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

TL;DR

This study demonstrates a Ta/CoFeB/MgO-based spin-orbit torque magnetic field sensor with active offset compensation in all three spatial directions, enabling true 3D field sensing with a single sensitive element. By formulating an extended LLG model including damping-like and field-like SOTs and deriving analytic expressions for x- and z-field responses, the authors show how to cancel cross-sensitivities and recover offset-free measurements. They experimentally achieve offsets on the order of tens of microtesla and high directional sensitivities, and extract the SOT parameters $\eta_{DL}$ and $\eta_{FL}$ by fitting a single-spin model to the data, validating the approach with simulations. The work introduces a robust 3D sensing approach that is compatible with CMOS integration and provides a practical path to precise, offset-free magnetic field measurements in three dimensions, while also revealing the limitations imposed by complex magnetization states and the single-domain assumption.

Abstract

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.

Figures (7)

• Figure 1: a The analyzed structure is designed as a cross like structure, with a ferromagnetic layer on top of a heavy metal layer. b Spin separation via the Spin Hall effect (SHE). Spin polarized current acts like a torque, through the components $\bm{m} \times \bm{H}_{DL}$ and $\bm{m} \times\bm{H}_{FL}$, on the magnetization of the FM layer under the influence of an external magnetic field ($\bm{H}_{ext}$).
• Figure 2: a Measured $R_{xy}$ for $2.7 \, \mathrm{mA}$ current strength under external $H_x$ fields for $I_{xx}^+$ (blue dashed curve with circles) and $I_{xx}^-$ (red dashed curve with circles). b Measured $R_{yx}$ for $2.7 \, \mathrm{mA}$ current strength under external $H_y$ fields. c Measured $R_{xy}$ and $R_{yx}$ for $2.7 \, \mathrm{mA}$ current strength under external $H_z$ fields for $I_{xx}^\pm$ (dashed curves with circles) and $I_{yy}^\pm$ (dashed curves with rectangles). d The sensor response (blue curve with squares) for $2.7 \, \mathrm{mA}$ current strength and single spin simulation results (red curve with circles) under external $H_x$ fields. e The same plot but for an external $H_y$ field sweep. f The response under external $H_z$ fields.
• Figure 3: a Measured $R_{xx}$ data over an external $H_x$ field. Visible is the reduced resistance due to the combined AMR and SMR effect around weak external $H_x$ fields. b The result of the single spin simulation (solid lines with circular markers) and the micromagnetic simulation (dotted lines with point markers), of the same situation. Plotted is the AMR effect ($\propto$$m_x^2$) as the red curve and the SMR effect ($\propto \left(1-m_y^2\right)$) as the blue curve over external $H_x$ field.
• Figure 4: a Comparison of $S_x$ over an external $H_x$ field sweep of the single spin simulation (blue curve) and the micromagnetic simulation (red curve) with an applied SOT current density $j_e= 1.71 \cdot 10^{11} \, \mathrm{Am^{-2}}$. b Snapshots of the micromagnetic simulation over an external $H_x$ field sweep for positive (top row) and negative (bottom row) SOT current. Visualized is the $m_z$ component of the magnetization for the same $H_x$ field sweep. Blue areas denote negative magnetization values and red positive values, which can be seen in the colorbar on the right side.
• Figure 5: a The measured response curve for an external $H_x$ field sweep, with zero bias field (blue curve with squares) and $\mu_0 H_y = 0.5 \, \mathrm{mT}$ bias field (red curve with squares), for SOT current in $\pm$x-direction. b The simulated data for the same two cases, utilizing a single spin simulation. c The calculated sensor curve for the measured data, using Eq. \ref{['SOT_signalx_quation']}.