Vortex-lattice melting front in thin superconductors with pinning

Magneto-optical observations of a second flux front, which occurs at the second peak in the magnetization of Bi₂Sr₂CaCu ₂O_x single crystals related to the known first-order "vortex-lattice melting," are reconsidered. We show that, in thin samples, electrodynamics necessarily leads to an extended region in which the magnetic induction adopts a nearly constant value close to that at which the phase transition occurs at thermal equilibrium. In this region a dynamical phase mixture of vortex "solid" and "liquid" should exist. Interestingly, the observed second flux front does not mark the "melting" front, as it was naively interpreted earlier, but indicates the disappearance of the last "solid droplets.".