🔬 materials science

Temperature dependence of charge-to-spin conversion in rhombohedral (110) bismuth thin film

This study investigates the temperature dependence of charge-to-spin conversion in epitaxial rhombohedral (110) bismuth films, revealing that the observed enhancement of spin Hall conductivity and spin diffusion length at lower temperatures indicates that spin scattering is dominated by the Elliott-Yafet mechanism while the conversion itself is primarily driven by skew scattering.

Original authors: K. Tatsuoka (Kyoto Univ), N. Fukumoto (Kyoto Univ), S. Sakamoto (ISSP, Univ. Tokyo), S. Miwa (ISSP, Univ. Tokyo), Y. Fuseya (Kobe Univ), J. Fujimoto (Saitama Univ), R. Ohshima (Kyoto Univ), J. Puebla

Published 2026-07-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: K. Tatsuoka (Kyoto Univ), N. Fukumoto (Kyoto Univ), S. Sakamoto (ISSP, Univ. Tokyo), S. Miwa (ISSP, Univ. Tokyo), Y. Fuseya (Kobe Univ), J. Fujimoto (Saitama Univ), R. Ohshima (Kyoto Univ), J. Puebla (Kyoto Univ), Y. Ando (Osaka Metropolitan Univ), M. Shiraishi (Kyoto Univ)

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 a tiny, super-thin sheet of bismuth, a silvery metal that acts like a magical traffic cop for electrons. In the world of electronics, we often want to turn a flow of electric charge (like cars on a highway) into a flow of spin (like all the cars suddenly deciding to drive on the left side of the road). This trick is called the "spin Hall effect," and bismuth is famous for being one of the best at it. But here's the mystery: why does it work so well in some directions and barely at all in others?

In this study, researchers took a close look at a specific type of bismuth crystal, shaped like a rhombohedron and oriented along the (110) direction, sandwiched against a layer of nickel. They wanted to figure out how this magic happens and what happens when the temperature changes. Think of it like testing a race car not just at noon, but also at midnight, to see how the engine behaves in the cold.

The Big Discovery: Cold Makes It Cooler
The team used a clever technique called the "second harmonic Hall method." Imagine tapping a drum with a specific rhythm and listening to the echo; this method lets them hear the faint "echo" of the spin current without the loud noise of heat messing things up. They cooled their sample down from a warm 300 K (room temperature) all the way to a chilly 10 K.

What they found was surprising and exciting: as the temperature dropped, the bismuth got better at converting charge to spin. Both the "spin Hall conductivity" (how efficiently the conversion happens) and the "spin diffusion length" (how far the spin can travel before getting lost) increased as it got colder. It's as if the bismuth sheet woke up and started running a marathon faster and further the colder the air got.

Solving the Mystery: The "Skew Scattering" Detective
Now, the researchers had to play detective to figure out why this happened. There are a few suspects in the world of spin physics:

The Intrinsic Effect: A built-in property of the material's atomic structure, like a natural talent.
Side-Jump: A mechanism where electrons bump into impurities and jump sideways.
Skew Scattering: A mechanism where electrons bounce off impurities in a lopsided way, like a billiard ball hitting a cushion at a weird angle and shooting off in a new direction.

The paper argues strongly that skew scattering is the main culprit here. Here's the logic: The researchers noticed that as the temperature dropped, the electrons moved much more freely (their mobility went up). In the "Elliott-Yafet" mechanism (a specific type of spin relaxation), when electrons move more freely, they also keep their spin direction longer. This is exactly what they saw: the spin diffusion length got longer as the electrons got faster.

This behavior points a giant finger at skew scattering. The paper suggests that because the electrons are bouncing off impurities in a lopsided way, and because they are moving so smoothly in the cold, the conversion efficiency skyrockets. The data shows a straight-line relationship between how far the spin travels and how well the conversion works, which is the fingerprint of skew scattering.

What They Ruled Out
The team was careful to cross off other suspects.

Orbital Hall Effect: They considered if the bismuth was creating a flow of "orbital" angular momentum (a different kind of spin) that was tricking them. However, they argued this is unlikely because the effect was similar in bismuth paired with nickel and bismuth paired with iron, even though nickel is much better at converting orbital momentum to spin. If the orbital effect were the star, the nickel setup should have been way more powerful, but it wasn't.
Side-Jump: The data suggests this mechanism isn't the main player.
Interface Tricks: They confirmed the effect wasn't just happening at the boundary between the bismuth and the nickel (like a surface glitch) because the effect changed depending on how thick the bismuth layer was.

How Sure Are They?
The authors are quite confident in their main conclusion but keep a humble tone about the details. They state that the results suggest the spin relaxation is dominated by the Elliott-Yafet mechanism and that the charge-to-spin conversion is mainly attributed to skew scattering. They acknowledge that a tiny bit of the "intrinsic" effect (the natural talent of the material) might still be hiding in the mix, especially because the energy gaps in the material change slightly when it gets cold. However, they point out that in other materials where the intrinsic effect is the boss, the conductivity doesn't get better in the cold. Since their bismuth does get better, they deduce that skew scattering is the true hero of the story.

In short, this paper tells us that in these special bismuth films, getting cold makes the electrons bounce off impurities in a way that creates a massive spin current, and this "skew scattering" is the key to the magic. It's a step forward in understanding how to build better spintronic devices, turning the quiet hum of cold electrons into a powerful spin engine.

