🔬 mesoscale physics

Quantitative Disentanglement of Terahertz Spin and Orbital Pumping in 3d Ferromagnetic Heterostructures

This study establishes a quantitative framework for disentangling ultrafast spin and orbital angular momentum currents in 3d ferromagnetic heterostructures by leveraging opposite-sign Hall angles in nonmagnetic layers, revealing that orbital pumping contributes significantly more than predicted—especially in Ni—and becomes essential in thin-layer regimes.

Original authors: Tongyang Guan, Jiahao Liu, Yuxiao Mo, Liangliang Zhu, Yizheng Wu, Zhensheng Tao

Published 2026-09-01

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CC BY 4.0

Original authors: Tongyang Guan, Jiahao Liu, Yuxiao Mo, Liangliang Zhu, Yizheng Wu, Zhensheng Tao

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

In the microscopic world of magnets, there is a constant, invisible traffic of tiny spinning particles. When a magnet is jolted by a flash of light, it does not just sit still; it sends a rush of energy and momentum into the materials touching it. For decades, scientists have focused on one specific type of this traffic: a flow of "spin." Imagine these spins as tiny, spinning tops that carry a specific kind of angular momentum. When a magnet is shaken, these tops roll off into an adjacent metal layer, creating a current that can be detected as a burst of electromagnetic radiation. This process is well understood and forms the backbone of modern data storage and computing. However, a second, more elusive type of traffic has long been predicted to exist alongside the spin flow. Just as a spinning top has a spin, it also has an orbit, a path it traces around a center. This orbital motion carries its own momentum, known as orbital angular momentum. Theory suggests that when a magnet is disturbed, it should also pump this orbital momentum into its neighbors, but because this flow is so similar to the spin flow and happens at the same time, separating the two has been nearly impossible. Understanding how much of each type of flow exists is crucial, because they behave differently and could power a new generation of ultrafast electronic devices.

A team of researchers at Fudan University in Shanghai has now succeeded in untangling these two intertwined flows, providing the first clear, quantitative picture of how orbital pumping works in real materials. They studied a simple but powerful setup: a thin layer of a magnetic metal, such as iron, cobalt, or nickel, placed directly on top of a non-magnetic metal layer. When they hit the magnetic layer with an ultrafast laser pulse, it launched both spin and orbital currents into the non-magnetic layer. The challenge was that both currents produced the same type of signal, a burst of terahertz radiation, making it impossible to tell which was which. The researchers solved this by exploiting a subtle difference in how the two currents behave. They chose non-magnetic metals that react to spin and orbital flows in opposite ways. For some metals, a spin flow creates a signal with a positive polarity, while an orbital flow creates a signal with a negative polarity. By carefully varying the thickness of the non-magnetic layer, they could watch how the total signal changed. Because the two types of currents travel different distances before fading away, their contributions to the signal shifted as the layer got thicker, allowing the researchers to mathematically separate them.

The results revealed a surprising hierarchy in how different magnetic metals generate these flows. As the researchers moved from iron to cobalt to nickel, the contribution of the orbital flow grew significantly. While iron was long thought to be a source of almost pure spin flow, the team found that even iron generates a measurable amount of orbital flow, which becomes especially important when the non-magnetic layer is very thin. In these thin layers, the spin and orbital flows cancel each other out, creating a "threshold" where the signal barely appears until the layer is thick enough for one to dominate. This effect was most dramatic in nickel. The team found that in nickel-based structures, the orbital flow is not just a minor side effect; it can reach several tens of percent of the strength of the spin flow. This is far higher than current theories predicted, suggesting that our understanding of how nickel generates these currents is incomplete.

The study also shed light on how far these flows can travel. The researchers measured how quickly the signals died out as the non-magnetic layer got thicker, a property known as the diffusion length. They found that orbital flows consistently travel shorter distances than spin flows across all the materials tested. However, the distance an orbital flow could travel depended heavily on the material it was moving through. In heavier metals like tantalum and tungsten, the orbital flow vanished very quickly, within less than a nanometer. But in a lighter metal called niobium, the orbital flow traveled much farther, extending to about 1.5 nanometers. This suggests that the ability of orbital momentum to move through a material is linked to the strength of the interaction between the material's electrons and their spins. The researchers also considered whether the orbital flow might be converting back into a spin flow further down the line, which could confuse the measurements, but their data showed this was not a significant factor in their results.

By establishing a method to measure these two flows separately, the researchers have provided a new tool for the scientific community. Their work confirms that orbital pumping is a real and significant phenomenon, one that is stronger in some materials than previously imagined. The findings challenge existing theoretical models, particularly regarding nickel, and highlight that the behavior of these currents changes depending on the specific materials used. This quantitative framework opens the door to designing new devices that can harness both spin and orbital momentum, potentially leading to faster and more efficient ways to process information. The key takeaway is that the magnetic world is richer than we thought, with a second, hidden current of momentum flowing alongside the familiar spin, waiting to be engineered.

Technical Summary: Quantitative Disentanglement of Terahertz Spin and Orbital Pumping in 3d Ferromagnetic Heterostructures

Problem Statement
Spin and orbital pumping—the injection of spin and orbital angular momentum from a driven ferromagnet (FM) into an adjacent nonmagnetic (NM) layer—are fundamental to angular-momentum transport in magnetic heterostructures. While femtosecond optical excitation has extended these phenomena into the ultrafast regime, detectable via spintronic terahertz emission spectroscopy (STES), a critical limitation remains: spin and orbital currents are generated simultaneously and contribute additively to the same terahertz emission signal. This superposition prevents their quantitative separation. Although microscopic theory predicts that orbital-pumping efficiency increases from Fe to Ni across the 3d series, it remains unclear whether these predictions hold under ultrafast excitation or how the relative contributions of spin and orbital currents compare quantitatively. Previous attempts to isolate orbital channels using weak spin-to-charge converters (e.g., Cu, Ti) failed to determine relative amplitudes, polarities, or propagation lengths within a single framework.

