## Introduction

The field of spintronics1 emerged following the discovery of spin-dependent scattering of electrons at ferromagnetic/nonmagnetic (F/N) interfaces2 and giant magnetoresistance (GMR) in F/N/F structures3. In a F/N/F spin-valve, GMR is the difference in electrical resistance (ΔR) between antiparallel (AP) and parallel (P) magnetisation states of the F layers and is current-bias independent. In the AP-state, both the majority and minority spin-electrons are strongly scattered and ΔR = R(AP) − R(P) > 0 with the magnitude of ΔR dependent on the spin-polarization of the F layers, interfacial spin-flip, and the spin decay length in N4,5. In superconducting F/S/F spin-valves6,7,8 (where S is a superconductor) the superconducting critical temperature (Tc) depends on the magnetic moment orientation of the F layers due to the superconducting spin valve effect: in the P-state, the magnetic exchange fields suppress Tc(P) relative to Tc(AP), in which the magnetic exchange fields partially cancel, meaning $${{\Delta }}{T}_{{{{{{{{\rm{c}}}}}}}}}={T}_{{{{{{{{\rm{c}}}}}}}}}^{AP}-{T}_{{{{{{{{\rm{c}}}}}}}}}^{P} > 0$$. This effect allows the superconducting spin-valve to act as a valve for superconducting current flow, demonstrating infinite magnetoresistance, via switching the magnetic state of a device with suitably large ΔTc held at constant temperature. This current-bias independent behaviour is observed in current-in-plane (CIP) F/S/F spin-valves with ΔTc reaching tens of mK for transition metal Fs9,10,11,12,13,14,15,16,17,18 and several hundred mK for rare-earth ferromagnetic metals and insulators19,20,21. These experimental values of ΔTc are orders of magnitude smaller than values predicted by theory6,7,8, as it has proven experimentally challenging to reach the theoretically indicated optimum parameter space. Negative ΔTc values have also been reported14,22,23,24,25,26,27,28,29,30, attributed either to quasiparticle (QP) spin-accumulation23,26,28 suppressing Tc in the AP-state31,32, or flux penetration in S from out-of-plane domain walls in the F layers14,24,27,30. Other superconducting spin valves featuring a tunnel barrier have also been demonstrated33. Current-perpendicular-to-plane (CPP) devices have larger values of GMR than CIP devices34,35,36,37, but are less investigated due to the extra complications of fabrication compared to CIP spin-valves, and so investigation into CPP devices with superconducting spin-valves has been limited. One reported CPP device38 was a F/S/F spin-valve, which showed GMR behaviour (ΔR > 0) due to quasiparticle transport ("QP GMR") with a reduced spin decay length relative to the normal state for superconducting Nb layer thicknesses exceeding 30 nm. We note that the superconducting spin-valve effect (ΔR < 0) was not observed and that superconducting devices with thicknesses below 30 nm were not reported in that study38.

In this article, we systematically investigate superconducting CPP F/S/F spin-valves with Py(15)/Cu(10)/Nb(dNb)/Cu(10)/Py(15)/FeMn(10) layers (numbers in nm units) sandwiched between 200-nm-thick Cu electrodes (Fig. 1b). CPP devices have been used to investigate the interaction of non-equilbrium spin currents and superconductivity, by using the magnetoresistance of the CPP spin valve to quantify the spin decay through the superconductor. As expected, with decreasing Nb thickness (dNb) QP GMR increases; however, below a critical thickness of superconducting Nb (dNb = 26 nm) a sign change in ΔR is observed, consistent with the appearance of the superconducting spin valve effect in these CPP devices, which dominates the QP GMR behaviour at these thicknesses. We show a systematic crossover between these competing behaviours, dependent on dNb.

## Results and discussion

### Experimental setup

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 layers39,40,41, 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 Tdevice, and Tc as the temperature at 50% of the resistance change below Tdevice (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.

### Device behaviour

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 dNb = 28.5 nm, Tc(AP) < Tc(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 dNb = 25 nm ΔR is negative (Fig. 2c), and Tc(P) < Tc(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 Hc2 values (being mid-transition at measurement temperatures), and therefore exhibit visible resistance increases within an applied magnetic field.

### Normal state spin decay

In Fig. 3 we show the absolute value AΔR versus dNb, 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/Tdevice = 0.3. Blue points are devices demonstrating the superconducting spin valve effect. By fitting a simple decaying exponential, $$\exp (-{d}_{{{{{{{{\rm{Nb}}}}}}}}}/{l}_{{{{{{{{\rm{sf}}}}}}}}})$$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: $${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{N}}}}}}}}}=25\pm 3$$ nm, and $${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{S}}}}}}}}}=12\pm 4$$ 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 ΔRnorm = [RAP(H = 0) − RP(0)]/RP(0) range from ΔRnorm = 0.00024–0.0045 in the normal state, from ΔRnorm = 0.00032–0.0054 for QP GMR devices, and from ΔRnorm = −0.011 to −0.053 for devices demonstrating the superconducting spin valve effect.

