Dissipation in Mesoscopic Superconductors with Ac Magnetic Fields

The response of mesoscopic superconductors to an ac magnetic field is investigated both experimentally and with numerical simulations. We study small square samples with dimensions of the order of the penetration depth. We obtain the ac susceptibitity $\chi=\chi'+i\chi''$ at microwave frequencies as a function of the dc magnetic field $H_{dc}$. We find that the dissipation, given by $\chi''$, has a non monotonous behavior in mesoscopic samples. In the numerical simulations we obtain that the dissipation increases before the penetration of vortices and then it decreases abruptly after vortices have entered the sample. This is verified experimentally, where we find that $\chi''$ has strong oscillations as a function of $H_{dc}$ in small squares of Pb.