (d_Nb = 25 nm, dark blue) and a device showing quasiparticle giant magnetoresistance (d_Nb = 37 nm, light blue). Error bars represent measurement uncertainty.

We have considered alternative explanations for the negative ΔR in our devices (Fig. 2e) including anisotropic magnetoresistance⁴⁴. However, this is ruled out since anisotropic magnetoresistance is not observed in these superconducting spin-valve effect devices above T_c (Fig. 2b). Additionally, the zero field R(T) measurements show distinct differences between P- and AP-states and anisotropic magnetoresistance would not lead to such differences in the absence of an applied magnetic field³. Negative magnetoresistance could also result from crossed Andreev reflection^45–49 of electrons across the superconducting layer, when the layer is less than one superconducting coherence length thick. Crossed Andreev reflection has previously been considered as a source of magnetoresistance in CIP spin valves⁵⁰, but is generally considered as a non-local effect. We note that there is one report of crossed Andreev reflection measured in a local setup⁵¹, but the origin of magnetoresistance in this case is uncertain.

The values for spin decay length calculated in our devices (lsfN=25±3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{N}}}}}}}}}=25\pm 3$$\end{document} nm, and lsfS=12±4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{S}}}}}}}}}=12\pm 4$$\end{document} nm) can be compared with other values from the literature. A similar CPP structure has been used previously³⁸ to measure values of lsfN=48±3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{N}}}}}}}}}=48\pm 3$$\end{document} nm and lsfS=17.5±0.6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{S}}}}}}}}}=17.5\pm 0.6$$\end{document} nm. Additionally, a value of lsfN=40±5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{N}}}}}}}}}=40\pm 5$$\end{document} nm was extracted from a fit to ferromagnetic resonance data⁵². These literature values are larger than the values measured here; we attribute this difference to increased scattering due to impurities and defects introduced during the nanopatterning process. These defects may also contribute to the separation of device and ‘contact lead’ superconducting transitions. This separation is inconsistent even between devices on the same substrate, as demonstrated in Fig. 6b, which we cannot currently explain. If the focused ion-beam milling were accountable for this transition separation, the separation would scale with nanopillar area. However, as shown in the inset to Fig. 6b, the transition temperature of the device transition, represented by the starting temperature T_device, does not demonstrate any dependence on device area. This uncertainty around the two transitions does not affect the main observation of this paper; the appearance of the superconducting spin valve effect in both R(H) and R(T) measurements and a thickness dependent crossover between them.

The comparison of positive magnetoresistance data above and below T_c supports the suggestion that CPP devices demonstrate QP GMR, as originally demonstrated by Gu et al.³⁸. Similarly to that paper, we also observe a decrease in spin decay length in the superconducting state which is consistent with the additional impact of Andreev reflection causing decay of quasiparticles that cause this magnetoresistance. Unlike Gu et al.³⁸, we have also measured superconducting devices with d_Nb smaller than the thickness at which Andreev reflection does not appear to play a role. These devices are those that demonstrate the superconducting spin-valve effect, having negative AΔR. The crossover between these two effects appears to occur at around d_Nb = 2ξ_S,d, from Fig. 5, supported by the crossover thickness of d_Nb = 26 nm, which is close to twice lsfS=12±4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{S}}}}}}}}}=12\pm 4$$\end{document} nm, similar to the results of Gu et al.³⁸.

A simple model for this setup³⁸ assumes QP GMR in CPP F/S/F spin-valves decays due to Andreev reflection as quasiparticles pass a potential barrier with a temperature-dependent height i.e. Δ^AP = Δ^P = Δ(T), and reduced thickness d_Nb − d₀, where d₀/2 is the thickness of the region near each F/S interface where the superconducting gap and Andreev reflection are suppressed, expected to be equal to the coherence length. This approximation captures the QP GMR results in Fig. 4 beyond d_Nb = 26 nm, but cannot describe our superconducting spin-valve effect data.

