🔬 materials science

Exchange scaling of ultrafast angular momentum transfer in 4 $\it{f}$ antiferromagnets

By combining time-resolved soft x-ray diffraction with ab-initio calculations, this study demonstrates that the rate of ultrafast angular momentum transfer in 4f antiferromagnets is directly determined by the magnitude of the RKKY interaction, offering a new pathway to fine-tune the speed of magnetic devices by varying 4f occupation.

Original authors: Y. W. Windsor, S-E. Lee, D. Zahn, V. Borisov, D. Thonig, K. Kliemt, A. Ernst, C. Schüßler-Langeheine, N. Pontius, U. Staub, C. Krellner, D. V. Vyalikh, O. Eriksson, L. Rettig

Published 2026-08-18

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CC BY 4.0

Original authors: Y. W. Windsor, S-E. Lee, D. Zahn, V. Borisov, D. Thonig, K. Kliemt, A. Ernst, C. Schüßler-Langeheine, N. Pontius, U. Staub, C. Krellner, D. V. Vyalikh, O. Eriksson, L. Rettig

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

The magnetic properties of matter are not just about which way a compass needle points; they are about the invisible, swirling motion of electrons that gives materials their magnetic personality. In many metals, this magnetism comes from electrons that are free to roam, carrying their magnetic influence with them as they move. In other materials, specifically those containing rare-earth elements, the magnetic electrons are tightly locked to their parent atoms, unable to wander freely. For decades, scientists have known that when you hit a magnet with a burst of light, it loses its magnetism. In the roaming-electron materials, this happens because the energy dissipates into the surrounding crystal structure, much like a spinning top slowing down as it rubs against a table. However, in the locked-electron materials, there is a different possibility: the magnetic atoms could simply swap their spin direction with a neighbor, passing the angular momentum directly from one to the other without needing the crystal lattice to absorb the energy. This direct transfer promises to be much faster, potentially allowing for magnetic devices that switch states in the blink of an eye. The question that has remained unanswered is whether this direct swapping actually happens in these locked-electron materials, and if so, what controls its speed.

A team of researchers set out to answer this by studying a specific family of crystals made from rare-earth elements combined with rhodium and silicon. They chose these materials because they share an identical, layered structure where the magnetic atoms are arranged in alternating layers, pointing in opposite directions. This perfect arrangement allowed the scientists to compare different rare-earth elements side-by-side without the confusion of changing crystal shapes or magnetic patterns. The only thing that changed from one sample to the next was the number of locked electrons orbiting the central atom. By shining an ultrafast laser pulse at these crystals, the researchers excited the electrons and then used extremely short pulses of X-rays to watch how the magnetic order collapsed over time. They observed that the magnetism didn't just fade away; it dropped in two distinct steps. The first was a rapid, tiny dip, followed by a slower, more significant decline. The speed of this decline varied wildly across the different materials, taking anywhere from one trillionth of a second to over one hundred trillionths of a second depending on which rare-earth element was used.

To understand why the speed changed so dramatically, the researchers looked for a pattern in the data. They found that the rate at which the magnetic atoms swapped their angular momentum was directly linked to the strength of the invisible force connecting them. This force, known as the Ruderman-Kittel-Kasuya-Yosida interaction, is a kind of magnetic handshake mediated by the sea of free electrons that float between the locked atoms. The researchers discovered that the stronger this handshake was, the faster the magnetic atoms could swap their spins. They confirmed this connection by performing detailed computer simulations that calculated the strength of the magnetic coupling for each element. The simulations showed a perfect match with the experimental data: the speed of the spin swap scaled directly with the strength of the interaction between the atoms. This confirmed that the primary way these materials lose their magnetism is not by dumping energy into the crystal lattice, but by passing the spin directly from one atom to its neighbor.

The study also revealed that this direct transfer is not the only thing happening. Even in the fastest materials, there was a baseline speed limit that could not be beaten, suggesting that some energy still had to find its way into the crystal lattice eventually. However, the dominant factor controlling the speed was clearly the strength of the connection between the atoms. This finding is significant because it suggests a new way to control magnetic devices. Instead of trying to change the atoms themselves, engineers could tune the speed of magnetic switching by manipulating the free electrons that connect them. This could be done by applying pressure, changing the chemical composition, or using electric fields to alter the electron sea. The research demonstrates that by understanding and tuning these invisible connections, it is possible to design magnetic materials that operate at speeds previously thought impossible, opening the door to a new generation of ultrafast information technology.