Methodology
To overcome the challenge of simultaneous generation and additive detection, the authors developed a quantitative disentanglement strategy combining STES with precise wedge-sample thickness control. The experimental design relies on two complementary properties of spin and orbital currents:

Opposite Polarities: The researchers selected NM layers (Ta, W, and Nb) where the spin Hall angle ( $\gamma_{SH}^{NM}$ ) and orbital Hall angle ( $\gamma_{OH}^{NM}$ ) possess opposite signs. Consequently, spin-current-induced and orbital-current-induced terahertz emissions exhibit opposite polarities.
Distinct Decay Lengths: Spin and orbital currents decay over different characteristic lengths within the NM layer. By utilizing wedge-shaped samples with continuous thickness gradients (0.75–2.5 nm/mm), the authors performed high-precision, thickness-dependent measurements to separate contributions based on their spatial decay profiles.

The study systematically investigated heterostructures of Fe, Co, and Ni (fixed at 5 nm thickness) capped with wedge-shaped Ta, W, or Nb layers. Terahertz waveforms were recorded using free-space electro-optic sampling. To quantitatively extract the individual contributions, the authors employed a Multi-Component Terahertz-Emission Model (MC-TEM). This model treats the total emission as a coherent sum of three components: bare-FM emission, inverse spin Hall effect (ISHE)-mediated spin-to-charge conversion, and inverse orbital Hall effect (IOHE)-mediated orbital-to-charge conversion. Interfacial Rashba-Edelstein effects were excluded via control experiments.

Key Results

Polarity Evolution and Threshold Behavior:
- Fe|Ta: Exhibited a negative polarity throughout the thickness range but displayed a distinct "threshold-like" regime below $d_{Ta} \approx 0.5$ nm, where the amplitude growth was suppressed. This was attributed to the near-cancellation of negative spin and positive orbital contributions.
- Ni|Ta: Showed a single polarity reversal from negative to positive at $d_{Ta} \approx 0.3$ nm, indicating orbital dominance at thin thicknesses.
- Co|Ta: Displayed a double polarity reversal (negative $\to$ positive $\to$ negative), revealing a complex competition where orbital contributions dominate at thin layers and spin contributions dominate at thicker layers.
- FM|W: Fe|W and Co|W maintained negative polarity across the entire thickness range, indicating spin dominance. Ni|W exhibited two polarity reversals: a first reversal at $d_W \approx 0.2$ nm (orbital dominance) and a second at $d_W \approx 2.6$ nm (spin dominance re-emerging).
- FM|Nb: Fe|Nb maintained negative polarity. Ni|Nb exhibited a single polarity reversal from negative to positive near $d_{Nb} \approx 0.6$ nm. Co|Nb showed two polarity reversals (negative $\to$ positive $\to$ negative), with the second occurring at $d_{Nb} \approx 5.4$ nm.
- Threshold-like regimes (suppressed amplitude growth at thin NM layers) were observed in Fe|Ta, Co|W, and Fe|Nb, arising from the near-cancellation of spin and orbital signals.
Quantitative Decomposition:
- The MC-TEM fitting successfully reproduced the amplitude and waveform evolutions for all systems.
- The extracted orbital-to-spin amplitude ratios ( $\tilde{A}_L / \tilde{A}_S$ ) increased systematically from Fe to Co to Ni.
- For Fe and Co, the orbital-current contribution ranged from a few percent to approximately 20% of the spin-current contribution.
- For Ni, the orbital contribution reached several tens of percent, with estimates up to ~70% in Ni|Nb, significantly exceeding current theoretical predictions for the 3d series.
- Even Fe, traditionally viewed as a spin-dominant source, was found to generate a non-negligible orbital current, which becomes essential for interpreting the threshold behavior in thin-NM regimes.
Diffusion Lengths:
- The extracted orbital diffusion lengths ( $\lambda_L$ ) were consistently shorter than the corresponding spin diffusion lengths ( $\lambda_S$ ) across all NM materials.
- Notably, $\lambda_L$ was markedly longer in Nb (~1.5 nm) compared to the heavier 5d metals Ta and W (0.3–0.8 nm), suggesting that orbital propagation depends on the spin-orbit coupling (SOC) strength of the NM layer.

Significance and Claims
The paper establishes a quantitative framework for investigating ultrafast spin and orbital pumping in magnetic heterostructures. By resolving the coexisting contributions of spin and orbital currents within a single STES platform, the work provides a basis for benchmarking microscopic theories of orbital angular momentum (OAM) generation and transport.

The authors highlight that while their results confirm the progressive enhancement of orbital pumping from Fe to Ni, the magnitude of the orbital contribution in Ni is substantially larger than predicted by existing theories. They attribute this discrepancy to potential differences between coherent, adiabatic dynamics (theoretical basis) and ultrafast non-equilibrium dynamics (experimental reality), or to variations in interfacial transmission efficiencies. Furthermore, the observation that orbital diffusion lengths vary with NM SOC challenges recent simulations suggesting SOC independence.

The study concludes that STES, when combined with wedge-sample analysis and multi-component modeling, serves as a robust quantitative probe for coupled spin and orbital pumping. This approach opens new avenues for engineering ultrafast spin-orbital interconversion in orbitronic materials and devices, though the authors remain modest regarding the precise quantification of current densities due to uncertainties in theoretical values of spin and orbital Hall conductivities.

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