### Crossover

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/Tdevice = 0.3 versus dNb, which shows a systematic dependence of AΔR on dNb, with a crossover from positive to negative AΔR occurring at dNb = 26 nm. The inset shows the equivalent trend of ΔTcversus dNb. For dNb = 21 nm, the superconducting spin valve effect reaches a positive ΔTc 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 mK9,10,11,12,13,14,15,16,17,18,22,23,24,25,26,27,28,29,30. However, we note that these large values of ΔTc 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 ΔTc 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 dNb, using Tdevice as the independent parameter, the outlier points at dNb = 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 dNb/ξS,d, where ξS,d is the dirty limit coherence length in the superconductor, calculated using

$${\xi }_{S,d}=\sqrt{\frac{\hslash D}{1.764{k}_{{{{{{{{\rm{B}}}}}}}}}{T}_{{{{{{{{\rm{device}}}}}}}}}}},$$

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 kB is Boltzmann’s constant. Using this normalised dNb, we account for both thickness and processing effects which may affect the superconductivity in the devices. Figure 5 shows AΔR at T/Tdevice = 0.3 and (Inset) ΔTc vs. dNb/ξS,d, which shows that the crossover between the two behaviours occurs at around dNb = 2ξS,d.

Both Figs. 4 and 5 show the same overall trend: with decreasing dNb, 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 dNb. 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/Tdevice = 0.3 normalised by ΔR in the normal state (Supplementary Note 1: Supplementary Fig. 4b).

### Background effects

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 dNb, 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 dNb = 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.

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 Tc (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 reflection45,46,47,48,49 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 ($${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{N}}}}}}}}}=25\pm 3$$ nm, and $${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{S}}}}}}}}}=12\pm 4$$ nm) can be compared with other values from the literature. A similar CPP structure has been used previously38 to measure values of $${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{N}}}}}}}}}=48\pm 3$$ nm and $${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{S}}}}}}}}}=17.5\pm 0.6$$ nm. Additionally, a value of $${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{N}}}}}}}}}=40\pm 5$$ 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 Tdevice, 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 Tc 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 dNb 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 dNb = 2ξS,d, from Fig. 5, supported by the crossover thickness of dNb = 26 nm, which is close to twice $${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{S}}}}}}}}}=12\pm 4$$ nm, similar to the results of Gu et al.38.

### Phenomenological model

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. ΔAP = ΔP = Δ(T), and reduced thickness dNb − 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 dNb = 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,

$${{\Delta }}R=A\exp \left[\frac{-({d}_{{{{{{{{\rm{Nb}}}}}}}}}-{d}_{0})}{{l}_{{{{{{{{\rm{S}}}}}}}}}}\right]-B\exp \left[\frac{-({d}_{{{{{{{{\rm{Nb}}}}}}}}}-{d}_{0})}{{{{\Lambda }}}_{{{{{{{{\rm{S}}}}}}}}}}\right]$$

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 ΛS. In the thinner Nb regime of our data, Tc(AP) > Tc(P) meaning that the superconducting spin-valve effect enhances ΔAP7,8; 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 ΔTc data, which fits both data sets. We find d0 = 28.8 ± 4.4 nm, lS = 7.1 ± 2.0 nm and ΛS = 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 dNb, 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 lS to the value $${l}_{{{{{{{{\rm{sf}}}}}}}}}^{{{{{{{{\rm{S}}}}}}}}}=12$$ nm. We find a value for ΛS = 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 ΛS = 2.2 ± 0.7 nm value is very small and does not initially appear to represent a physical length, unlike lS and d0; however, we note previous superconducting spin-valve investigations11 have seen a dramatic shift from a ΔTc of 41 mK to "only a few mK” for an increase in dNb 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 lS 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 layers14,29,53. 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 dNb, such as the crossover we show here.

## Conclusion

In summary, we have presented evidence for a competition between QP GMR and the superconducting spin valve effect in superconducting CPP spin-valves. Below a Nb thickness of dNb ≈ 26 nm, ΔR is negative and determined by the superconducting spin valve effect; beyond this critical thickness, ΔR is positive with a magnitude that is determined by QP Andeev reflection. Figure 5 suggests this thickness appears to correspond to twice the dirty limit coherence length of the devices. These results are relevant to development of quasiparticle spintronics devices, suggesting devices utilising QP GMR effects should be fabricated with dNb > 26 nm, or consider using the superconducting spin valve effect.

## Methods

### Pillar fabrication

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.

### Measurement

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.