SOT Enabled 3D Magnetic Field Sensor with Low Offset and High Sensitivity

In this work we demonstrate a spin-orbit torque (SOT) magnetic field sensor, designed as a Ta/CoFeB/MgO structure, with high sensitivity and capable of active offset compensation in all three spatial directions. This is described and verified in both experiment and simulation. The measurements of magnetic fields showed an offset of 36, 50, and 37$\mathrm{μT}$ for x-, y-, and z-fields. Furthermore, the sensitivities of these measurements had values of 590, 580, and 490$\mathrm{V,A^{-1},T^{-1}}$ in the x-, y-, and z-direction. In addition, the robustness to bias fields is demonstrated via experiments and single spin simulations by applying bias fields in y-direction. Cross sensitivities were further analyzed via single spin simulations performing a parameter sweep of different bias fields in the y- and z-direction up to $\pm$1mT. Finally, the extraction of the SOT parameters $η_\mathrm{DL}$ and $η_\mathrm{FL}$ is shown via optimization of a single-spin curve to the experimental measurements.

💡 Research Summary

This paper presents a spin‑orbit‑torque (SOT) based three‑dimensional magnetic field sensor built from a Ta/CoFeB/MgO heterostructure. The authors combine analytical modeling, single‑spin simulations, micromagnetic calculations, and experimental measurements to demonstrate that the device can sense magnetic fields along the x, y, and z axes with low offset and high sensitivity while providing active offset compensation in all three directions.
The sensor is fabricated as a cross‑shaped element (overall length 10 µm, arm width 2 µm) where a 1 nm CoFeB ferromagnetic layer sits on a 6 nm Ta heavy‑metal layer, capped by MgO/Ta. When a charge current flows through Ta, the spin Hall effect generates a spin current polarized along +y. This spin current exerts both field‑like (FL) and damping‑like (DL) torques on the CoFeB magnetization, described by an augmented Landau‑Lifshitz‑Gilbert equation. By linearizing the LLG equation for small external fields (Hx, Hz) and zero Hy, the authors derive closed‑form expressions for the out‑of‑plane magnetization component mz for positive and negative current directions. Subtracting mz(+I) and mz(‑I) yields a signal Sx that is first‑order sensitive only to Hx, canceling y‑cross‑sensitivity; adding the two gives Sz, which is first‑order sensitive only to Hz.
To achieve offset‑free operation, the authors adopt a spinning‑current technique: the current is alternated between the x‑ and y‑oriented arms, and the corresponding anomalous Hall resistances (Rxy for x‑current, Ryx for y‑current) are combined according to equations (9)–(11). This procedure eliminates static voltage offsets that would otherwise dominate the measurement, especially for the z‑axis where the signal does not reverse with current polarity.
Experimentally, a current density of 1.71 × 10¹¹ A m⁻² (2.7 mA total) is applied while sweeping external magnetic fields from –10 mT to +10 mT. The sensor exhibits linear response up to ±0.5 mT in the x and y directions and ±1 mT in the z direction. Extracted sensitivities are –590 V A⁻¹ T⁻¹ (x), –580 V A⁻¹ T⁻¹ (y), and +490 V A⁻¹ T⁻¹ (z). Offsets measured without magnetic shielding are 36 µT (x), 50 µT (y), and 37 µT (z), demonstrating that the active compensation reduces the offset to well below the Earth’s field.
Single‑spin simulations using the measured material parameters (γ = 2.2128 × 10⁵ m A⁻¹ s⁻¹, α = 0.01, Ms = 1.2 µ₀ A m⁻¹, Hk = 3049 A m⁻¹, ηFL = 0.0360, ηDL = 0.0436) reproduce the experimental curves within the linear regime. Micromagnetic simulations (GPU‑accelerated magnumnp) incorporating exchange, perpendicular anisotropy, and DMI further confirm the dominance of the spin‑Hall magnetoresistance (SMR) over anisotropic magnetoresistance (AMR) in the observed Rxx variation.
A key contribution is the extraction of the SOT efficiencies ηDL and ηFL, as well as the perpendicular anisotropy field Hk, from the measured slopes κx and κz. By minimizing the mean‑square error between simulated and experimental Sx and Sz curves while varying Hk, the authors determine μ₀Hk = 3.83 mT, ηDL = 0.0436, and ηFL = 0.0360. These values are then fed back into the simulations, achieving excellent agreement across all three axes.
Cross‑sensitivity analysis is performed by sweeping bias fields in y and z up to ±1 mT and evaluating the impact on the orthogonal signal. The results show that, owing to the SOT‑based detection scheme, cross‑sensitivities remain below 1 % for bias fields within the linear range, confirming the robustness of the sensor design.
In summary, the work demonstrates that a SOT‑enabled Hall‑type sensor can deliver true three‑dimensional magnetic field detection with sub‑50 µT offset, sensitivities approaching 600 V A⁻¹ T⁻¹, and CMOS‑compatible fabrication. The combination of analytical modeling, parameter extraction, and comprehensive simulation provides a clear pathway for further optimization and integration of SOT sensors in automotive, consumer electronics, and robotics applications.