Spin‑Orbit Torque–Driven Domain Wall Dynamics and Tilting in Perpendicularly Magnetized Pt/Co/Ta Racetracks

Background

Current‑induced magnetic domain wall motion (CIDWM) is a key mechanism for next‑generation racetrack memory devices. Early studies focused on ferromagnets (FMs) with in‑plane anisotropy, where spin‑transfer torque (STT) drove DWs. Later, CIDWM was demonstrated in perpendicular magnetic anisotropy (PMA) systems, yet the direction of DW propagation sometimes contradicted STT predictions. In heavy‑metal (HM)/FM bilayers, spin‑orbit torques (SOTs) generated by the spin Hall effect (SHE) and/or Rashba effect, together with interfacial DMI, produce chiral DWs that move along the current direction. Enhancing CIDWM efficiency therefore requires HM layers with large spin Hall angles (θ_SH) and careful engineering of interfacial properties. Various strategies—thickness tuning, interface decoration, crystallinity control, and oxygen incorporation—have been employed to maximize θ_SH and the effective SOT efficiency. HM/FM/HM trilayers, where two HM layers contribute opposing θ_SH signs, can further boost the net torque. The DMI strength in such structures is also modified, influencing DW velocity and tilting behavior. Recent models predict that DMI and pinning landscapes determine the extent of DW tilting under current.

In prior work, we examined the effect of inserting a thin carbon (C) layer between Co and Ta in Pt/Co/Ta stacks, observing changes in anisotropy, switching fields, and SOT effective fields. Here, we extend that study to analyze current‑driven DW motion and tilting, quantifying how C insertion influences DMI, pinning potential, and SOT efficiency in micro‑sized Pt/Co/Ta racetracks.

Methods

Two film stacks—Ta(3 nm)/Pt(5 nm)/Co(0.6 nm)/Ta(5 nm) and Ta(3 nm)/Pt(5 nm)/Co(0.6 nm)/C(2 nm)/Ta(5 nm)—were deposited on Corning glass at room temperature by DC magnetron sputtering (base pressure < 4.0 × 10⁻⁵ Pa). The bottom Ta serves as a seed layer, while the top Ta forms a ~1.5 nm TaO_x cap after air exposure. The films were patterned into 8.5 µm and 3.0 µm wide racetracks, respectively, using standard lithography and Ar‑ion milling. Hall bars of identical width were fabricated to measure the out‑of‑plane field (H_z)-dependent anomalous Hall resistance (R_Hall) under various in‑plane bias fields (H_x) along the current direction. By extracting the shift of the R_Hall-H_z loops (H_SHE), we quantified the SOT efficiency χ = H_SHE/J. A polar Kerr microscope monitored DW motion under applied fields or current pulses at room temperature.

Results and Discussion

Using the chiral Néel DW model, we first determined DMI and SOT parameters from anomalous Hall measurements. The effective DMI fields (H_DMI) for Pt/Co/Ta and Pt/Co/C/Ta were ~1370 Oe and ~1055 Oe, respectively, while the saturated SOT efficiencies χ^sat were 10.0 Oe/(10⁶ A cm⁻²) and 8.3 Oe/(10⁶ A cm⁻²). The slight reduction in χ^sat for the C‑decorated stack likely reflects increased interfacial spin‑flip scattering. Calculated DMI exchange constants |D| were 1.01 ± 0.16 mJ m⁻² (Pt/Co/Ta) and 1.15 ± 0.14 mJ m⁻² (Pt/Co/C/Ta), indicating that the Pt/Co interface dominates DMI in both stacks. Since H_DMI/H_K < 2/π, the Néel character of the DWs is stable, as confirmed by CIDWM experiments.

Field‑driven DW velocities were measured under out‑of‑plane magnetic pulses. Both stacks exhibited a creep‑like dependence v ∝ exp[−(U_c/k_BT)(H_dep/H)^1/4]. The depinning field H_dep was roughly twice that of Pt/Co/Ta in the C‑decorated stack, and the slope parameter s was larger (37.4 Oe^1/4 vs. 76.5 Oe^1/4), confirming a higher pinning potential. Domain images showed more irregular DW shapes in Pt/Co/C/Ta, consistent with a non‑uniform pinning landscape.

Current‑driven DW motion was then studied. DW velocities increased with current density, but achieving the same velocity in Pt/Co/C/Ta required about twice the current density, reflecting reduced SOT efficiency and enhanced pinning. Remarkably, the CIDWM velocity was ~10³ times larger than that driven by an equivalent magnetic field, underscoring the impact of Joule heating and possibly the Oersted field. At high currents (± 19.2 MA cm⁻²), we observed reduced velocities, increased nucleation sites, and altered DW tilting, suggesting thermally activated processes and a reshaped pinning landscape.

DW tilting emerged only under current drive. The tilt angle ψ grew approximately linearly with current density for both stacks, in agreement with recent theoretical predictions. Field‑driven experiments did not show tilting, implying that the Oersted field—generated by the current—plays a crucial role. Calculated Oersted fields (~19.6 Oe for Pt/Co/Ta and ~37.4 Oe for Pt/Co/C/Ta at maximum current) are comparable to H_SHE, and since both fields act in the same direction at specific positions along the racetrack, the DW experiences a non‑uniform effective field, producing the observed trapezoidal domain shapes. In-plane bias fields (H_x, H_y) modify the DW chirality and the relative strength of H_SHE and H_Oersted, further affecting tilting and domain expansion.

Conclusions

We demonstrate that both DW motion and tilting are strongly influenced by SOT efficiency, pinning potential, Joule heating, and the Oersted field in Pt/Co/Ta and Pt/Co/C/Ta racetracks. The DMI strength (~1 mJ m⁻²) is dominated by the Pt/Co interface, while C insertion modestly reduces SOT efficiency and increases pinning. Current‑driven DW velocities reach tens of m/s at a few MA cm⁻², but the presence of a sizable Oersted field can distort domain shapes, which may limit practical racetrack memory designs. These insights guide the engineering of SOT‑based racetracks with optimized DW dynamics.

Abbreviations

CIDWM:

Current‑induced domain wall motion

DMI:

Dzyaloshinskii–Moriya interaction

D-U:

Down‑to‑up

DW:

Domain wall

FIDWM:

Field‑induced domain wall motion

FMs:

Ferromagnets

HM:

Heavy metal

PMA:

Perpendicular magnetic anisotropy

SOT:

Spin‑orbit torque

STT:

Spin transfer torque

U-D:

Up‑to‑down