Reduced decay in Josephson coupling across ferromagnetic junctions with spin–orbit coupling layers

The superconducting proximity effect at interfaces between conventional superconductor (SC) and ferromagnetic (FM) layers enables unconventional Cooper pairing such as odd-frequency correlations, which may carry a non-zero total spin.^3–5 Such systems have sparked a significant interest within the research community in recent years, as they may give rise to dissipationless spin-polarized currents. The effect of magnetization on supercurrents has been studied extensively and has found applications in cryogenic memory^6–8 and quantum technologies.^9–12 The spin-polarization induced in Cooper pairs by passage through magnetic layers is governed by a combination of spin-mixing and spin-rotation effects.¹³ This process is illustrated by the example of a non-collinear (NC) magnetic structure that is proximitized to a SC state. When a spin-singlet Cooper pair diffuses from a SC into a FM, it experiences an exchange interaction and acquires a finite momentum.^4,14 This leads to the spatial oscillation of the singlet ground state wave function, known as $0−π$ phase oscillations. Along with such short-range singlet oscillations, this process generates short-range triplet correlations (SRTCs) with S_z = 0, which also oscillate spatially. In a quantization axis orthogonal to the initial magnetization direction at the SC/FM interface, the SRTCs are “rotated” into long-range triplet correlations (LRTCs) with S_z = 1. Unlike singlet correlations and SRTCs, LRTCs are not as susceptible to depairing and therefore can maintain coherence over relatively large distances across a FM. The most common method to experimentally investigate spin-polarized supercurrent is via transport experiments in Josephson junctions (JJs) in which the weak link contains magnetic non-collinearities, for example, non-collinear ferromagnetic layers,^15,16 helical ferromagnets,¹⁷ Heusler alloys,¹⁸ and artificial domain walls (DWs).¹⁹ Most recently, long-range supercurrents have been observed in JJs with a chiral Kagome antiferromagnet as the weak link.²⁰ Historically, LRTCs have been demonstrated in JJs with half-metallic ferromagnetic oxides, some with collinear magnetic structures.^21–23 These systems host LRTCs over significantly longer distances than conventional FMs. However, the transport through these JJs is more complicated as the half-metallic weak link also acts as a spin filter.^24,25

As an alternative to a magnetic non-collinearity, spin–orbit coupling (SOC) at the SC/FM interface has been proposed as a source of LRTCs.^1,2,26–28 The required SOC at the interface can be obtained by placing a thin heavy metal layer between the SC and the FM. The optimal magnetization direction of the FM depends on the geometry of the JJ: the FM should be canted at $45°$ from the direction of the supercurrent in a vertical JJ^2,29 or directed along the supercurrent for a lateral JJ.³⁰ Despite the reduced complexity of magnetic layering, earlier transport studies in JJs have not established the presence of LRTCs in these systems.^31–33 However, recent studies with non-equilibrium spin-pumping experiments have established the connection between spin absorption and LRTCs in the presence of SOC.^34–36 

In this work, we investigate transport in vertical JJs with the structure SC/NM/FM/NM/SC, where NM are non-magnetic layers formed from Pt, Ir, Cu, or Pt/Cu, and FM are ferromagnetic layers with perpendicular magnetic anisotropy (PMA) formed from Co/Ni/Co multilayers. For the case of Pt/Cu, Pt is, in each case, sandwiched between the SC layer and Cu. We vary the thickness of the FM for a given NM layer thickness. We show that the critical current (⁠ $Ic$⁠) in JJs with Pt and Ir layers decays similarly with FM thickness. On the other hand, this decay in “Pt” and “Ir” JJs is qualitatively different from that in JJs with “Cu” and “Pt/Cu.” We compare these dependencies with the established $0−π$ mechanism and conclude the possible presence of LRTCs in our Pt and Ir JJs.

Multilayer thin films with the structure of Si/SiO_x/TaN(2)/Nb(50)/NM/Co(0.7)/[Ni(0.3)/Co(0.7)]_n/NM/Nb(10)/Pt(2) were grown on Si(100) in a high vacuum sputter deposition system, where n is the number of Ni/Co bilayer repeats (see Sec. I of the supplementary material for more details). Note that the layer thicknesses are given in nanometers throughout the text unless otherwise noted. A few Pt samples were grown on a thinner Nb(20) layer. In the stack, the top Nb(10) layer ensures that the SC/NM and NM/SC interfaces in the junctions are as similar as possible and the Pt capping layer helps to prevent oxidation. Atomic force microscopy (AFM) measurements of the films show smooth growth with rms roughnesses averaging between 0.14 and 0.22 nm over an area of 1 × 1 μm². The superconducting critical temperature (T_c) of the bottom Nb layer, as determined from transport measurements in the complete stack, is 7.5 K for Nb(50) and 5.9 K for Nb(20) in the absence of any external magnetic field. Vibrating sample magnetometry (VSM) of the films was performed at room temperature using a LakeShore 8600 Series magnetometer. Magnetization mapping at room temperature was carried out using polar magneto-optical Kerr microscopy (p-MOKE).

