Experimental verification and quantitative validation of exchange-coupling-torque-driven domain-wall motion in fully compensated synthetic antiferromagnets

Current-driven motion of the composite domain walls that connect antiferromagnetically exchange-coupled magnetic sub-layers in a synthetic antiferromagnet (SAF) was shown by Yang, Ryu and Parkin (Nature Nanotechnology 10, 221–226, 2015) to reach about 750 m s$^{-1}$ in nearly compensated SAF racetracks, powered by a novel exchange-coupling torque (ECT) proportional to the antiferromagnetic interlayer exchange coupling. An extended one-dimensional (1D) analytical model attributes this to torque from the interlayer exchange field acting on the wall magnetizations, and predicts that domain-wall velocities exceed $1000\ \mathrm{m\,s^{-1}}$ in a perfectly compensated SAF. Later work has reused and extended the 1D model, probed the dependence of velocity on exchange coupling with several spacer materials, and discovered additional interlayer coupling mechanisms (a chiral exchange drag on the coupled walls, mediated by an interlayer Dzyaloshinskii–Moriya interaction). However, the predicted ultrafast regime in fully compensated SAFs has not been experimentally verified, the rigid coupled-wall assumptions of the 1D model have not been systematically validated in the high-velocity, strong-coupling limit, and the quantitative mapping of velocity onto independently controlled exchange coupling and spin-current penetration into the upper layer remains incomplete. The problem posed here is to close this gap: determine the current-driven composite domain-wall dynamics of exchange-coupled SAFs all the way to full compensation, and establish the physical basis for dense, fast, low-power domain-wall racetrack devices.

Background

Racetrack memory stores data as a sequence of magnetic domain walls (the thin transition regions, typically tens of nanometres wide, separating domains of opposite magnetization) that are translated along a nanowire by short current pulses. In perpendicularly magnetized ultrathin wires interfaced with heavy metals, spin–orbit coupling at the interface produces a Dzyaloshinskii–Moriya interaction (DMI) — an antisymmetric exchange interaction that fixes the handedness (chirality) of the wall — and spin–orbit torques (SOT): torques on the magnetization generated by spin currents, produced for example by the spin Hall effect in an adjacent heavy-metal layer such as Pt. Chiral Néel walls (walls whose magnetization rotates in the plane of the film) can then be moved efficiently by current. A synthetic antiferromagnet (SAF) is a stack of two such ferromagnetic layers separated by an ultrathin ruthenium (or rhodium) spacer, through which the Ruderman–Kittel–Kasuya–Yosida (RKKY) mechanism gives an antiferromagnetic interlayer exchange coupling of strength $J^{\mathrm{ex}}$; the two layers' magnetizations are then antiparallel and the net stray field of a domain wall in one layer is compensated by the wall in the other, allowing densely packed walls. Yang, Ryu and Parkin (2015) showed with nanosecond current pulses that the two coupled walls in such a stack move together as a composite object at up to about $750\ \mathrm{m\,s^{-1}}$ when the two sub-layers are nearly matched (almost zero net magnetization) — several times faster than comparable ferromagnetically coupled stacks — and explained this with an extended one-dimensional (1D) analytical model. In that model the wall in each layer $i$ ($i = L, U$ for lower and upper) is described by collective coordinates: a position $q_i$ and an azimuthal angle $\psi_i$ of the wall magnetization. The model assumes a rigid wall profile (only the $\psi_i$ vary during motion) and locked wall positions ($q_L = q_U$). Its central new ingredient is the exchange-coupling torque (ECT): the antiferromagnetic interlayer exchange field $H_i^{\mathrm{ex}} \propto J^{\mathrm{ex}}$ acting on the tilted wall magnetizations produces torques $\tau_i^{\mathrm{ex}}$ that add constructively in an SAF (and oppose each other in a ferromagnetically coupled stack), giving a driving force that scales with $2J^{\mathrm{ex}}/(M_L + M_U)$, where $M_L, M_U$ are the sub-layer saturation magnetizations; in the samples studied it was roughly an order of magnitude larger than the DMI-field torque. The model extrapolates to domain-wall velocities above $1000\ \mathrm{m\,s^{-1}}$ as the net magnetization approaches zero, a regime that is hard to reach experimentally because standard magneto-optical imaging and readout signals vanish as the stack becomes perfectly compensated. The same authors elaborated the model in a 2017 review, and in 2021 used it again to describe velocity versus the sub-layer magnetization ratio in ionitronic experiments — experiments in which ionic-liquid gate voltages reversibly oxidize and reduce one magnetic layer, thereby tuning its properties. Later work also discovered additional interlayer coupling physics in SAFs — a long-range chiral (interlayer-DMI-mediated) exchange interaction and a resulting chiral exchange drag on coupled walls — so that any quantitative validation of the ECT picture must now be compared against these mechanisms as well.

