Magneto-Chiral Anisotropy in Josephson Diode Effect of All-Metallic Lateral Junctions with Interfacial Rashba Spin-Orbit Coupling

This study demonstrates that interfacial Rashba spin-orbit coupling in all-metallic Fe/Pt and Cu/Pt Josephson junctions induces a magneto-chiral anisotropic Josephson diode effect, distinguishing it from the axis-symmetric behavior observed in control samples with plain copper weak links.

The Gist

The Big Picture: Superconducting Diodes and "One-Way Streets"

Imagine electricity flowing through a wire. Usually, it flows just as easily in both directions. But in this paper, the researchers are looking at a special kind of "super-highway" called a Josephson junction. In these junctions, electricity flows without any resistance (superconductivity).

The researchers discovered that under certain conditions, these super-highways can act like a diode. A diode is a one-way street for electricity: it lets current flow easily in one direction but blocks or makes it much harder to flow in the other. This is called the Josephson Diode Effect.

The paper asks a simple question: What creates this one-way street in all-metal devices, and why does it behave strangely when we change the magnetic field?

The Key Ingredient: The "Spin-Orbit" Twist

To understand the cause, imagine electrons as tiny spinning tops. Usually, how an electron spins is independent of how fast it moves. But in this experiment, the researchers used a special trick at the interface where two different metals meet (like Copper touching Platinum, or Iron touching Platinum).

At this meeting point, the structure is slightly "broken" (lacking symmetry). This creates a force called Rashba Spin-Orbit Coupling.

• The Analogy: Imagine a hallway with a spinning floor. If you walk down the hallway, the spinning floor forces you to lean left or right depending on which way you are walking.
• The Result: The electrons' "spin" (their leaning direction) gets locked to their "momentum" (which way they are walking). This creates a specific, chiral (handed) pattern of spins at the metal interface.

The Experiment: Testing the "Handedness"

The team built three types of devices to test this:

1. Sample A (Iron/Platinum): A strong magnetic metal next to Platinum.
2. Sample B (Copper/Platinum): A non-magnetic metal next to Platinum.
3. Sample C (Just Copper): A plain copper bridge with no special metal interface.

They applied a magnetic field and measured how much current could flow in the positive direction versus the negative direction.

The Findings:

• Samples A and B (The "Twisted" Interfaces): Both showed a strong diode effect. The "one-way street" was very clear. Crucially, the direction of this effect changed in a specific, predictable way as they rotated the magnetic field. This pattern perfectly matched the "handedness" (chirality) expected from the Rashba Spin-Orbit Coupling at the metal interfaces.
• Sample C (The "Plain" Interface): This device also showed a diode effect, but its behavior was different. It didn't have the specific "handed" pattern. This proved that the effect in Samples A and B wasn't just a random glitch; it was specifically caused by the special interface between the two metals.

The Conclusion: The "one-way street" in these all-metal devices is created by the unique spin-twisting force that happens right where two different metals touch.

The Mystery: The "Inverted Hysteresis" Ghost

While studying these devices, the researchers noticed something very strange and confusing.

Usually, if you measure a magnet's effect while turning the magnetic field up and then down, the results follow a predictable loop (hysteresis). But in these devices, the loop was inverted.

• The Analogy: Imagine you are walking through a forest. When you walk forward, you expect to see a tree on your left. But when you walk backward, the tree appears on your right in a way that doesn't make sense with normal physics. It looks like the forest is playing tricks on you.

The researchers initially wondered if this "inverted ghost" was a sign of some new, exotic quantum physics. However, they realized it was actually a very old, boring problem: magnetic vortices getting stuck.

• The Explanation: The superconducting leads (the wires leading to the junction) act like a sponge for magnetic fields. Tiny magnetic whirlpools (vortices) get trapped or "pinned" in the metal. When the researchers changed the magnetic field, these trapped vortices didn't move immediately. They created their own "stray" magnetic fields that fought against the external field.
• The Result: This created a "ghost" field that made the measurements look inverted. It wasn't a new quantum effect; it was just the magnetic field getting stuck in the wires, like a car getting stuck in mud.

