We analyze the mixing properties of a floating stirrer driven electromagnetically in a thin layer of electrolyte, consisting of two free-floating magnets with opposite polarities connected by a rigid coupling. The magnetic rotor is set in circular motion using Lorentz forces created due to the interaction of the magnetic field of the rotor with dc currents actuated in logic sequence. We identify a coherent structure similar to a tripolar vortex whose central vortex rotates in the same direction of the rotor promoting chaotic mixing of the fluid in the laminar regime (Re=45). Dyed water visualization and particle image velocimetry were performed to characterize experimentally the mixing and flow dynamics at the surface of the electrolyte layer. A quasitwo-dimensional numerical simulation based on the immersed boundary method, which incorporates the fluid-solid interaction and reproduces the experimental observations satisfactorily, was carried out. Optimal mixing conditions are determined through the exponential growth of the material interfaces, which are established mainly by varying the distance separating the magnets of the rotor.