Problem Statement

Establish the current-driven dynamics of the composite domain walls of exchange-coupled synthetic antiferromagnets in the regime of full compensation, and thereby test the exchange-coupling-torque picture and its device implications. Concretely, four linked, unfinished tasks remain: (1) test experimentally whether exchange-coupling-torque-driven domain-wall velocities exceed $1000\ \mathrm{m\,s^{-1}}$ in a perfectly compensated SAF, either confirming or refuting the prediction of the extended one-dimensional (1D) model; this requires measurement and readout techniques that remain sensitive as the net magnetization approaches zero, since conventional magneto-optical imaging and readout signals vanish at compensation; (2) test the model's assumptions of a rigid wall profile (only the azimuthal angles $\psi_i$ — the in-plane orientations of the wall magnetizations in the two sub-layers $i = L, U$ — varying) and locked wall positions ($q_L = q_U$, the two coupled walls staying coincident) in the highest-velocity and strongest-coupling regimes, by comparing full micromagnetic simulations with the 1D analytical predictions and with experiment, including the role of the interfacial DMI and of the chiral interlayer exchange discovered after 2015; (3) determine quantitatively how the domain-wall velocity depends on the interlayer exchange coupling constant $J^{\mathrm{ex}}$ when it is independently controlled and measured (including its materials dependence across spacer choices such as Ru versus Rh and its translation into the effective exchange field $H_i^{\mathrm{ex}}$, the interlayer exchange field acting on the wall in sub-layer $i$), and measure directly the attenuation of the spin current entering the upper magnetic layer, which the model currently takes from literature estimates; and (4) establish whether the demonstrated high-speed motion extrapolates to device-relevant racetrack architectures — narrow nanowires, many closely spaced domain walls, and full device stacks — quantifying the energy-per-bit and the reliability under repeated current pulsing. These four results jointly support one objective: a quantitative, validated account of exchange-coupling-torque-driven wall motion in compensated SAFs from mechanism to device, so that the projected dense, fast, low-power domain-wall racetracks rest on measured physics rather than on an untested extrapolation. Sub-task (2) assesses the rigid-profile and locked-position assumptions together with the roles of the interfacial DMI and the chiral interlayer exchange.