Summary

1. The Discovery: The researchers proved that you can create a superconducting "one-way street" (diode effect) in all-metal devices just by putting two different metals together. The secret sauce is the Rashba Spin-Orbit Coupling at the interface, which twists the electrons' spins.
2. The Confirmation: By comparing different metal combinations, they showed that this effect relies on the specific "handedness" of the metal interface, not just the presence of a magnetic metal.
3. The Correction: They also solved a mystery about "inverted" measurement loops. They showed that these weird loops weren't a sign of new physics, but rather the result of magnetic vortices getting stuck in the wires, creating stray fields that confused the measurements.

In short, the paper teaches us how to build a magnetic diode using simple metal layers, while also warning us to be careful about "stuck" magnetic fields when measuring these delicate devices.

Technical Summary

1. Problem Statement

The Josephson Diode Effect (JDE), characterized by non-reciprocal critical currents ($I_c^+ \neq |I_c^-|$), typically arises when both time-reversal symmetry (TRS) and inversion symmetry are broken. While JDE has been extensively studied in semiconductor weak links (e.g., InAs, InSb) with strong Rashba spin-orbit coupling (SOC), its manifestation in all-metallic diffusive Josephson junctions remains less explored.

A specific challenge in this field is the interpretation of "inverted hysteresis" observed in magnetic field sweeps of critical currents. Previous studies on metallic weak links (e.g., Cu/Pt) reported inverted hysteresis patterns, often hypothesized to be signatures of Rashba SOC or triplet superconductivity. However, no consensus existed on the origin of this phenomenon, and distinguishing between intrinsic SOC effects and extrinsic magnetic artifacts (like vortex pinning) was difficult.

2. Methodology

The authors investigated the role of interfacial Rashba SOC in the JDE using Nb-based lateral Josephson junctions with different metallic weak links. They employed a comparative approach across three distinct sample types:

• Sample A (Fe/Pt Weak Link): An epitaxial heterostructure (GaAs/Fe/Al/Pt/Nb). The Fe/Pt interface is known for strong interfacial SOC. An Al spacer prevents magnetic proximity effects while maintaining spin transport transparency.
• Sample B (Cu/Pt Weak Link): A sputtered stack (Si/SiO2/Cu/Pt/Nb). The Cu/Pt interface induces Rashba SOC due to charge transfer and broken inversion symmetry, but with weaker SOC strength compared to Fe/Pt.
• Sample C (Plain Cu Weak Link): A control sample with a 50 nm Cu film and no metal-metal interfaces, possessing negligible bulk SOC.

Experimental Techniques:

• Critical Current Measurements: $I-V$ curves were measured at low temperatures (30 mK for Sample A, 1.8 K for others) under in-plane ($B_{||}$) and out-of-plane ($B_z$) magnetic fields.
• Diode Efficiency Calculation: The diode efficiency $\eta$ was calculated as $\eta = 2(I_c^+ - |I_c^-|)/(I_c^+ + |I_c^-|)$.
• Angular Dependence: Measurements were performed by rotating the in-plane magnetic field angle ($\theta$) relative to the current direction to map the symmetry of the diode effect.
• Alignment Control: A sensitive Al stripe probe was used to ensure precise alignment of the magnetic field relative to the sample plane, minimizing spurious out-of-plane components.

3. Key Contributions

1. Demonstration of Rashba-Driven JDE in All-Metallic Junctions: The paper provides experimental evidence that interfacial Rashba SOC in purely metallic weak links (Fe/Pt and Cu/Pt) is sufficient to generate a Josephson diode effect with magneto-chiral anisotropy.
2. Symmetry Analysis: The authors established that the diode efficiency $\eta$ in Rashba-coupled junctions exhibits a point-symmetric (odd) dependence on the magnetic field angle ($\theta$), changing sign at $\theta = 0^\circ$ (field parallel to current). This contrasts with the even symmetry observed in the control sample (plain Cu), ruling out bulk effects or simple uniaxial anisotropy as the primary cause.
3. Resolution of "Inverted Hysteresis": The study identifies that the previously mysterious "inverted hysteresis" in critical current vs. magnetic field curves is not a signature of SOC or triplet pairing. Instead, it is attributed to hysteretic vortex pinning in the Nb leads, which generates stray fields that oppose the external field sweep direction.
4. Time-Reversal Symmetry (TRS) Verification: The authors demonstrated that to restore TRS in the presence of pinned vortices, one must reverse not only the current and magnetic field but also the direction of the field sweep.

