🔬 materials science

Perpendicular magnetic anisotropy tuning of macrospin-to-vortex transitions in Co-based artificial spin-vortex ice

This study demonstrates that perpendicular magnetic anisotropy effectively enhances the macrospin-to-vortex transition probability in Co-based artificial spin-vortex ice, a finding validated by both micromagnetic simulations and experimental measurements on multilayer stacks, thereby offering a tunable parameter for optimizing physical reservoir computing systems.

Original authors: Yu Maruyama (Kyoto Univ), Amrit Kumar Mondal (Univ. Delaware), Bijaya Kharel (Univ. Delaware), Ryo Ohshima (Kyoto Univ, CSRN, Kyoto Univ), Jorge Puebla (Kyoto Univ, CSRN, Kyoto Univ), M. Benjamin Jung

Published 2026-07-10

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CC BY 4.0

Original authors: Yu Maruyama (Kyoto Univ), Amrit Kumar Mondal (Univ. Delaware), Bijaya Kharel (Univ. Delaware), Ryo Ohshima (Kyoto Univ, CSRN, Kyoto Univ), Jorge Puebla (Kyoto Univ, CSRN, Kyoto Univ), M. Benjamin Jungfleisch (Univ. Delaware), Masashi 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, microscopic city made of thousands of stadium-shaped magnets, each no wider than a human hair. In this city, the magnets usually act like little compass needles, pointing in one direction. But sometimes, they decide to spin in a circle, forming a tiny whirlpool called a "vortex." This switch from pointing straight to spinning in a circle is the key to a special kind of computer memory that can "forget" old information just enough to learn new things—a concept called "fading memory."

For a long time, scientists thought the only way to control how often these magnets switched to the spinning vortex state was by changing the shape of the stadiums themselves. It was like saying the only way to get a car to turn a corner is to build a sharper curve in the road. Once the road was built, the turning ability was fixed forever.

But this paper suggests a different, more flexible idea: maybe we can tune how often the magnets spin by changing the material they are made of, without reshaping the stadiums at all. Specifically, the researchers looked at a property called "perpendicular magnetic anisotropy" (PMA). Think of PMA as a magnetic "gravity" that pulls the tiny magnets to stand up straight, rather than lie flat.

To test this, the team built two different versions of these magnetic cities. One version (called TCT) had a standard layer of titanium under a layer of cobalt. The other version (called TCP) swapped that titanium for platinum. The scientists suspected that the platinum would create a stronger "upward pull" (PMA) on the magnets.

First, they ran computer simulations using a program called MuMax3. These simulations acted like a virtual wind tunnel, showing that when you increase that "upward pull" (PMA), it becomes much easier for the magnets to form those spinning vortices. The simulations suggested that the energy landscape changes, making the vortex state more comfortable for the magnets to live in.

Then, they built the real thing. Using a vibrating sample magnetometer (VSM), they measured the magnetic properties of flat films made from their TCT and TCP stacks. The results confirmed their suspicion: the TCP film, with its platinum layer, had a stronger perpendicular magnetic anisotropy (PMA) than the TCT film. The numbers were clear: the TCP film had a magnetic anisotropy constant ( $K_u$ ) of $609 \pm 5$ kJ/m³, while the TCT film was lower at $539 \pm 6$ kJ/m³.

Next, they created the actual magnetic cities (ASVIs) using these two different materials. They used a technique called Magnetic Force Microscopy (MFM) to take pictures of the magnets. They saw that after applying a specific training process (repeatedly flipping the magnetic field), the magnets in the TCP cities were much more likely to switch from pointing straight to spinning in a vortex.

To get a big-picture view of the whole city, they used a tool called Vector-Network-Analyzer-based Ferromagnetic Resonance (VNA-FMR). This is like listening to the hum of the entire city to hear what state the magnets are in. As they trained the cities, the "hum" changed. They found that the TCP cities switched to the vortex state much faster and more often than the TCT cities.

The paper quantifies this by looking at the "transition probability" ( $p$ ), which is the chance of a magnet switching to a vortex in each step. They found that for every width of stadium they tested (220 nm, 230 nm, and 240 nm), the TCP cities had a higher probability of switching than the TCT cities. For example, in the 220 nm wide magnets, the TCT city took about 10 training loops to get roughly 86% of its magnets to switch, but the TCP city was even more eager to switch.

So, what's the big takeaway? The paper doesn't claim to have solved all of computing, but it strongly suggests that you don't need to rebuild your magnetic cities to change their memory. By simply swapping a layer of metal (like using platinum instead of titanium), you can tune how easily the magnets switch to a vortex state. This means we might be able to design computers that can be "reprogrammed" on the fly by changing their material properties, perhaps even with an electric field, to fit different tasks. The authors propose that this material-based tuning is a promising route for making better physical reservoir computers, but they note that the electric-field control is still a future possibility to explore, not a current reality.

