A Dichotomy in the Metastable-to-Ground State Vortex Lattice Transition in MgB$_2$

The vortex lattice (VL) in the type-II superconductor MgB$_2$ can serve as a model for out-of-equilibrium systems. Previous small-angle neutron scattering (SANS) studies of the VL in this material have revealed an unprecedented degree of metastability that is demonstrably not due to vortex pinning, [C. Rastovski $et$ $al.$, Phys. Rev. Lett. {\bf 111}, 107002 (2013)]. We used a stop-motion SANS technique to image the VL between successive applications of a controlled number of AC magnetic field cycles. This allows us to study in detail how the metastable VL is driven back to the ground state. Our results show a dichotomy in the behavior for metastable configurations induced by crossing the equilibrium, second order phase transition in different directions. For a metastable state induced by super heating, the VL returns to the ground state through a continuous domain rotation. In contrast, in the super cooled case, VL ground state domains nucleate and grow at their final orientation.