  The magnetic response is a state-defining property of superconductors. The
magnetic flux penetrates type-II bulk superconductors by forming quantum
vortices when the enclosed magnetic flux is equal to the magnetic flux quantum.
The flux quantum is the universal quantity that depends only on the ratio of
fundamental constants: the electron charge and the Planck constant. This work
investigates the vortex state in the hole-overdoped Ba$_{1-x}$K$_x$Fe$_2$As$_2$
by using scanning superconducting quantum interference device (SQUID)
magnetometry. We observed quantum vortices that carry only a fraction of the
flux quantum, which vary continuously with temperature. This finding
establishes the phenomenon that superconductors support quantum vortices with
non-universally quantized magnetic flux. Furthermore, the demonstrations of the
mobility of the fractional vortices and the manipulability of their positions
open up a route for future fluxonics applications.
