  Two-dimensional superconductors have attracted growing interest because of
their scientific novelty, structural tunability, and useful properties. Studies
of their magnetic responses, however, are often hampered by difficulties to
grow large-size samples of high quality and uniformity. We report here an
imaging method that employed NV- centers in diamond as sensor capable of
mapping out the microwave magnetic field distribution on an ultrathin
superconducting film of micron size. Measurements on a 33nm-thick film and a
125nm-thick bulk-like film of $Bi_2Sr_2CaCu_2O_{8+\delta}$ revealed that the ac
Meissner effect (or repulsion of ac magnetic field) set in at 78K and 91K,
respectively; the latter was the superconducting transition temperature (Tc) of
both films. The unusual ac magnetic response of the thin film presumably was
due to thermally excited vortex-antivortex diffusive motion in the film.
Spatial resolution of our ac magnetometer was limited by optical diffraction
and the noise level was at 14 ${\mu}T/Hz^{1/2}$. The technique could be
extended with better detection sensitivity to extract local ac
conductivity/susceptibility of ultrathin or monolayer superconducting samples
as well as ac magnetic responses of other two-dimensional exotic thin films of
limited lateral size.