Technical Summary: Temperature Dependence of Charge-to-Spin Conversion in Rhombohedral (110) Bismuth Thin Films

Problem Statement
Bismuth (Bi) possesses the largest spin-orbit interaction among non-radioactive elements, making it a candidate for significant charge-to-spin interconversion via the spin Hall effect (SHE). However, the magnitude of this conversion has been a subject of debate, with reports ranging from negligible to sizable values. Recent studies established that the conversion efficiency is highly anisotropic, with rhombohedral (110) oriented Bi [Bi(110)R] exhibiting large efficiency (17–27%) at room temperature, while Bi(111)R shows almost zero conversion. Despite the observation of this large effect, the underlying physical mechanisms—specifically the nature of the SHE (intrinsic vs. extrinsic) and the dominant spin scattering mechanisms (Elliott-Yafet vs. D'yakonov-Perel')—remain elusive. Furthermore, distinguishing the SHE from thermal artifacts (such as the planar Nernst effect) in materials with large thermoelectric responses is challenging using standard measurement techniques like spin torque ferromagnetic resonance (ST-FMR).

Methodology
The authors investigated the temperature dependence of charge-to-spin conversion in epitaxial Bi(110)R/Ni bilayer systems grown on MgO(001) substrates via molecular beam epitaxy (MBE). The samples featured a wedged Bi layer structure capped with SiO2/MgO to prevent oxidation.

To isolate the spin-orbit torque (SOT) from thermal effects, the study employed the second harmonic Hall (SHH) method. This technique allows for the quantitative separation of the damping-like SOT from unwanted thermal contributions (e.g., anomalous Nernst effect, spin Seebeck effect, and ordinary Nernst effect) which typically superimpose on the signal in materials with large thermoelectric responses.

Experimental Setup: An alternating current ( $I_0 = 5$ mA, 17 Hz) was applied to Hall bar devices while an in-plane magnetic field was rotated from 0° to 360°.
Data Analysis: The second harmonic Hall voltage ( $V_{xy}^{2\omega}$ ) was decomposed into components representing the damping-like SOT ( $A_{DL}$ ), field-like SOT/Oersted field ( $A_{FL}$ ), and planar Nernst effect ( $A_{PNE}$ ).
Parameters Extracted: The effective field of the damping-like SOT ( $\mu_0 H_{DL}$ ) and the effective spin Hall conductivity ( $\sigma_{SH}^{eff}$ ) were calculated across a temperature range of 10 K to 300 K. The study also analyzed the dependence of these parameters on Bi layer thickness to extract the intrinsic spin Hall conductivity ( $\sigma_{SH}$ ) and spin diffusion length ( $\lambda_{Bi}$ ).

Key Results

Temperature Dependence: Both the effective spin Hall conductivity ( $\sigma_{SH}^{eff}$ ) and the spin diffusion length ( $\lambda_{Bi}$ ) were observed to augment as the temperature decreased from 300 K to 10 K. This enhancement was particularly substantial in thicker Bi layers.
Spin Relaxation Mechanism: The increase in spin diffusion length with decreasing temperature, coupled with the known enhancement of carrier mobility in bismuth at low temperatures, indicates that spin relaxation is dominated by the Elliott-Yafet mechanism. In this mechanism, the spin lifetime is proportional to the momentum relaxation time, consistent with the observed trends.
SHE Mechanism: The study found a linear relationship between the spin Hall conductivity ( $\sigma_{SH}$ ) and the spin diffusion length ( $\lambda_{Bi}$ ). Since $\lambda_{Bi}$ is proportional to the momentum relaxation time ( $\tau_p$ ) in the Elliott-Yafet regime, and the extrinsic skew scattering contribution to $\sigma_{SH}$ is also proportional to $\tau_p$ , the results suggest that the charge-to-spin conversion in Bi(110)R is primarily driven by skew scattering.
Exclusion of Other Mechanisms:
- Orbital Hall Effect (OHE): The contribution of OHE was deemed negligible. Experimental comparisons showed that Bi(110)R/Ni conversion was not significantly larger than Bi(110)R/Fe, despite Ni's higher orbital-to-spin conversion efficiency. Theoretical calculations also suggest the orbital Hall conductivity in Bi is roughly three times smaller than the spin Hall conductivity.
- Side-jump Mechanism: The dominance of skew scattering implies the side-jump contribution is not the primary driver.
- Intrinsic SHE: While the intrinsic SHE (arising from the Dirac-like band structure at the L-point) is expected to increase slightly at low temperatures due to band gap shrinking, the authors argue that the observed enhancement is dominated by the skew scattering contribution. This is supported by the contrast with Bi-Sb alloys, where intrinsic SHE dominates and $\sigma_{SH}$ does not increase with decreasing temperature.

Significance and Claims
The paper claims to provide a detailed physical understanding of the large charge-to-spin conversion observed in Bi(110)R, moving beyond the initial observation of the effect to elucidate its microscopic origins.

Mechanism Clarification: The work establishes that the large SHE in Bi(110)R is not purely intrinsic but is significantly driven by extrinsic skew scattering, facilitated by the material's large spin-orbit interaction and high carrier mobility.
Methodological Validation: The study demonstrates the efficacy of the second harmonic Hall method in quantitatively separating thermal artifacts from SOT signals in high-thermoelectric-response materials, offering a more precise characterization than ST-FMR for such systems.
Device Relevance: By identifying the Elliott-Yafet scattering and skew scattering as the governing mechanisms, the findings offer a framework for understanding the scaling relations between conductivity and conversion efficiency, which is crucial for the design of future spintronic devices utilizing bismuth.

The authors conclude that while intrinsic contributions may exist, the observed temperature-dependent enhancement of charge-to-spin conversion in their epitaxial Bi(110)R films is mainly ascribed to skew scattering.

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