Large critical current density Josephson $π$ junctions with PdNi barriers

Abstract

We report large $π$-state critical current densities, $J_c(π)$, in Nb/Pd$_{89}$Ni$_{11}$/Nb Josephson junctions at Pd$_{89}$Ni$_{11}$ thicknesses near the first $π$-state. We observe oscillations in the critical current with ferromagnetic barrier thickness consistent with a $0$-$π$ transition. For a junction with a 9.4~nm Pd$_{89}$Ni$_{11}$ barrier, we obtain $J_c(π) = 410~\mathrm{kA/cm^{2}}$ at 4.2~K, exceeding values reported in prior PdNi-based studies. Magnetization measurements on continuous films, together with coercivity tests on patterned arrays, confirm that Pd$_{89}$Ni$_{11}$ exhibits perpendicular magnetic anisotropy, enabling zero-field operation without magnetic initialization. The combination of large $J_c(π)$ and intrinsic anisotropy establishes Pd$_{89}$Ni$_{11}$ as a promising barrier material for passive $π$-shifters in superconducting digital logic and qubit architectures.

Figures (5)

• Figure 1: Magnetic characterization of continuous 35-nm-thick single-layer $\text{Pd}_{89}\text{Ni}_{11}$ film. (a) Magnetic field-dependent magnetization at 5 K with the applied field out-of-plane and in-plane. (b) Temperature-dependent magnetization for an out-of-plane applied field of 1 T. The data are fitted to Eq. \ref{['eq:MT']}, and the Curie temperature is approximately 170 K. Magnetization values are calculated from the nominal film thickness, measured total magnetic moment, and the areas of the samples. The measurements were performed using vibrating sample magnetometry. The uncertainty in each point is dominated by the area measurements, with an uncertainty of less than 10%. Lines connecting the data points are intended as guides for the eye.
• Figure 2: (a) Out-of-plane magnetization at 5 K for two Pd$_{89}$Ni$_{11}$ films fabricated in the same deposition run: a 35 nm continuous film and a patterned array of circular elements with measured diameter $\sim 3.5~\mu$m on a $9~\mu$m pitch. The inset shows an optical micrograph of the array; image analysis yields an areal fill factor of $\sim 12\%$. (b) Out-of-plane magnetization loop at 5 K for an additional 10 nm continuous Pd$_{89}$Ni$_{11}$ film. (c) In-plane minor hysteresis loop for the patterned array measured within $\pm 25$ mT, corresponding to the field range used in the Josephson junction measurements. Magnetization values were calculated from the total moment, nominal film thickness, and sample area. Lines connecting data points are guides to the eye.
• Figure 3: Critical current density, $J_c$, versus applied magnetic field for the $\text{Nb} / \text{Pd}_{89}\text{Ni}_{11} / \text{Nb}$ Josephson junction with $\text{Pd}_{89}\text{Ni}_{11}$ thickness of 9.4 nm at 5.75 K. The $J_c$ is calculated from the nominal size of the 3 µ m diameter circular junction and measurements of the $I-V$ characteristic at each field. The solid red line is a fit to the data of Eqs. \ref{['eq:Ic']} and \ref{['eq:phii']}. Inset: The $I-V$ characteristic of the same 3 $\mu$m circular junction at zero applied magnetic field. The critical current, $I_c$, is determined from these data by fitting to Eq. \ref{['eq:VI']}.
• Figure 4: (a) The product of the maximum critical current and normal state resistance, $I_cR_N$ (right axis) plotted with the critical current density, $J_c$ (left axis) of the $\text{Nb} / \text{Pd}_{89}\text{Ni}_{11} / \text{Nb}$ Josephson junctions versus nominal $\text{Pd}_{89}\text{Ni}_{11}$ thickness at 5.75 K. The data are described by Eq. \ref{['eq:ic_rn']} assuming the extrapolated fitting parameters of Khaire et al.Khaire_PRB_2009 Each data point represents one Josephson junction, and the uncertainty in determining $I_c R_N$ and $J_c$ is smaller than the data points and (b) comparison of this work (blue circle) at 5.75 K with the work of Khaire et al.Khaire_PRB_2009(green square) and Pham et al.Pham_2022 (black triangle) at 4.2 K.
• Figure 5: Critical current density, $J_c$, versus temperature at zero magnetic field and without any magnetic initialization for the $\text{Nb} / \text{Pd}_{89}\text{Ni}_{11} / \text{Nb}$ Josephson junctions with $\text{Pd}_{89}\text{Ni}_{11}$ thicknesses of 6.8 nm and 9.4 nm. The critical temperature is approximately 8 K, and the trend of $J_c (T)$ is well described by the phenomenological expression, Eq. \ref{['eq:J_c(T)']}. The data points at each temperature are averaged from three $I-V$ curve measurements, and the statistical uncertainty in $J_c$ is smaller than the data points.