4. Key Results

A. Josephson Diode Effect and Rashba Symmetry

• Samples A (Fe/Pt) and B (Cu/Pt): Both exhibited a significant JDE. The diode efficiency $\eta(B_{||}, \theta)$ showed a characteristic 2$\pi$-periodic magneto-chiral anisotropy.
  • At $\theta = \pm 90^\circ$ (field perpendicular to current), $\eta$ reached maximum values ($\approx \pm 18-20\%$ for Sample A).
  • As $\theta$ rotated to $0^\circ$ (field parallel to current), $\eta$ vanished and changed sign.
  • This point symmetry confirms the presence of Rashba-type SOC at the metal-metal interfaces.
• Sample C (Plain Cu): Showed a finite diode efficiency but with even symmetry in $\theta$ (no sign change at $0^\circ$). This indicates the effect arises from a mechanism other than interfacial Rashba SOC (likely geometric or bulk anisotropy), confirming that the Rashba effect is the specific driver in Samples A and B.
• Comparison: The JDE was more pronounced in Sample A (Fe/Pt) than Sample B (Cu/Pt), correlating with the known strength of SOC at these interfaces, further validating the Rashba origin.

B. Origin of Inverted Hysteresis

• Observation: All samples (A, B, and C) displayed an "inverted hysteresis" in $I_c(B_z)$, where the critical current curve for a backward sweep was shifted in the opposite direction compared to a forward sweep (e.g., the central lobe appeared at negative fields for forward sweeps).
• Mechanism: The authors attribute this to Bean's critical state model.
  • Pinned vortices in the Nb leads create a stray magnetic field ($b_s$) that opposes the external field.
  • When the external field is swept back to zero, the pinned vortices do not immediately exit, leaving a residual field in the junction area.
  • This results in a net zero flux condition being reached at a non-zero external field, creating the apparent "inverted" shift.
• Evidence:
  • The effect was observed in Sample C (no Rashba SOC), proving it is independent of SOC.
  • Random "flux jumps" in $I_c$ were observed, corresponding to spontaneous depinning events of vortices.
  • Numerical modeling based on the critical state model estimated stray fields of 3–4 mT, consistent with the observed $\sim 10$ mT hysteresis shifts.

C. Time-Reversal Symmetry Check

• Standard TRS requires $I_c(B) = I_c(-B)$. However, due to the hysteretic vortex pinning, simple reversal of $B$ and $I$ did not match the curves.
• The authors showed that reversing the field sweep direction (Forward $\to$ Backward) in addition to reversing $B$ and $I$ was necessary to recover the symmetry, confirming that the hysteresis is a dynamic pinning effect rather than an intrinsic symmetry breaking of the superconducting state.

5. Significance

• Fundamental Physics: This work clarifies the distinction between intrinsic SOC-driven phenomena (JDE with specific symmetry) and extrinsic magnetic artifacts (vortex pinning hysteresis) in hybrid superconducting devices. It establishes that interfacial Rashba SOC is a robust mechanism for inducing the JDE in all-metallic systems, expanding the material platform beyond semiconductors.
• Device Engineering: The findings are crucial for the development of superconducting electronics and quantum computing.
  • Understanding the Rashba-driven JDE allows for the design of non-reciprocal superconducting diodes without relying on complex semiconductor heterostructures.
  • Identifying the origin of inverted hysteresis as vortex pinning in Nb leads provides a critical guideline for device fabrication. Engineers must account for stray fields from pinned vortices when designing phase-biased circuits or qubits, as these fields can mimic symmetry-breaking effects or cause instability.
• Methodological Rigor: The paper sets a standard for analyzing JDE by emphasizing the need to control for field sweep direction and vortex dynamics, preventing misinterpretation of hysteresis as a novel topological or symmetry-breaking effect.