Size-dependent performance of three-dimensional magnetic field sensors based on spin–orbit torque effect

Three-dimensional (3D) anomalous Hall magnetic sensors based on the spin–orbit torque (SOT) effect have garnered significant attention due to their simple structure and high spatial resolution. Previous studies have revealed that sensing accuracy is closely related to the sensor’s size, particularly the width of the device, thereby limiting device optimization and miniaturization. In this work, we systematically investigated the impact of device width on the 3D SOT magnetic sensor through experiments and micromagnetic simulations. It is found that the fluctuation is approximately inversely proportional to the device width, which roughly represents the spatial resolution. The fluctuation can be significantly reduced by averaging multiple outputs, thus retaining the ability to sense magnetic fields accurately as the sensor is scaled down from tens of micrometers to hundreds of nanometers. The generalized average anomalous Hall resistance is universally proportional to the magnetic field. Meanwhile, the fluctuation reaches its maximum and the anomalous Hall resistance (RH) approximately follows a normal distribution at zero magnetic field, with the standard deviation reflecting the magnitude of fluctuation. This work provides valuable insights into the size-dependent properties of 3D SOT magnetic sensors and highlights their potential for miniaturization to achieve higher spatial resolution.