The films were subsequently patterned into JJs via photo-lithography and Ar-ion milling etching processes (see Sec. I of the supplementary material for fabrication details). The structure of a fabricated JJ is schematically depicted in Fig. 1(a). The transport measurements were carried out in a Quantum Design PPMS using Keithley 2182a nanovoltmeters and 6221 current sources.

Figure 1(b) shows the out-of-plane (OOP) moment per unit area as a function of OOP magnetic field for typical films before device fabrication. All films exhibit PMA and have nearly 100% remnant magnetization. We note an additional magnetization for films with Pt layers compared to those with Cu and Pt/Cu, which arises from the proximity-induced magnetization in Pt.³⁷ Conversely, films with Ir layers exhibit the lowest magnetization although Ir exhibits a relatively smaller proximity-induced magnetization.³⁸ In Fig. 1(c), we compare the magnetization switching process of films with NM = Pt(2 nm) and n = 1, 4, and 6 (which correspond to summed FM layer thicknesses, $dF$ = 1.3, 4.3, and 6.3 nm). The increase in $dF$ results in a denser domain structure as it is energetically favorable. Thus, we observe a gradual transition in the magnetization switching mechanism from the propagation of a single domain wall (DW) to the percolation of stripe domains.

Figure 2 shows various cases of the dependence of the normalized critical current (I_c) on the external in-plane magnetic field, capturing the magnetic diffraction pattern measured in our junctions, where I_c was extracted from fitting the voltage (V) vs current (I) curves to the relation, $V=Re(RNI2−Ic2)$⁠, where R_N is the resistance of the junction in the dissipative state.^39, Figure 2(a) represents a typical diffraction pattern for the Cu and Pt/Cu JJs with the thinnest FM layer, i.e., n = 1. A skewed pattern indicates self-field effects arising from the magnetic field generated by the large supercurrent in these JJs. However, the self-field effect is not expected to considerably alter the maximum critical current in the diffraction pattern.⁴⁰ We do not observe skewing for any of the Pt and Ir JJs or for Cu and Pt/Cu JJs with $n≥2$ due to reduced Josephson coupling and lower supercurrents, and we measure an expected Airy diffraction pattern with minor deviations at higher order diffraction lobes. Figure 2(b) represents a typical diffraction pattern for junctions with thicker magnetic layers measured for Cu JJs with n = 6. With increasing n, we observe increasing deviations from Fig. 2(a). These patterns are asymmetrical with respect to zero field and the local maxima of the lobes decrease non-monotonically. Such diffraction patterns are often measured in JJs formed from Co/Ni multilayers with relatively large diameters.^16,31,32 This has been associated with the spatial non-uniformity of the magnetic field inside a JJ.^41,42 We find that the diffraction pattern is highly dependent on the magnetic initialization procedure of our junctions before cooling to below T_c. Saturating the PMA layer by applying an OOP $H=1 T$ before cooling results in a wide and prominent peak centered around zero field. However, fitting to an Airy-like function leads to errors due to asymmetry in the pattern. Therefore, we obtain the $Ic$ maxima of the JJ from the experimental data without fitting. In Fig. 2(c), we show the diffraction measured on the same device as Fig. 2(a) but under different cooling conditions, highlighting the unwanted effects of trapped flux within the junction. Unlike the continuous patterns observed in Figs. 2(a) and 2(b), Fig. 2(c) exhibits clear discontinuities, which have been attributed to trapped flux in the JJs.⁴³ The issue of Abrikosov vortices (AVs) is significant as it complicates accurate identification of the maximum $Ic$⁠. To mitigate the parasitic effects, we perform the following protocol until the desired condition without AVs is achieved: we measure diffraction pattern at the working temperature, 2 K; if discontinuities are detected, we warm the device to 10 K, saturate it with an OOP $H=1 T$⁠, cool slowly to the working temperature, and then reexamine the pattern.

In Fig. 3, we plot the decay of $IcRN$ across JJs with fixed NM layers (referred to as “3.5Cu,” “2Pt,” “3Ir,” and “2Pt3.5Cu,” where the numbers preceding the layers are their thicknesses in nm) for varying n. We fix Pt thickness at 2 nm and Ir thickness at 3 nm for further experiments because at these thicknesses, we obtain an optimum balance between superconducting properties, magnetic properties, and flux channeling (see Sec. II of the supplementary material). $Ic$ is multiplied by $RN$⁠, to account for variations in JJ area during device fabrication. However, this does not account for variations in $Ic$ due to supercurrent transmission across different layers and their interfaces. The highest $IcRN$ values at n = 1 are observed for 2Pt3.5Cu and 3.5Cu JJs, while those for 2Pt and 3Ir JJs are nearly an order of magnitude lower. This disparity may be attributed to the difference in supercurrent transmission across the Cu/Co, Pt/Co, and Ir/Co interfaces. Reduced Josephson coupling in JJs with Pt/Co and Ir/Co might be connected to the strong interfacial Dzyaloshinskii–Moriya exchange interaction at these interfaces,³⁸ which may lead to additional depairing mechanisms. The Nb/Cu and Nb/Pt interfaces appear to contribute similarly to the attenuation of $IcRN$⁠, since the values for the 2Pt3.5Cu and 3.5Cu layers are nearly the same. We also highlight the difference in supercurrent transmission between Cu/Co and Cu/Ni interfaces in Sec. IV of the supplementary material, noting that Cu/Ni has higher $IcRN$⁠. The variability of attenuation at interfaces with different materials complicates the identification of LRTC in JJs with SOC layers based solely on the absolute values of $IcRN$⁠.

