Quantifying inhomogeneous magnetic fields at the micrometer scale using graphene Hall-effect sensors

The response of a graphene Hall-effect sensor to the inhomogeneous magnetic field generated by a dipole located above it is investigated numerically at room temperature as a function of the dipole position and orientation and as a function of the sensor conduction regime, i.e., diffusive or ballistic. By means of dedicated models, we highlight that the correction factor alpha frequently used to relate the Hall voltage to the magnetic field averaged over the sensor area can be greatly improved in the high proximity situation enabled by the use of graphene, particularly in the ballistic regime. In addition, it is demonstrated that by fine-tuning the dipole position in the sensor plane, the Hall response becomes highly selective with respect to the dipole orientation. These analyses show that diffusive graphene Hall sensors may be preferred for particle detection, while ballistic ones used as close as possible to a nanomagnet would be preferred for magnetometry. Then, with the help of micromagnetic simulations, the principle of measuring the magnetic hysteresis loop of an isolated nanomagnet with a ballistic Hall sensor is investigated. A large signal-to-noise ratio is demonstrated, which allows for effective probing of magnetization reversal. This shows that devices based on specially designed ballistic graphene Hall crosses promise to outperform state-of-the-art ballistic Hall sensors based on semiconductor quantum wells or micro-SQUID, especially for nano-magnetometry.