  The vortex core radius \rv, defined as the peak position of the supercurrent
around the vortex, has been determined by muon spin rotation measurements in
the mixed state of \lscox for $x=0.13$, 0.15, and 0.19. At lower doping (x=0.13
and 0.15), \rv(T) increases with decreasing temperature T, which is opposite to
the behavior predicted by the conventional theory. Moreover, \rv(T\to0) is
significantly larger than the Ginsburg-Landau coherence length determined by
the upper critical field, and shows a clear tendency to decrease with
increasing the doping x. These features can be qualitatively reproduced in a
microscopic model involving antiferromagnetic electronic correlations.