Technical Summary: Exchange Scaling of Ultrafast Angular Momentum Transfer in 4f Antiferromagnets

Problem Statement
Ultrafast manipulation of magnetic states is a critical objective for future information technologies. While demagnetization in ferromagnets is typically governed by the dissipation of angular momentum to the lattice, materials with multiple spin sublattices, such as antiferromagnets (AF), offer the potential for direct angular momentum transfer between opposing spins, potentially enabling faster functionality. However, in lanthanide-based 4f antiferromagnets, the magnetic 4f electrons are highly localized and lie several eV below the Fermi level, meaning they are not directly optically excited. Instead, optical pulses excite conduction electrons, which mediate the indirect Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange coupling between 4f spins. The extent to which the magnitude of this RKKY coupling influences the rate of direct spin-to-spin angular momentum transfer in 4f systems remains largely unexplored. Previous studies were limited by the variety of crystal structures and magnetic phases in elemental lanthanides, or focused on ferromagnets where direct spin-transfer channels are difficult to isolate from lattice interactions.

Methodology
To isolate the influence of 4f occupation on ultrafast dynamics, the authors investigated a series of isostructural lanthanide intermetallic antiferromagnets with the formula LnRh $_2$ Si $_2$ (where Ln = Pr, Nd, Sm, Gd, Tb, Dy, Ho). These materials share nearly identical crystal and magnetic structures (collinear, layer-by-layer antiferromagnetic order along [001]), ensuring that the only significant variable is the 4f shell occupation of the Ln ion.

The experimental approach combined:

Time-Resolved Resonant Magnetic Soft X-ray Diffraction (RXD): Experiments were conducted at the BESSY II "FemtoSpeX" facility using ultrashort X-ray pulses tuned to the Ln M $_{4,5}$ edges (3d $\to$ 4f transitions) to achieve exclusive sensitivity to the 4f moments. The samples were excited by 1.55 eV (800 nm) femtosecond laser pulses. The decay of the magnetic Bragg reflection intensity was monitored to extract the demagnetization dynamics.
Systematic Variation: The study varied the excitation fluence and analyzed the response across the entire lanthanide series to determine scaling relations.
Ab-initio Calculations: Density Functional Theory (DFT) calculations, utilizing both Green's function methods (GGA+U) and the RSPt code, were performed to calculate the RKKY exchange coupling parameters ( $J$ ) between the 4f moments.

Key Results

Two-Step Demagnetization: All materials exhibited a qualitatively identical two-step demagnetization process: a fast sub-picosecond drop followed by a slower drop. However, the absolute time scales varied significantly, ranging from ~1 ps to over 100 ps depending on the specific lanthanide.
Universal Scaling: Despite the vast differences in time scales and 4f filling, the angular momentum transfer rates ( $\Gamma$ ) exhibited a linear scaling relation with the de Gennes factor ( $g^2 = (J-1)^2 J(J+1)$ ), which approximates the squared projection of the spin and is proportional to the strength of the RKKY interaction.
Direct Correlation with RKKY: The ab-initio calculations confirmed that the interplanar RKKY coupling ( $J_{\perp}$ ) between antiparallel spins scales linearly with the de Gennes factor. In contrast, in-plane couplings did not show a clear trend.
Transfer Mechanism: The linear relationship between the transfer rate and the de Gennes factor (and thus RKKY strength) indicates that the dominant demagnetization channel is the direct transfer of angular momentum between antiparallel 4f moments mediated by conduction electrons.
Offset Contribution: The linear fit of the transfer rates versus the de Gennes factor does not pass through the origin. This suggests an additional, constant contribution to the angular momentum transfer rate that is independent of 4f occupancy. The authors attribute this to the dissipation of angular momentum from the 4f system to the lattice via conduction electrons, a process that acts as a bottleneck and is similar across all LnRh $_2$ Si $_2$ materials.

Significance and Claims
The paper claims to demonstrate that the rate of direct angular momentum transfer between opposing 4f spins in antiferromagnets is directly determined by the magnitude of the RKKY exchange coupling. This finding establishes a "de Gennes scaling" for ultrafast spin dynamics in these systems.

The authors posit that this result offers a novel approach for fine-tuning the speed of magnetic devices. Because the RKKY interaction is highly sensitive to the conduction electron environment, the speed of magnetic switching or demagnetization could be controlled by manipulating these electrons through external means such as doping, voltage biasing, applied pressure, or transient photodoping, without necessarily altering the magnitude of the 4f moments themselves. The authors note that while their study focuses on antiferromagnets, the principles of direct momentum transfer may also apply to ferrimagnets and alloys, which is relevant for technologies like ultrafast all-optical switching that rely on momentum transfer between magnetic sublattices.

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