We extend these ideas in a toy model that simply illustrates the two competing effects within our devices, capturing the overall trend as the difference of two exponential decays,ΔR=Aexp−(dNb−d0)lS−Bexp−(dNb−d0)ΛS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\Delta }}R=A\exp \left[\frac{-({d}_{{{{{{{{\rm{Nb}}}}}}}}}-{d}_{0})}{{l}_{{{{{{{{\rm{S}}}}}}}}}}\right]-B\exp \left[\frac{-({d}_{{{{{{{{\rm{Nb}}}}}}}}}-{d}_{0})}{{{{\Lambda }}}_{{{{{{{{\rm{S}}}}}}}}}}\right]$$\end{document}where the first term relates to QP GMR (ΔR > 0), as in the model from³⁸ and the second to the superconducting spin valve effect (ΔR < 0), with a characteristic decay Λ_S. In the thinner Nb regime of our data, T_c(AP) > T_c(P) meaning that the superconducting spin-valve effect enhances Δ^AP7,8; leading to decreased resistance as a greater proportion of the Nb is superconducting. We choose an exponential for this decay to reproduce the distinct shape of the data in Fig. 4, but note that a different thickness dependence may also be usable to describe the data, and the superconducting spin valve effect in particular. Here, our aim is to demonstrate that two competing effects can describe this crossover, rather than to definitively model the trend, as theoretical development of the interaction of these effects will be necessary for such a model. Initially, we fit this model with all parameters free and find values as an average and deviation from orthogonal distance regression on the AΔR and ΔT_c data, which fits both data sets. We find d₀ = 28.8 ± 4.4 nm, l_S = 7.1 ± 2.0 nm and Λ_S = 2.2 ± 1.2 nm, with the resulting curves shown in grey in Fig. 4. Whilst this curve successfully illustrates that two competing effects can be responsible for this dependence on d_Nb, we were also interested to see if the same could be achieved by linking the parameters to more physical values (further information on our model fitting is reported in Supplementary Note 3). We set d₀ = 26 nm, the crossover thickness, causing ∣A/B∣ = 1, and set l_S to the value lsfS=12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{S}}}}}}}}}=12$$\end{document} nm. We find a value for Λ_S = 2.2 ± 0.7 nm, resulting in the black curve in the main plot and inset of Fig. 4, and demonstrating that physical values used in the model can still give rise to the key peak in the data. The Λ_S = 2.2 ± 0.7 nm value is very small and does not initially appear to represent a physical length, unlike l_S and d₀; however, we note previous superconducting spin-valve investigations¹¹ have seen a dramatic shift from a ΔT_c of 41 mK to "only a few mK” for an increase in d_Nb of only 1 nm, which could only be modelled by theory using parameters that did not match the estimates of the authors. These short decay lengths may reflect some experimental effects not accounted for by theory based fits, but due to the uncertainty within the model, such as alternative dependencies that could be used, we do not feel these values and the model should be considered more than illustration of the potential for a more complete theory of this system.

The toy model illustrates coexistence of the superconducting spin-valve effect and QP GMR, which compete within these devices. We believe that whilst the two effects of superconducting spin-valve effect and QP GMR are not strictly linked, both heavily depend on the coherence length. The crossover thickness d₀ occurs at roughly twice the coherence length, as suggested in Fig. 5, and the QP GMR decay length l_S is dominated by the coherence length as found previously³⁸.

Previous studies showing both positive and negative values of ΔR are explained on the basis of stray magnetic fields or vortex flow from a multi-domain state of one or both coupled F layers^14,29,53. In our spin-valves positive ΔR is expected due to QP GMR, and a multidomain state with out-of-plane stray magnetic fields would cause positive magnetoresistance within the transition region, which is far from the measurement temperature of our QP GMR data (Fig. 2b). No studies that we are aware of have demonstrated a systematic change of sign of magnetoresistance with d_Nb, such as the crossover we show here.

Heterostructures are deposited by dc magnetron sputtering in an ultra-high vacuum chamber with a base pressure better than 10⁻⁸ mbar. Films are deposited onto (001) single crystal silicon with a 250 nm-thick surface oxide, with an in-plane magnetic field (100 mT) applied during growth to set in-plane uniaxial anisotropy. Powers of 60 W are used for Cu contact layers and the bottom Py layer, 15 W for other Cu layers and 30 W for all other layers.

The spin-valves are patterned into nanopillars using optical lithography and Ar-ion milling to form a wire pattern, followed by Ga-ion focused ion-beam etching⁵⁴ to form the pillars. A 100 pA beam current is used to thin down a wire section, followed by a wall cleaning step with a 10 pA beam current. The beam angle is then changed so that it is parallel to the surface of the substrate to enable cuts into the heterostructure to isolate the nanopillar from the rest of the ‘wire’ section. To enable this rotation, the substrate is mounted on a custom 45^∘ wedge holder. The lengths and widths of the nanopillars vary between 400–1500 nm and 300–1000 nm, respectively. Dimension and resistance values for each device are reported in Supplementary Table 1, and Supplementary Fig. 9 illustrates the focused ion-beam steps.

Resistance of the CPP spin-valves vs. temperature [R(T)] or in-plane magnetic field [R(H)] is measured using a ‘quasi’ four-point current-bias setup in a pulse-tube measurement system, which removes contact resistance. Measurements were made on devices in both the normal state (above the superconducting transition of the nanopillar device and contact leads, but below 10 K) and in the superconducting state, although many devices had such a suppressed transition temperature that they could not be measured in the superconducting state. The current used was 50 μA, which is not large enough to affect the superconducting critical temperature.