Technical Summary: Perpendicular Magnetic Anisotropy Tuning of Macrospin-to-Vortex Transitions in Co-based Artificial Spin-Vortex Ice

Problem Statement
Artificial spin-vortex ice (ASVI) is a promising platform for physical reservoir computing, leveraging the probabilistic transition from a macrospin (MS) state to a vortex (V) state to generate "fading-memory" characteristics. The memory capacity of such systems is governed by the MS-to-V transition probability ( $p$ ). While $p$ can be tuned via nanomagnet geometry (shape anisotropy), this approach is static; once a device is fabricated, its memory characteristics are fixed. The authors identify a need for a material-based parameter that allows for the tuning of $p$ without altering the device geometry, thereby enabling task-adapting reservoir computing. The study investigates whether perpendicular magnetic anisotropy (PMA) can serve as this tunable parameter by modifying the relative energy stability of the MS and V states.

Methodology
The research combines micromagnetic simulations with a multi-modal experimental approach:

Micromagnetic Simulations: Using MuMax3, the authors simulated stadium-shaped nanomagnets (600 nm × 220 nm × 10 nm) to evaluate the energy difference ( $\Delta E_{V-MS}$ ) between the V and MS states as a function of the perpendicular anisotropy constant ( $K_u$ ). The total energy ( $E_{total}$ ) was decomposed into demagnetization, exchange, and anisotropy components.
Material Fabrication and Characterization: Two multilayer stacks were fabricated via electron beam deposition on sapphire substrates:
- TCT: Ti (3 nm)/Co (10 nm)/Ti (3 nm)/Pt (2 nm)
- TCP: Ti (3 nm)/Co (10 nm)/Pt (2 nm)
  The TCP stack was designed to exhibit higher PMA due to the Co/Pt interface, which has a higher interfacial anisotropy energy ( $K_s$ ) than the Co/Ti interface in the TCT stack. Vibrating Sample Magnetometry (VSM) was used to measure the effective anisotropy ( $K_{eff}$ ) and saturation magnetization ( $M_s$ ) to confirm the difference in $K_u$ between the two stacks.
Device Fabrication: ASVI devices were created using electron-beam lithography and lift-off techniques. Stadium-shaped nanomagnets with varying widths (220, 230, and 240 nm) were patterned from both TCT and TCP stacks onto coplanar waveguides (CPW).
Experimental Probes:
- Magnetic Force Microscopy (MFM): Used to visualize the magnetic state evolution (MS to V) during a training process involving minor field loops.
- Vector Network Analyzer Ferromagnetic Resonance (VNA-FMR): Used to probe the collective spin dynamics. The transition probability was quantified by analyzing the evolution of FMR spectra (specifically the intensity of the lower-frequency mode, $L_{S2}$ ) as a function of the number of training cycles ( $N$ ).

Key Results

Simulation Findings: The simulations revealed that increasing $K_u$ monotonically increases $\Delta E_{V-MS}$ , making the vortex state energetically more favorable relative to the macrospin state. This is attributed to the out-of-plane magnetization component at the vortex core, which benefits more from PMA than the in-plane macrospin state.
Material Characterization: VSM measurements confirmed that the TCP stack possesses a larger perpendicular anisotropy ( $K_u \approx 609 \pm 5$ kJ/m³) compared to the TCT stack ( $K_u \approx 539 \pm 6$ kJ/m³). The difference in $K_u$ corresponded to an interfacial anisotropy difference consistent with literature values for Co/Pt versus Co/Ti interfaces.
Transition Probability:
- MFM images of TCT ASVIs showed a gradual transition from the MS state to the V state over 10 training cycles, with approximately 86% of nanomagnets transitioning.
- VNA-FMR spectra evolved from a two-mode profile (characteristic of MS states) to an inverted-V-shaped feature (characteristic of V states) as training cycles increased.
- Quantitative analysis of the FMR data extracted the transition probability $p$ . For all nanomagnet widths tested, TCP ASVIs (higher PMA) exhibited a significantly higher transition probability $p$ than TCT ASVIs (lower PMA).
- Consistent with previous studies, $p$ also increased with nanomagnet width due to reduced shape anisotropy.

Significance and Claims
The paper demonstrates that perpendicular magnetic anisotropy is an effective design parameter for controlling the MS-to-V transition probability in ASVI. By validating that higher PMA enhances the formation of vortex states, the authors establish a materials-based route to tune the fading-memory characteristics of artificial spin lattices. This finding suggests that reservoir computing devices based on ASVI can be optimized for specific tasks not only through geometric design but also through material engineering. Furthermore, the authors note that since interfacial PMA can be modulated by electric fields, this approach offers a potential pathway for on-chip, dynamic tuning of memory capacity in future reservoir computing architectures.

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