Pt and CoB trilayer Josephson \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}π junctions with perpendicular magnetic anisotropy

We report on the electrical transport properties of Nb based Josephson junctions with Pt/Co\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{68}$$\end{document}68B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{32}$$\end{document}32/Pt ferromagnetic barriers. The barriers exhibit perpendicular magnetic anisotropy, which has the main advantage for potential applications over magnetisation in-plane systems of not affecting the Fraunhofer response of the junction. In addition, we report that there is no magnetic dead layer at the Pt/Co\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{68}$$\end{document}68B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{32}$$\end{document}32 interfaces, allowing us to study barriers with ultra-thin Co\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{68}$$\end{document}68B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{32}$$\end{document}32. In the junctions, we observe that the magnitude of the critical current oscillates with increasing thickness of the Co\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{68}$$\end{document}68B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{32}$$\end{document}32 strong ferromagnetic alloy layer. The oscillations are attributed to the ground state phase difference across the junctions being modified from zero to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}π. The multiple oscillations in the thickness range \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.2~\leqslant ~d_\text {CoB}~\leqslant ~1.4$$\end{document}0.2⩽dCoB⩽1.4 nm suggests that we have access to the first zero-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}π and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document}π-zero phase transitions. Our results fuel the development of low-temperature memory devices based on ferromagnetic Josephson junctions.

at Nb/ferromagnet interfaces [2]. Another interfacial effect in thin films is the polarization of the adjacent layer. At some ferromagnet/non-ferromagnet interfaces, the ferromagnetic layer can create a polarization inside the non-ferromagnetic layer by the magnetic proximity effect. Polarization is particularly common at interfaces with Pd and Pt since they are stoner enhanced paramagnets.
To model a magnetic slab with possible magnetic dead layers and/or polarized adjacent layers, one can again plot moment/area versus d and fit to the expression, where d i is the x-axis intercept. A positive x-axis intercept is indicative of magnetic dead layer formation and the thickness of the dead layer at each interface can be estimated as d i /2.
A negative x-axis intercept is indicative that at least one of the adjacent layers has gained a polarization. In this instance, the y-intercept provides the magnitude of the contribution of the polarized layer(s) to the overall measured moment/area.
To describe our Pt/Co 68 B 32 /Pt data, we first attempt fitting to Equations S1 and S2.
The results of these fittings are shown in Figure S1. We find that these fits overestimate the magnetization of our Co 68 B 32 layer and underestimate the polarization in the Pt layer. The extracted M = 1200 ± 50 emu/cm 3 (Equation S1) and M = 1100 ± 100 emu/cm 3 (Equation

S2
) are not consistent with the reported literature value of 730 emu/cm 3 for Co 68 B 32 [3]. It S2 is very well established from the literature that the Pt gains a considerable polarization in thin film multilayers such as ours, which is not accounted for in the fits to Equations S1 and S2 presented in Figure S1.
A simple slab model is, therefore, insufficient to fully describe our Pt/Co 68 B 32 /Pt system.
To fully describe our data on the Pt/Co 68 B 32 /Pt system presented in the main text we create a toy model based on partial layer coverage. For very thin layers (1 or 2 monolayers), it is possible that the layer coverage is not uniform or that the ferromagnet only partially covers the surface. Such a picture is consistent with common thin-film growth modes, where adatoms initially form islands, which coalesce into complete layer coverage as the film thickness increases. Such incomplete layer coverage will affect the polarization of adjacent layers, as the adjacent layer will only gain polarization in the vicinity of the magnetic islands.
To model the partial layer coverage, we assume that: at zero thickness, the layer coverage is 0%; at a critical thickness, d critical , the islands connect and layer coverage is 100%; layer coverage % increases linearly between those two thicknesses; and at thicknesses above d critical , the data should be described by Equation S2. The equation describing this toy model is, The results fitting to this toy model returns a magnetisation M = 760 ± 90 emu/cm 3 , which is consistent with the bulk value of 730 emu/cm 3 [3]. Equation S3 therefore best represents our Pt/Co 68 B 32 /Pt system as shown in Figure S1, and so this best fit model is presented in the main text.

