Ordered creation and motion of skyrmions with surface acoustic wave

The study addresses how to efficiently generate and manipulate magnetic skyrmions in ferromagnets while suppressing the skyrmion Hall effect (SkHE), a major obstacle to reliable skyrmion transport and device operation. Prior approaches have reduced SkHE in ferrimagnets and synthetic antiferromagnets, but achieving organized creation and current-driven motion with negligible SkHE in prototypical ferromagnets remains difficult. The authors propose using surface acoustic waves (SAWs) to provide both strain (via magnetoelastic coupling) and thermal effects to generate skyrmions and to create an energy landscape that organizes and guides skyrmions, thereby suppressing their transverse motion. The purpose is to demonstrate ordered skyrmion generation and near-zero SkHE motion in Co/Pd-based ferromagnetic multilayers integrated into a SAW delay line.

The paper reviews methods for skyrmion generation at room temperature in multilayers with interfacial DMI, including magnetic fields, electric currents/fields, and thermal gradients. It highlights the SkHE as a key challenge due to the Magnus force from nonzero topological charge, causing transverse deflection during current-driven motion. Reduced SkHE has been demonstrated in ferrimagnets and synthetic antiferromagnets, yet ordered creation and negligible SkHE in ferromagnets remain challenging. The authors point to strain as a controllable route to manipulate magnetic textures. SAWs have been used for magnetization oscillations, assisted switching, and control of magnetic texture dynamics, including skyrmion creation and manipulation. This prior work motivates the integration of SAW devices with ferromagnetic multilayers to exploit magnetoelastic coupling and thermal effects for organized skyrmion generation and motion control.

• Materials and stack: Ferromagnetic multilayer Co(0.3 nm)/Pd(0.9 nm)/Co(0.3 nm)/Pd(0.9 nm)/Co(0.3 nm)/Pt(1.4 nm) deposited on 128°-rotated, Y-cut LiNbO3 piezoelectric substrates by d.c. magnetron sputtering. For magnetic property measurements, films were deposited at room temperature with base vacuum better than 8.0 × 10^-5 mTorr and Ar working pressure of 3 mTorr.
• Device: Integrated SAW delay line comprising two-port interdigital transducers (IDTs) with the magnetic multilayer patterned as a channel between them. IDT design: 5 µm finger width and gap, 70 pairs of single-type fingers, 300 µm spacing between IDTs. Magnetic channel width: 60 µm. The geometry supports SAW excitation with well-defined wavelengths.
• SAW excitation and characterization: RF signals applied to IDTs to excite SAWs and induce both strain and heating. Transmission spectra measured with a vector network analyzer reveal three modes determined by the substrate velocity and IDT geometry: first Rayleigh SAW (R1) at 181.63 MHz, longitudinal leaky SAW (LLSAW) at 365.65 MHz, and third Rayleigh SAW (R3) at 546.03 MHz, corroborated by finite element method (FEM) simulations.
• Thermal characterization: An infrared camera measured temperature at the center of the magnetic channel after 2 minutes of RF power. At 365.65 MHz (LLSAW), temperature rose from ~28.6 °C to ~38.6 °C as power increased from 17 to 22 dBm, indicative of significant leaky power dissipation as heat. At 181.63 and 546.03 MHz, temperature changes were <1 °C over the same power range.
• Magnetic imaging and phase mapping: Real-space domains and skyrmions were observed by polar magneto-optical Kerr effect (MOKE) microscopy while sweeping perpendicular magnetic field Hz. With LLSAW excitation (365.65 MHz, P up to 21–23 dBm), domain evolution from maze to mixed stripe/skyrmion phases and ordered alignment along the y-direction were recorded; without SAW, coherent domain reversal occurred with no skyrmion formation.
• Skyrmion density quantification: Skyrmion density n_sk measured as a function of RF power under Hz = −12.96 Oe, and as a function of Hz to construct phase diagrams with and without SAW.
• Current-driven dynamics: Current pulses were applied along the channel to drive skyrmion motion. Typical parameters: current density j ≈ 2.5 × 10^10 A m^−2, pulse duration 50 µs, Hz ≈ 10.86 Oe, with SAW on (P = 21 dBm). Trajectories tracked to extract velocities in x and y and compute the skyrmion Hall angle θ_sk = arctan(vx/vy). Comparative measurements without SAW used a similar sample where skyrmions were thermally generated by an on-chip heater.
• Simulations: FEM identified SAW modes and field distributions. Micromagnetic simulations modeled magnetization dynamics with magnetoelastic coupling under SAW. The magnetoelastic energy density considered dominant strain components ε_xx, ε_xz, ε_zz from LLSAW, leading to E = b1 ε_xx m_x^2 + b1 ε_zz m_z^2 + 2 b2 ε_xz m_x m_z. Simulations examined evolution from multi-domain to skyrmion states, and reorganization under SAW into antinode-pinned alignments. Total and SAW energy evolution versus time were computed to interpret energy redistribution.
• Controls: Experiments at other SAW frequencies (181.63, 546.03 MHz) showed negligible heating and no skyrmion formation under similar conditions. A device at 2.79 GHz produced skyrmions without ordered alignment, attributed to too-short wavelength relative to skyrmion size.

