  Coexistence of phases, characterized by different electronic degrees of
freedom, commonly occurs in layered superconductors. Among them, alkaline
intercalated chalcogenides are model systems showing microscale coexistence of
paramagnetic (PAR) and antiferromagnetic (AFM) phases, however, temporal
behavior of different phases is still unknown. Here, we report the first
visualization of the atomic motion in the granular phase of
K$_{x}$Fe$_{2-y}$Se$_2$ using X-ray photon correlation spectroscopy. Unlike the
PAR phase, the AFM texture reveals an intermittent dynamics with avalanches as
in martensites. When cooled down across the superconducting transition
temperature T$_c$, the AFM phase goes through an anomalous slowing behavior
suggesting a direct relationship between the atomic motions in the AFM phase
and the superconductivity. In addition of providing a compelling evidence of
avalanche-like dynamics in a layered superconductor, the results provide a
basis for new theoretical models to describe quantum states in inhomogeneous
solids.