Both these models [Eqs. (2) and (3)] imply the presence of LRTCs. In the latter case, fitting 2Pt data to Eq. (3) produces $ξLR$ = 3 nm and $ξSR$ = 0.4 nm. Although $ξSR$ = 0.4 nm is much shorter compared to 3.5Cu and 2Pt3.5Cu JJs from previously considered models, the ratio $ξLR/ξSR=7.5$ is a realistic reduction of decay from LRTC with respect to SRTC in the studied FM (see Sec. IV of the supplementary material). We note that theory predicts that the LRTC generation in our system depends on the relative orientation of the magnetization with respect to the direction of current flow, peaking at $45°$⁠, and vanishing at $0°$ or $90°$⁠.^2,29 Therefore, LRTCs are unlikely in JJs with fully OOP saturated FM. The dependence of supercurrent on the angle of magnetization naturally brings into consideration the magnetic origin of Eq. (2). One possible way to reliably achieve $45°$ magnetization is by utilizing a domain wall (DW). Indeed, the magnetization in a $180°$ DW in a FM with PMA will always contain $45°$ and $−45°$ orientations, regardless of the thickness of the FM or the lateral size of the magnetic film. Next, junctions with thicker d_F are expected to have a higher density of DWs as was demonstrated in Fig. 1(c). The asymmetric diffraction pattern in Fig. 2(b) resulting from non-uniform magnetic field in the weak link is consistent with this hypothesis. However, this would also imply that the Meissner effect takes part in a competition between exchange, anisotropy, and magnetostatic energies in the FM and that DWs are spontaneously nucleated at the superconducting transition of Nb. In additional M(T) measurements on an array of 6 μm pillars for 3.5Cu S/FM(n = 6)/S (see Sec. V of the supplementary material), we do not find any indication of such nucleation at T_c. Therefore, we can rule out spontaneous DW nucleation. On the other hand, the absence of DWs does not exclude possible canting because of the Meissner effect in Nb. By ensuring the absence of AVs in the Nb of the JJs via our initialization protocol, we expect the SC layer to expel the field lines into the NM layers between the SC and FM layers, directing the lines tangentially to the surface of the FM. This channeling of the field may act as an effective external in-plane field $HIPMeiss∝Ms∝dF$⁠, and thereby introduce a slight canting of the FM moment without breaking into DWs. Therefore, the magnetostatic interaction of the PMA FM with SC may lead to a reduction of supercurrent decay in JJs with SOC layers.

In conclusion, we have investigated vertical FM JJs with Pt, Ir, Cu, and Pt/Cu layers sandwiched between a FM and the SC. The $IcRN$ vs d_F data for JJs with Pt/Co and Ir/Co interfaces can be fitted with the established $0−π$ model with the assumption that the data are aliased by $0−π$ oscillations. From this analysis, we observe that Josephson coupling decays slower in JJs with Pt/Co interfaces with increasing d_F than in JJs with Cu/Co interfaces. We also suggest an inverse power law dependence of $IcRN$ on d_F in JJs with Pt/Co and Ir/Co and speculate its origin being a result of the interaction between the magnetization and the Meissner effect. Although the supercurrent transmission is attenuated, its reduced decay with d_F may indicate an unoptimized generation of S_z = 1 spin-triplet Cooper pairing in JJs with the SOC layers. We note that the choice of materials in this study makes our JJs compatible with contemporary spintronic devices.³⁸ 

See the supplementary material for details concerning sample preparation and fabrication, a comparison of different SOC thicknesses, a table with parameters from fitting models, a comparison of different FM types, a verification of the absence of DWs and the dependence of JJ critical current on temperature.

We thank J.-C. Jeon, J. Yoon, Y. Guan, and P. K. Sivakumar for valuable discussions. We also thank P. Grunewald, H. Deniz, D. Knyazev, and A. Stakhnova for technical help. We thank the reviewers for their feedback as it resulted in a significantly improved manuscript.

The authors have no conflicts to disclose.

Ivan Kindiak: Conceptualization (equal); Formal analysis (lead); Investigation (lead); Writing – original draft (lead); Writing – review & editing (lead). Swapna Sindhu Mishra: Conceptualization (lead); Investigation (lead); Writing – original draft (lead); Writing – review & editing (lead). Andrea Migliorini: Investigation (equal). Banabir Pal: Writing – original draft (supporting); Writing – review & editing (supporting). Stuart S. P. Parkin: Conceptualization (lead); Project administration (lead); Resources (lead); Writing – original draft (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.