Phase dynamics and dissipation in tunnel ferromagnetic Josephson junctions

The gist: The study investigates tunnel ferromagnetic Josephson junctions based on Superconductor-Insulator-thin superconductor-Ferromagnet-Superconductor multilayers to compare their electrodynamic properties across different materials and dimensions.

Junction Types and Materials

The research focuses on tunnel ferromagnetic Josephson junctions based on Superconductor-Insulator-thin superconductor-Ferromagnet-Superconductor multilayers The comparative study of their electrodynamic properties is performed for junctions with niobium and aluminum (Al) electrodes, featuring different ferromagnetic interlayer materials and lateral dimensions ranging from the micrometric to the submicrometric scale For the aluminum samples, the F layer is permalloy, instead for the Nb-based micrometric junctions the ferromagnetic barrier is a (Ni80Fe20)80Nb20 alloy The Al-based micrometric junctions (Sample B) have the same nominal thickness layer as their Nb counterparts; however, the ferromagnetic barrier is a 3 nm-thick Py layer Submicrometric Al-based junctions (Sample C) were fabricated using the Manhattan process, employed for the realization of standard transmon qubits This process yields submicrometric junctions with thicknesses Al (20 nm)/AlOx (2 nm)/Al (25 nm)/Py (3 nm)/Al (70 nm).

Fabrication and Measurement Methods

Two distinct fabrication processes were employed depending on the lateral dimensions of the SIsFS junctions For the micrometric SIsFS junctions, the Nb/AlOx/Nb (or Al/AlOx/Al) trilayer was patterned using optical lithography and a liftoff procedure The Nb-based micrometric junctions (hereafter, referred to as Sample A) follow the multilayer sequence: Nb (200 nm) /AlOx(2 nm) /Nb(30 nm) /(Ni80Fe20)80Nb20(6 nm) / Nb (350 nm). The Al-based micrometric junctions (Sample B) have the same nominal thickness layer as their Nb counterparts; however, the ferromagnetic barrier is a 3 nm-thick Py layer: Al (200 nm)/AlOx(2 nm)/Al (30 nm)/Py (3 nm)/Al (350 nm). Submicrometric Al-based junctions (Sample C) were fabricated using the Manhattan process, employed for the realization of standard transmon qubits. The SIsFS junctions were measured by thermally anchoring the samples to the mixing chamber of a Triton 400 dry dilution refrigerator, equipped with customized low-noise filtering stages. For SCD measurements, a voltage threshold is set close to the zero voltage state in order to accurately detect the actual switching event and track its occurrence over time.

Transport Modeling and Phase Dynamics

The transport behavior of the SIsFS JJs can be discussed within the theoretical framework proposed by Bakurskiy et al. [40] According to this model, when the thickness of the intermediate superconducting layer ds exceeds the critical value dsc, defined as the minimum thickness required for the superconductivity to persist in an sF bilayer, the pair potential ∆ in the s layer approaches the bulk value. In devices operating in low-to-moderate damping conditions, SCD measurements are particularly informative, revealing dissipation mechanisms quantified by the quality factors of the JJs. The TJM model provides a microscopic description of a JJ within the tunnelling Hamiltonian formalism and is widely used for SQUIDs and SFQ circuits. The TJM simulations were performed using the PSCAN2 software, which computes the timeaveraged voltage V (I) for a JJ embedded in a circuit.

Key Findings on Dissipation and Coherence

The experimental results reveal a more subtle scenario regarding the critical current-normal resistance product IcRN. For sample A, we observe a suppression of the critical current-normal resistance product IcRN of approximately 60% with respect to its SIS counterparts. This suppression suggests a weakening of the superconductivity in the s interlayer due to the proximity effect with the Py barrier, which induces a local reduction of the gap ∆s relative to its bulk value and results in a higher dissipation in the subgap branch compared to the SIS I-V curve. Regarding samples B and C, they exhibit I-V curves that overlap with their SIS counterparts, thereby preserving all fundamental electrodynamic features. The TJM fit of the I-V characteristics demonstrates the model’s capability to accurately describe the subgap branch and low-frequency dynamics of the junctions.

Quality Factor Analysis

A more accurate determination requires adopting a two–quality–factor model for the junction phase dynamics High-frequency dissipation at ω ∼ ωp, relevant during escape phenomena, is dominated by the electromagnetic environment, defining the highfrequency damping Q1. Low-frequency dissipation, associated with the subgap branch of the I–V curves, determines the low-frequency quality factor Q0, governed by the subgap resistance Rsg. The TJM model provides a microscopic description of a JJ within the tunnelling Hamiltonian formalism and is widely used for SQUIDs and SFQ circuits. For sample A, βC ∼ 50, corresponding to a junction capacitance C ∼ 300 fF The quality factor Q0 is found to be 7, in contrast to the value of 10 for the standard Nb-based SIS junction. For sample B, βC ∼ 100, giving Q0 ∼ 10 and C ∼ 300 fF finally for sample C, the parameter βC ∼ 1, which corresponds to a junction capacitance C ∼ 2 fF and a charging energy EC ∼ 40 µeV.

