Nonlinear Hall effect as a local probe of plasmonic magnetic hot spots

Recently developed plasmonic nanostructures are able to generate intense and localized magnetic hot spots in a large spectral range from the terahertz to the visible. However, a direct measurement of the magnetic field at the hot spot has not been performed yet, due to the absence of magnetic field detectors that work at those high frequencies and that fit the hot-spot area. We propose to place a graphene ribbon in the hot spot of a plasmonic nanostructure driven by a laser beam, such that a current is generated due to both the magnetic field at the hot spot and the electric field of the laser. We demonstrate that a nonlinear Hall voltage, which can be measured by standard electrical means, builds up across the ribbon, making it possible to directly probe the magnetic field at the hot spot.