• SAW modes and thermal effects: The delay line exhibits three modes: 181.63 MHz (R1), 365.65 MHz (LLSAW), and 546.03 MHz (R3). LLSAW causes substantial heating: center temperature increases from ~28.6 °C to ~38.6 °C as RF power increases from 17 to 22 dBm; other modes cause <1 °C change.
• Ordered skyrmion generation: With LLSAW at 365.65 MHz and P ≈ 21–23 dBm, skyrmions are generated and align along the y-direction (antinodes of the standing SAW), while without SAW only coherent domain reversal occurs and no skyrmions are observed under comparable field scans.
• Phase behavior with SAW: As a function of Hz, three regimes are observed: (i) |Hz| < ~4 Oe: maze domains; (ii) 4 Oe < |Hz| < ~21 Oe: mixed skyrmions and stripe domains, with skyrmion density first increasing then decreasing with |Hz|; (iii) |Hz| > ~21 Oe: uniform magnetization and disappearance of skyrmions.
• Power dependence: Under Hz = −12.96 Oe, skyrmion density n_sk increases from 0 to 8.2 × 10^6 mm^−2 as RF power rises from 19 to 23 dBm.
• Current-driven motion with suppressed SkHE: With SAW (P = 21 dBm), skyrmions move along nearly straight trajectories under current pulses (e.g., j = 2.5 × 10^10 A m^−2, 50 µs), indicating negligible transverse motion. Quantitatively, θ_sk remains < ~7° across j from 1.25 × 10^10 to 1 × 10^11 A m^−2. In contrast, without SAW (thermal generation via heater), θ_sk increases rapidly up to ~30° over the same current range, evidencing substantial SkHE.
• Mechanism and simulations: Micromagnetic simulations show that SAW-induced magnetoelastic coupling creates a spatially periodic energy landscape; skyrmions migrate toward SAW antinodes where they are energetically favored, producing ordered alignment. SAW excitation shifts the system to a new energy state with oscillatory SAW energy contributions, consistent with experimental alignment and suppressed transverse motion. At very high SAW frequency (2.79 GHz), the wavelength is too small relative to skyrmion size, preventing effective antinode pinning and ordered alignment.

The work demonstrates that integrating a Co/Pd-based ferromagnetic multilayer into a SAW delay line enables both the creation and organization of skyrmions via combined thermal and strain effects from LLSAWs. The SAW-induced strain gradient and associated magnetoelastic energy landscape pin skyrmions at antinodes, aligning both skyrmions and stripe domains. This ordered arrangement suppresses transverse components of current-driven motion, effectively reducing the skyrmion Hall effect in a ferromagnet without resorting to ferrimagnetic or synthetic antiferromagnetic compensation. The quantitative reduction of θ_sk to below ~7° across a broad current range, versus ~30° without SAW, indicates a robust suppression mechanism. Simulations corroborate the energy-redistribution mechanism and show that SAW frequency/wavelength relative to skyrmion size is critical. These findings address the longstanding challenge of controlled skyrmion motion in ferromagnets, highlighting SAWs as a versatile tool in skyrmionics and spin acousto-electronics.

An integrated SAW device was used to realize ordered creation and current-driven motion of skyrmions in Co/Pd/Co/Pd/Co/Pt ferromagnetic multilayers. Longitudinal leaky SAWs at 365.65 MHz simultaneously provide thermal assistance for skyrmion nucleation and a strain-gradient-induced energy landscape that aligns skyrmions at antinodes. The resulting ordered configurations significantly suppress the skyrmion Hall effect, with θ_sk maintained below ~7° over a wide current range, compared with ~30° without SAW. Micromagnetic simulations validate that SAWs redistribute system energy and stabilize skyrmions at antinodes, explaining the observed ordering and reduced transverse motion. This approach opens a new avenue for manipulating topological solitons and advancing skyrmion-based device concepts. Future work could optimize SAW frequency and wavelength relative to skyrmion size, explore different material stacks and substrates, engineer standing-wave patterns for programmable conduits, and assess device-level endurance and scalability.

• The approach relies on LLSAW-induced heating and strain; at SAW frequencies with minimal heating (e.g., 181.63 and 546.03 MHz), skyrmions were not generated under similar conditions, indicating a dependence on thermal assistance.
• At very high SAW frequency (2.79 GHz), the SAW wavelength is too short relative to skyrmion size to provide effective antinode pinning, leading to random distributions; thus, ordering depends on matching SAW wavelength to skyrmion dimensions.
• Partial misalignment and skyrmion/stripe interactions were observed, and pinning in the film led to elongation/disappearance of some skyrmions during motion, indicating material inhomogeneities affect performance.
• Demonstrations were performed on a specific Co/Pd/Co/Pd/Co/Pt stack on LiNbO3; generalization to other ferromagnets and substrates requires validation.
• The temperature rise under LLSAW confounds isolation of pure strain effects; disentangling thermal versus magnetoelastic contributions would require further controls.