  Recent Atacama Large Millimeter/submillimeter Array (ALMA) observations have
revealed an increasing number of compact protostellar disks with radii of less
than a few tens of astronomical units and that young Class 0/I objects have an
intrinsic size diversity. To deepen our understanding of the origin of such
tiny disks, we performed the highest-resolution configuration observations with
ALMA at a beam size of $\sim$0$''$03 (4 au) on the very low-luminosity Class 0
protostar embedded in the Taurus dense core MC 27/L1521F. The 1.3 mm continuum
measurement successfully resolved a tiny, faint ($\sim$1 mJy) disk with a major
axis length of $\sim$10 au, one of the smallest examples in the ALMA
protostellar studies. In addition, we detected spike-like components in the
northeastern direction at the disk edge. Gravitational instability or other
fragmentation mechanisms cannot explain the structures, given the central
stellar mass of $\sim$0.2 $M_{\odot}$ and the disk mass of $\gtrsim$10$^{-4}$
$M_{\odot}$. Instead, we propose that these small spike structures were formed
by a recent dynamic magnetic flux transport event due to interchange
instability that would be favorable to occur if the parental core has a strong
magnetic field. The presence of complex arc-like structures on a larger
($\sim$2000 au) scale in the same direction as the spike structures suggests
that the event was not single. Such episodic, dynamical events may play an
important role in maintaining the compact nature of the protostellar disk in
the complex gas envelope during the main accretion phase.
