Extended longitudinal vector and Bragg magneto-optic Kerr effect for the determination of the chirality distribution in magnetic vortices

We have measured longitudinal magneto-optic Kerr effect (MOKE) for off-specular beams diffracted by a square array of Permalloy nanodots outside the plane of incidence and found that only the measurements performed outside the plane of incidence are sensitive to the distribution of rotational sense of vortices (vortex chirality) in the dot array. An asymmetry was introduced into the dot shape to ensure a uniform vortex chirality distribution in the dot array and to obtain a clear, well-defined chirality contrast in the MOKE signal. We also demonstrate an alternative method to measure the vortex chirality in dots of asymmetric shape without switching the chirality during magnetization reversal. In addition to the experiment, we have developed a general formalism that can be used to describe MOKE measured for off-specular beams inside as well as outside of the plane of incidence in all three Kerr geometries (polar, longitudinal, and transversal) with an arbitrary polarization state of incident light. Combined with micromagnetic simulation, this formalism reproduces the experimental results well.