Competition between the superconducting spin-valve effect and quasiparticle spin-decay in superconducting spin-valves

In a ferromagnet/normal metal/ferromagnet spin-valve, spin dependent scattering causes a difference in resistance between antiparallel (AP) and parallel (P) magnetization states. The resistance difference, ΔR = R(AP) − R(P) is positive due to increased scattering of majority and minority spin-electrons in the AP-state. If the normal metal is substituted for a superconductor, the superconducting spin-valve effect occurs: in the AP-state the net magnetic exchange field acting on the superconductor is lowered and the superconductivity is reinforced meaning R(AP) decreases. For current-perpendicular-to-plane spin-valves, existing experimental studies show that the normal state effect dominates (ΔR > 0) over the superconducting spin valve effect (ΔR < 0). Here however, we report a crossover from giant magnetoresistance (ΔR > 0) to the superconducting spin-valve effect (ΔR < 0) in current-perpendicular-to-plane ferromagnet/superconductor/ferromagnet spin-valves as the superconductor thickness decreases below a critical value. Superconducting spintronics aims to utilise the interaction between magnetic order and superconductivity in order to enhance the performance of a spintronics-based device. Here, the authors experimentally investigate a superconducting spin valve and report a crossover from giant magnetoresistance to the superconducting spin-valve effect as function of material thickness.

T he field of spintronics 1 emerged following the discovery of spin-dependent scattering of electrons at ferromagnetic/ nonmagnetic (F/N) interfaces 2 and giant magnetoresistance (GMR) in F/N/F structures 3 . 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 currentbias 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 N 4,5 . In superconducting F/S/F spin-valves [6][7][8] (where S is a superconductor) the superconducting critical temperature (T c ) 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 T c (P) relative to T c (AP), in which the magnetic exchange fields partially cancel, meaning ΔT c ¼ T AP c À T P c >0. This effect allows the superconducting spinvalve to act as a valve for superconducting current flow, demonstrating infinite magnetoresistance, via switching the magnetic state of a device with suitably large ΔT c held at constant temperature. This current-bias independent behaviour is observed in current-in-plane (CIP) F/S/F spin-valves with ΔT c reaching tens of mK for transition metal Fs [9][10][11][12][13][14][15][16][17][18] and several hundred mK for rareearth ferromagnetic metals and insulators [19][20][21] . These experimental values of ΔT c are orders of magnitude smaller than values predicted by theory [6][7][8] , as it has proven experimentally challenging to reach the theoretically indicated optimum parameter space. Negative ΔT c values have also been reported 14,[22][23][24][25][26][27][28][29][30] , attributed either to quasiparticle (QP) spin-accumulation 23,26,28 suppressing T c in the AP-state 31,32 , or flux penetration in S from out-of-plane domain walls in the F layers 14,24,27,30 . Other superconducting spin valves featuring a tunnel barrier have also been demonstrated 33 . Current-perpendicular-to-plane (CPP) devices have larger values of GMR than CIP devices [34][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 device 38 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 study 38 .
In this article, we systematically investigate superconducting CPP F/S/F spin-valves with Py(15)/Cu(10)/Nb(d Nb )/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 (d Nb ) QP GMR increases; however, below a critical thickness of superconducting Nb (d Nb = 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 d Nb .

Results and discussion
Experimental setup. The antiferromagnetic layer of FeMn exchange biases the top layer of Py (Ni 80 Fe 20 ), ensuring a stable APstate (Fig. 1a). The Cu between the Nb and Py improves interface quality by limiting magnetic dead layers [39][40][41] , and also increases the magnitude of magnetoresistance 38 . 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 .
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 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.
Normal state spin decay. 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, expðÀd Nb =l sf Þ 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 nm 43 ), we estimate spin-diffusion lengths from the GMR data in both the normal and superconducting states: l N sf ¼ 25 ± 3 nm, and l S sf ¼ 12 ± 4 nm. The decay length for QP GMR (in the superconducting state) is shorter than the normal state decay length, as found previously 38 . 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.
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/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 c versus 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][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 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 using where D = 1.4 × 10 −4 m 2 s -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 .
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).
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 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.
We have considered alternative explanations for the negative ΔR in our devices (Fig. 2e) including anisotropic magnetoresistance 44 . 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 field 3 . Negative magnetoresistance could also result from crossed Andreev reflection [45][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 valves 50 , but is generally considered as a non-local effect. We note that there is one report of crossed Andreev reflection measured in a local setup 51 , but the origin of magnetoresistance in this case is uncertain.
The values for spin decay length calculated in our devices (l N sf ¼ 25 ± 3 nm, and l S sf ¼ 12 ± 4 nm) can be compared with other values from the literature. A similar CPP structure has been used previously 38 to measure values of l N sf ¼ 48 ± 3 nm and l S sf ¼ 17:5 ± 0:6 nm. Additionally, a value of l N sf ¼ 40 ± 5 nm was extracted from a fit to ferromagnetic resonance data 52 . 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 l S sf ¼ 12 ± 4 nm, similar to the results of Gu et al. 38 .
Phenomenological model. A simple model for this setup 38 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 − d 0 , where d 0 /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, where the first term relates to QP GMR (ΔR > 0), as in the model from 38 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 d 0 = 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 d 0 = 26 nm, the crossover thickness, causing |A/B| = 1, and set l S to the value l S sf ¼ 12 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 d 0 ; however, we note previous superconducting spin-valve investigations 11 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 d 0 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 previously 38 .
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.

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 d Nb ≈ 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 d Nb > 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 Arion milling to form a wire pattern, followed by Ga-ion focused ion-beam etching 54 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 inplane 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.

Data availability
The raw measurement data that support the findings of this study and are used for all figures are available in Apollo, the University of Cambridge repository with the identifier https://doi.org/10.17863/CAM.84715.
Received: 21 January 2022; Accepted: 24 August 2022; Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/.