🔬 mesoscale physics

Evidence for spin swapping from modulation of transverse resistance in magnetic heterostructures with Rashba interface

This study provides evidence for spin swapping in magnetic heterostructures with Rashba interfaces by demonstrating that the opposite signs of transverse resistance modulation in Cu/Bi2O3 and Ag/Bi2O3 systems directly correlate with the opposing spin/charge interconversion efficiencies of their respective interfaces.

Original authors: Heeman Kim, Shutaro Karube, Juan Borge, Junyeon Kim, Kouta Kondou, YoshiChika Otani

Published 2026-07-14

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CC BY 4.0

Original authors: Heeman Kim, Shutaro Karube, Juan Borge, Junyeon Kim, Kouta Kondou, YoshiChika Otani

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a tiny, high-tech highway made of metal layers, where invisible particles called electrons are zooming along. In this experiment, scientists built a special kind of road using a magnetic metal called Permalloy (Py) sandwiched between a copper or silver layer and a bismuth oxide layer. They wanted to see what happens when they push a current of 100 microamperes through this road while applying a strong magnetic field, sweeping it from –6 Tesla to +6 Tesla.

Here is the magic trick they discovered: When the electrons hit the interface between the metal and the bismuth oxide, something strange happens. It's like a dance floor where the dancers (electrons) suddenly swap partners. In physics terms, this is called spin swapping.

Normally, when electrons move, they carry a "spin" (a tiny magnetic direction) and a "flow" (the direction they are moving). The scientists found that at these special interfaces, the spin direction and the flow direction can trade places. If an electron was spinning one way while moving forward, after the swap, it might be spinning sideways while moving forward, or vice versa.

The team tested two different roads: one with a Copper/Bi2O3 interface and one with a Silver/Bi2O3 interface. They found that these two interfaces act like opposite mirrors. The Copper interface makes the electrons spin in one direction, while the Silver interface makes them spin in the exact opposite direction. Because of this, when the spin swapping happens inside the metal layer, the resulting "traffic jam" or resistance measured across the road (called transverse resistance) goes up for the Copper road but goes down for the Silver road.

The researchers measured this resistance by calculating the difference between the positive and negative magnetic field readings. They saw that as they made the Copper or Silver layer thicker (from 0 to 20 nanometers), the resistance changed in a very specific way. For the Copper road, the effect got stronger as the layer got thicker. For the Silver road, the effect got weaker and eventually flipped signs when the layer became thick enough.

Now, here is what the scientists are not saying. They explicitly ruled out a few other ideas that might seem like the answer. They said this isn't just the "Spin Hall Magnetoresistance" (SMR) effect, because that effect doesn't care about the direction of the spin (it's quadratic and insensitive to the sign). They also said it's not just the "Interfacial Spin Hall Effect," because that usually doesn't flip signs based on the material either. The paper suggests that the key is this specific "spin swapping" event, where the spin direction and flow direction literally swap places, creating a new kind of sideways flow that depends entirely on which way the electrons were originally spinning.

The authors are quite sure they measured these opposite effects in their devices, which were 4.0 micrometers wide and 120 micrometers long. They observed these changes at both 10 Kelvin and 300 Kelvin (room temperature). While they strongly suspect that spin swapping is the reason for this behavior, they present it as a compelling explanation for the data they collected, rather than a final, unshakeable proof of a new law of physics.

In short, the paper suggests that by using these special Rashba interfaces, they can control how electrons swap their spin and flow directions, which in turn creates a unique, opposite signal in the electrical resistance depending on whether they use copper or silver. It's a bit like finding that two different types of tires on a car cause the steering wheel to turn in opposite directions when you hit a specific bump, and figuring out that the tires are actually swapping their grip and direction at the same time.

Technical Summary: Evidence for Spin Swapping from Modulation of Transverse Resistance in Magnetic Heterostructures with Rashba Interface

Problem Statement
While spin/charge interconversion mechanisms, such as the Spin Hall Effect (SHE) in bulk materials and the Edelstein Effect (EE) at interfaces, are well-established for generating spin currents and modulating longitudinal resistance (e.g., via Spin Hall Magnetoresistance or Unidirectional Magnetoresistance), their influence on transverse resistance remains less understood. Specifically, recent theoretical proposals suggest that spin current scattering dependent on magnetization orientation could induce a transverse response similar to the Anomalous Hall Effect (AHE). However, the specific mechanism by which Rashba interfaces with opposite spin chiralities modulate transverse resistance in magnetic heterostructures requires clarification. The authors aim to investigate the transverse response ( $R_{xy}$ ) under an out-of-plane magnetic field in systems utilizing Cu/Bi $_2$ O $_3$ and Ag/Bi $_2$ O $_3$ Rashba interfaces, which are known to exhibit opposite signs of spin/charge interconversion.