References

1. See-Hun Yang, Kwang-Su Ryu, and Stuart Parkin, 'Domain-wall velocities of up to 750 m s−1 driven by exchange-coupling torque in synthetic antiferromagnets', Nature Nanotechnology 10, 221–226 (2015). DOI: 10.1038/nnano.2014.324, https://doi.org/10.1038/nnano.2014.324
2. See-Hun Yang and Stuart Parkin, 'Novel domain wall dynamics in synthetic antiferromagnets', Journal of Physics: Condensed Matter 29, 303001 (2017). DOI: 10.1088/1361-648X/aa752d, https://doi.org/10.1088/1361-648X/aa752d
3. Yicheng Guan, Xilin Zhou, Fan Li, Tianping Ma, See-Hun Yang, and Stuart S. P. Parkin, 'Ionitronic manipulation of current-induced domain wall motion in synthetic antiferromagnets', Nature Communications 12, 5002 (2021). DOI: 10.1038/s41467-021-25292-1, https://doi.org/10.1038/s41467-021-25292-1
4. Ziyang Yu, Yue Zhang, Zhenhua Zhang, Ming Cheng, Zhihong Lu, Xiaofei Yang, Jing Shi, and Rui Xiong, 'Domain-wall motion at an ultrahigh speed driven by spin–orbit torque in synthetic antiferromagnets', Nanotechnology 29, 175404 (2018). DOI: 10.1088/1361-6528/aaaf35, https://doi.org/10.1088/1361-6528/aaaf35
5. Alexander Cohen, Alexis Jonville, Zhentao Liu, Chirag Garg, Panagiotis Ch. Filippou, and See-Hun Yang, 'Current driven chiral domain wall motions in synthetic antiferromagnets with Co/Rh/Co', Journal of Applied Physics 128, 053902 (2020). DOI: 10.1063/5.0012453, https://doi.org/10.1063/5.0012453
6. Yu Min Hung, Yoichi Shiota, Shogo Yamada, Minoru Ohta, Tatsuo Shibata, Tomoyuki Sasaki, Ryusuke Hisatomi, Takahiro Moriyama, and Teruo Ono, 'Positive correlation between interlayer exchange coupling and the driving current of domain wall motion in a synthetic antiferromagnet', Applied Physics Letters 119, 032407 (2021). DOI: 10.1063/5.0056056, https://doi.org/10.1063/5.0056056
7. Teng Xu, Jiahao Liu, Xichao Zhang, Qihan Zhang, Heng-An Zhou, Yiqing Dong, Pierluigi Gargiani, Manuel Valvidares, Yan Zhou, and Wanjun Jiang, 'Systematic Control of the Interlayer Exchange Coupling in Perpendicularly Magnetized Synthetic Antiferromagnets', Physical Review Applied 18, 054051 (2022). DOI: 10.1103/PhysRevApplied.18.054051, https://doi.org/10.1103/PhysRevApplied.18.054051
8. Yuelei Zhao, Sheng Yang, Kai Wu, Xiaoguang Li, Xichao Zhang, Li Li, Zhiqin Chu, Chong Bi, and Yan Zhou, 'Controlling domain wall and field-free spin–orbit torque switching in synthetic antiferromagnets', Applied Physics Letters 120, 222401 (2022). DOI: 10.1063/5.0092945, https://doi.org/10.1063/5.0092945
9. Nisrit Pandey, Maxwell Li, Marc De Graef, and Vincent Sokalski, 'Stabilization of coupled Dzyaloshinskii domain walls in fully compensated synthetic anti-ferromagnets', AIP Advances 10, 015233 (2020). DOI: 10.1063/1.5130411, https://doi.org/10.1063/1.5130411
10. Kitae Kim, Woo Young Shim, Atsushi Okada, UngHwan Pi, Kwangseok Kim, and Sug-Bong Choe, 'Suppression of stochasticity in high-speed domain-wall motion of synthetic antiferromagnets', Applied Physics Letters 127, 212402 (2025). DOI: 10.1063/5.0301833, https://doi.org/10.1063/5.0301833
11. Christopher E. A. Barker, Simone Finizio, Eloi Haltz, Sina Mayr, Philippa M. Shepley, Thomas A. Moore, Gavin Burnell, Jörg Raabe, and Christopher H. Marrows, 'Domain wall motion at low current density in a synthetic antiferromagnet nanowire', Journal of Physics D: Applied Physics 56, 425002 (2023). DOI: 10.1088/1361-6463/ace6b4, https://doi.org/10.1088/1361-6463/ace6b4
12. R. Tomasello, V. Puliafito, E. Martinez, A. Manchon, M. Ricci, M. Carpentieri, and G. Finocchio, 'Performance of synthetic antiferromagnetic racetrack memory: domain wall versus skyrmion', Journal of Physics D: Applied Physics 50, 325302 (2017). DOI: 10.1088/1361-6463/aa7a98, https://doi.org/10.1088/1361-6463/aa7a98
13. See-Hun Yang, Chirag Garg, and Stuart S. P. Parkin, 'Chiral exchange drag and chirality oscillations in synthetic antiferromagnets', Nature Physics 15, 543–548 (2019). DOI: 10.1038/s41567-019-0438-3, https://doi.org/10.1038/s41567-019-0438-3
14. Dong-Soo Han, Kyujoon Lee, Jan-Philipp Hanke, Yuriy Mokrousov, Kyoung-Whan Kim, Woosuk Yoo, Youri L. W. van Hees, Tae-Wan Kim, Reinoud Lavrijsen, Chun-Yeol You, Henk J. M. Swagten, Myung-Hwa Jung, and Mathias Kläui, 'Long-range chiral exchange interaction in synthetic antiferromagnets', Nature Materials 18, 703–708 (2019). DOI: 10.1038/s41563-019-0370-z, https://doi.org/10.1038/s41563-019-0370-z
15. Robin Bläsing, Tianping Ma, See-Hun Yang, Chirag Garg, Fasil Kidane Dejene, Alpha T. N'Diaye, Gong Chen, Kai Liu, and Stuart S. S. Parkin, 'Exchange coupling torque in ferrimagnetic Co/Gd bilayer maximized near angular momentum compensation temperature', Nature Communications 9, 4984 (2018). DOI: 10.1038/s41467-018-07373-w, https://doi.org/10.1038/s41467-018-07373-w
16. Lucas Caretta, Maxwell Mann, Felix Büttner, Kohei Ueda, Bastian Pfau, Christian M. Günther, Piet Hessing, Alexandra Churikova, Christopher Klose, Michael Schneider, Dieter Engel, Colin Marcus, David Bono, Kai Bagschik, Stefan Eisebitt, and Geoffrey S. D. Beach, 'Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet', Nature Nanotechnology 13, 1154–1160 (2018). DOI: 10.1038/s41565-018-0255-3, https://doi.org/10.1038/s41565-018-0255-3
17. Stuart Parkin and See-Hun Yang, 'Memory on the racetrack', Nature Nanotechnology 10, 195–198 (2015). DOI: 10.1038/nnano.2015.41, https://doi.org/10.1038/nnano.2015.41
18. Pengxiang Zhang, Wilfried Haensch, Charudatta M. Phatak, and Supratik Guha, 'Error-Free and Current-Driven Synthetic Antiferromagnetic Domain Wall Memory Enabled by Channel Meandering', arXiv:2405.18261 (2024). DOI: 10.48550/arXiv.2405.18261, arXiv ID: 2405.18261, https://arxiv.org/abs/2405.18261