Conclusion

The Al-based SIsFS architecture emerges as a more suitable platform for quantum architectures where coherence is a fundamental requirement. By retaining low dissipation, the Al-based SIsFS architecture emerges as a more suitable platform for quantum architectures where coherence is a fundamental requirement. The results for submicron SIsFS junctions are comparable to those of standard Al-based junctions employed in conventional transmons, a finding further supported by the observation that they operate within the quantum phase diffusion limit. By retaining low dissipation, the Al-based SIsFS architecture emerges as a more suitable platform for quantum architectures where coherence is a fundamental requirement. Having demonstrated that the SIsFS layout preserves the coherence of the Josephson effect regardless of the materials used, ongoing work focuses on replacing the current ferromagnetic barrier with a softer ferromagnetic layer (e.g., Nb-doped permalloy), as the ferromagnetic material can be integrated ex-situ without significantly affecting the junction electrodynamics. The findings support the potential for hybridizing aluminum-based quantum technologies with ferromagnetic elements in next-generation superconducting circuits.

How it works

The study investigates tunnel ferromagnetic Josephson junctions based on Superconductor-Insulator-thin superconductor-Ferromagnet-Superconductor multilayers These structures are investigated for junctions with niobium and aluminum (Al) electrodes, featuring different ferromagnetic interlayer materials and lateral dimensions ranging from the micrometric to the submicrometric scale. The parameters extracted from the fitting of the current-voltage characteristics using the tunnel junction microscopic model are found to be consistent with those independently estimated from switching current distribution measurements.

1. Improved AI systems can accurately model and predict phase dynamics in hybrid ferromagnetic Josephson junctions by utilizing a combined framework of Tunnel Junction Microscopic (TJM) modeling and Switching Current Distribution (SCD) measurements, as this combined approach enables a more reliable extraction of key parameters, such as the junction capacitance, charging energy EC, Josephson energy EJ, and the ratio EC /EJ.

2. AI systems can distinguish between thermal activation and phase-diffusion regimes in superconducting circuits by analyzing temperature-dependent switching current distributions (SCDs), specifically identifying the crossover point where the ratio kBT /EJ is approximately 0.007, which indicates a crossover from thermal activation to a regime dominated by multiple retrapping and escape processes.

3. Improved AI systems can optimize superconducting circuit design by accurately estimating junction parameters like the quality factors Q0 and Q1, as the TJM model allows for extracting Q0 and separating environmental from intrinsic dissipative contributions, enabling precise determination of capacitance (e.g., For sample A, βC ∼ 50, corresponding to a junction capacitance C ∼ 300 fF).

4. AI systems can predict the low-temperature resistance behavior of SIsFS junctions by identifying the transition between regimes, such as the appearance and increase of R0 with T according to the Arrhenius law when thermal fluctuations strongly enhance the phase diffusion mechanism, which is crucial for understanding phenomena like Quantum Phase Diffusion (QPD) regime [20, 30, 42, 58] at low temperatures.

5. AI systems can assess the suitability of different junction architectures by comparing transport properties across materials; for instance, they can predict that aluminum-based junctions (Samples B and C) preserve all the feautures of their SIS counterparts even at submicrometric scales, suggesting they are a more suitable platform for quantum architectures where coherence is a fundamental requirement.

We investigate tunnel ferromagnetic Josephson junctions based on Superconductor-Insulator-thin superconductor-Ferromagnet-Superconductor multilayers. A comparative study of their electrodynamic properties is performed for junctions with niobium and aluminum (Al) electrodes, featuring different ferromagnetic interlayer materials and lateral dimensions ranging from the micrometric to the submicrometric scale. The parameters extracted from the fitting of the current-voltage characteristics using the tunnel junction microscopic model are found to be consistent with those independently estimated from switching current distribution measurements. Submicrometric Al-based devices exhibit electrodynamic properties comparable to those implemented in state-of-the-art transmon qubits and display clear signatures of quantum phase diffusion. The strong agreement between transport modelling and escape dynamics establishes a robust framework for describing hybrid ferromagnetic Josephson junctions consistent with their energy scales and supports their potential integration into superconducting quantum and classical digital circuits.