Methodology
The study utilizes magnetic heterostructures composed of a Permalloy (Py, Ni $_{80}$ Fe $_{20}$ ) ferromagnetic layer (10 nm) capped with either Cu or Ag (0–20 nm) and a Bi $_2$ O $_3$ layer (20 nm). Two primary sample sets were prepared:

Sample 1: Py/Cu/Bi $_2$ O $_3$
Sample 2: Py/Ag/Bi $_2$ O $_3$

Reference samples without the Bi $_2$ O $_3$ layer (Py/Cu and Py/Ag) were also fabricated to isolate interface effects. All devices were patterned into Hall bars (4.0 $\mu$ m width, 120 $\mu$ m length) using electron-beam evaporation, photolithography, and lift-off processes.

Measurements were conducted at 10 K and 300 K using a Physical Property Measurement System (PPMS). An external magnetic field was swept from –6 T to +6 T along the out-of-plane ( $z$ -axis) direction while a 100 $\mu$ A probe current was applied. The transverse resistance difference, $\Delta R_{xy} = [R_{xy}(+H) - R_{xy}(-H)]/2$ , was calculated to isolate the contribution of the magnetic state. To quantify the effect, the authors evaluated the "pure" anomalous Hall angle ( $\theta_{AH}$ ), correcting for current shunting and short-circuit effects in the non-magnetic (NM) layer. Furthermore, an additional anomalous Hall angle ( $\theta_{AH}^{add}$ ) was derived by subtracting the reference sample values from the main sample values to isolate the contribution specifically from the NM/Bi $_2$ O $_3$ interface.

Key Results

Opposite Modulation Trends: The sign of $\Delta R_{xy}$ remained unchanged regardless of the NM thickness ( $t_{NM}$ ) for Sample 1 (Cu/Bi $_2$ O $_3$ ). In contrast, for Sample 2 (Ag/Bi $_2$ O $_3$ ), the sign of $\Delta R_{xy}$ flipped as the Ag thickness increased.
Thickness Dependence of $\theta_{AH}$ : The pure anomalous Hall angle ( $\theta_{AH}$ ) for the reference samples was largely insensitive to $t_{NM}$ . However, for the samples with Bi $_2$ O $_3$ , $\theta_{AH}$ showed significant dependence on $t_{NM}$ . Specifically, $\theta_{AH}$ increased with Cu thickness in Sample 1 but decreased with Ag thickness in Sample 2, eventually reversing sign in Sample 2 at sufficient thickness.
Interface Contribution ( $\theta_{AH}^{add}$ ): The extracted $\theta_{AH}^{add}$ confirmed that the Cu/Bi $_2$ O $_3$ interface enhances the transverse resistance, while the Ag/Bi $_2$ O $_3$ interface suppresses it. These trends were consistent across both 10 K and 300 K and correlated directly with the known opposite signs of spin/charge interconversion efficiency for these two interfaces.
Exclusion of Alternative Mechanisms: The authors ruled out standard Spin Hall Magnetoresistance (SMR) for the transverse response, noting that SMR is quadratic and insensitive to the sign of conversion efficiency. Similarly, the interfacial spin Hall effect was deemed insufficient as it is typically insensitive to the sign of the Rashba parameter.

Proposed Mechanism: Spin Swapping
The paper proposes that the observed phenomena are driven by the spin swapping effect within the non-magnetic metal (NM) layer.

Mechanism: The Rashba interface generates a spin current with a specific polarization and flow direction (e.g., $q_{zy}$ for Cu/Bi $_2$ O $_3$ and $q_{z-y}$ for Ag/Bi $_2$ O $_3$ ). As this current traverses the NM layer, scattering events mediated by spin-orbit interaction cause a "spin swap," altering the current from $q_{ij}$ to $q_{ji}$ .
Outcome: This process converts the initial spin current into a transverse spin current polarized along the $z$ -axis. Because the initial spin directions from the two interfaces are opposite, the resulting transverse spin flow directions are also opposite ( $q_{yz}$ vs. $q_{-yz}$ ).
Interaction with Magnetization: This transverse spin flow interacts with the Py magnetization. When the spin direction is parallel to the magnetization, transport is less resistive; when anti-parallel, it is more resistive. This interaction modulates the transverse resistance, creating the observed sign difference between the Cu and Ag systems.

Significance and Claims
The authors claim that their work provides experimental evidence for the spin swapping effect in magnetic heterostructures. They assert that:

The modulation of transverse resistance is a direct consequence of the spin swapping of converted spin currents originating from Rashba interfaces.
The direction of the resulting transverse spin flow is determined by the spin chirality of the interface, explaining the opposite modulation trends observed in Cu/Bi $_2$ O $_3$ and Ag/Bi $_2$ O $_3$ systems.
Transverse resistance measurements serve as a viable platform for observing spin swapping, a phenomenon previously predicted theoretically but less explored experimentally in this context.
The findings highlight that spin swapping generates a considerable influence on spin transport, distinct from standard SHE or SMR effects.

The study concludes by noting that these results were supported by grants from the "Nano Spin Conversion Science" initiative and the JSPS Leading Graduate Schools program, without proposing specific future applications or commercial devices beyond the fundamental understanding of spin transport.

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