S2. TRAPPED FLUX IN SUPERCONDUCTING COILS
The cryostat has a single horizontal field coil. The sample can be rotated about the vertical axis, which we perform in increments of 90 • to bring that field in-and out-of-plane of the junctions. In order to avoid trapping flux in the superconducting Nb layers in the devices, we performed all sample rotations in zero field above the T c of the Nb and always cooled the sample in zero applied field (in practice there will inevitably be a small remanent field due to trapped flux in the magnet). The full sequence of setting the magnetic state of our samples and performing the measurement field sweeps is: warm to 15K, rotate sample to apply field out-of-plane, apply saturating field, remove saturating field, rotate sample by 90 • , cool sample, apply field in-plane, measure. Once we have finished measuring that magnetic state of the sample, we may wish to measure a further condition, such as reversing the magnetisation. To do so, we remove the in-plane field, warm to 15K and repeat the cycle described above.

S3. GOODNESS OF FIT ANALYSIS
The main conclusion of our work is that the transport properties of Josephson junctions with Pt/Co 68 B 32 /Pt barriers are consistent with intermediate limit zero-π oscillations. For convenience, we reproduce the equation governing this limit [4], where V 0 is the extrapolated I c R N at zero thickness, d zero-π is the position of the first zero-π transition, ξ F 1 = l e and ξ F 2 = ξ F are the lengthscales governing the decay and oscillation of I c R N , respectively. For ferromagnetic Josephson junctions where zero-π oscillations are not expected to occur, the decay of supercurrent can be described by the simple exponential decay, A possible null hypothesis for our reported zero-π oscillations in Pt/Co 68 B 32 /Pt barriers is if our junctions are best described by Equation S5 and not Equation S4, as this would suggest that zero-π oscillations may not have been observed. Figure S3 shows goodness of fit analysis of our result compared to the null hypothesis. For  Therefore, the χ 2 analysis allows us to reject the null hypothesis that a simple exponential decay can describe our experimental result.
In order to fully describe our magnetisation data, we constructed a toy model of partial layer coverage for samples with the thinnest layers. On the other hand, electrical transport measurements on junctions with the thinnest barriers do not appear to be sensitive to localised partial coverage, as the pair correlations which probe the barrier are averaged over the superconducting coherence length. Nonetheless, we consider next if our findings are robust even when excluding the data from the thinnest barriers. Figure S4 shows goodness of fit analysis on a reduced data range d CoB ≥ 0.6 nm. In Figure   S4 (a) we consider the results of two fits to Equation S4. For the first fit attempt, where all parameters in Equation S4 are free parameters (dotted line), the fitting struggles to fit the d zero−π parameter, as the reduced data range does not contain the first zero-π transition.
However overall, the trends in the fitted ξ F 1 = 0.22 ± 0.02 nm and ξ F 2 = 0.17 ± 0.02 nm are S6 consistent with our conclusion of intermediate limit transport. Alternatively, we can fix the d zero−π parameter (dot dash line), in which case the best fit returns ξ F 1 = 0.22 ± 0.02 nm and ξ F 2 = 0.20 ± 0.01 nm. By eye, this fit is a plausible explanation of our results over the entire data range. The returned ξ F 2 values from these two fitting methodologies, where ξ F 2 governs the period of the zero-π oscillation (the key result of our work), are consistent, within error, with ξ F 2 by fitting over the entire data range (0.20 ± 0.02 nm), providing us confidence in our reported result. In Figure S4 (b) we fit to the simple exponential decay Equation S5, over the reduced data range, and find ξ F = 0.28 nm and the reduced χ 2 = 89.5.
The χ 2 analysis allows us to reject the null hypothesis that a simple exponential decay can describe our experimental result, even over the reduced data range d CoB ≥ 0.6 nm.

S4. POSSIBLE SPIN-TRIPLET COMPONENT OF SUPERCURRENT
Josephson junctions containing a source of s-wave superconductivity, large spin-orbit coupling, and ferromagnetism are predicted to display transport properties consistent with spin-triplet supercurrents [5]. Assuming that the total supercurrent in the junction is the sum of the spin-singlet and spin-triplet components, we can describe the total supercurrent as; where V Triplet and ξ Triplet are the critical voltage and decay length of the spin-triplet component of supercurrent, respectively.
To determine if spin-triplet supercurrents contribute to our transport results, we fit Equation S6 to our junction data, shown in Figure S5. We find that V Triplet → 0, and the other fit parameters correspond to those of the singlet only fit described in the main text. This suggests that the data are well described by singlet transport physics alone and any spin-triplet component is below our experimental sensitivity.
An alternative methodology is to consider whether we might be able to observe a spintriplet supercurrent of the magnitude reported in literature. Figure S5  should be observable as the major suppression of the oscillations and higher I c R N in the thicker samples in this work.