In a variety of disordered elastic media, glassiness leads to metastable configurations and striking history effects closely connected to a rich dynamics where plasticity plays a key role. When driven away from equilibrium, these systems may adopt self-organized configurations and develop unusual dynamics, including non-equilibrium phase transitions (NEPT)--a trending research topic [Cugliangolo, C. R. Phys. 14, 685, 2013]. In particular, depinning transitions under the action of a continuous driving force and their connection with a NEPT have been long and thoroughly studied [Reichhardt, Rep. Prog. Phys. 80, 026501, 2017]. On the other hand, the dynamics of these systems driven by alternating (AC) forces had received but little attention before the last decade. However, in the last ten years, an amount of work showed that AC dynamics displays particular characteristics, not directly translatable from DC regimes, and may reorganize these systems into different configurations.

Vortex matter is an ideal playground for research on this topic. Our group has been working for more than ten years on studying AC dynamics in the vortex lattice (VL) of NbSe₂ clean single crystals, a system that undergoes an order-disorder transition.  By means of AC susceptibility and Neutron Scattering (SANS) experiments, we obtained results supporting the existence of a narrow transitional region between the ordered and the disordered phases, where the application of AC magnetic fields gives rise to bulk VL configurations with intermediate degrees of disorder, correlated with intermediate linear AC responses [Pasquini et al., PRL 100, 247003, 2008; Marziali Bermúdez et al., PRL 115, 067001, 2015]. Numerical simulations suggested that these intermediate configurations are originated from a VL reorganization driven by the oscillatory dynamics [Pérez Daroca et al., PRB 84, 012508, 2011].

In this work, we present new experimental results that provide clear evidence of dynamic reordering. Moreover, unambiguous signature of criticality suggests that this reorganization is closely associated with a dynamic phase transition. The relation with a critical AC depinning transition [Pérez Daroca et al., PRB 81, 184520, 2010; Y Kawamura, New J. Phys. 19 093001, 2017] is also discussed.