  Using an extended Anderson/Kondo impurity model to describe the magnetic
moments around an impurity doped in high-$T_{\text{c}}$ d-wave cuprates and in
the framework of the slave-boson meanfield approach, we study numerically the
impurity state in the vortex core by exact diagonalization of the
well-established Bogoliubov-de Gennes equations. The low-energy impurity state
is found to be good agreement with scanning tunnelingmicroscopy observation.
After pinning a vortex on the impurity site, we compare the unitary impurity
model with the extended Anderson impurity model by examining the effect of the
magnetic field on the impurity state. We find that the impurity resonance in
the unitary impurity model is strongly suppressed by the vortex; while it is
insensitive to the field in the extended Anderson impurity model.
