Vortex Lattice Metastability and Power Law Dynamics in MgB$_2$*

Previous small-angle neutron scattering (SANS) studies of the vortex lattice (VL) of MgB$_2$ with H $\parallel$ c found a triangular VL which undergoes a field-driven 30$^\circ$ reorientation transition, forming three distinct ground state phases. A high degree of metastability exists between the VL phases of MgB$_2$ that cannot be attributed to vortex pinning and may be a result of the jamming of VL domains [C.~Rastovski \emph{et al.}, Phys. Rev. Lett. {\bf 111}, 107002 (2013)]. To further investigate the effect of vortex motion on the metastable to ground state VL transition, we applied a small AC magnetic field parallel or perpendicular to the vortices to ``shake" the lattice. The metastable VL volume fraction decreased with a two-step power law dependence on the number of applied AC cycles. The slow and then fast power law decay of the metastable state may indicate first nucleation and then growth of ground state VL domains.