We report results of dc magnetic and ac linear low-frequency study of a polycrystalline MgB$_2$ sample. AC susceptibility measurements at low frequencies, performed under dc fields parallel to the sample surface, provide a clear evidence for surface superconducting states in MgB$_2$.
We report experimental studies of the low frequency electrodynamics of ZrB$_{12}$ and Nb single crystals. AC susceptibility at frequencies 3 - 1000 Hz have been measured under a dc magnetic field, $H_0$, applied parallel to the sample surface. In the
surface superconducting state, for several $H_0$, the real part of the ac magnetic susceptibility exhibits a logarithmic frequency dependence as for spin-glass systems. Kramers-Kronig analysis of the experimental data, shows large losses at ultra low frequencies ($<3$ Hz). The wave function slope at the surface was found. The linear response of the order parameter to the ac excitation was extracted from the experimental data.
The large nonlinear response of a single crystal ZrB$_{12}$ to an ac field (frequency 40 - 2500 Hz) for $H_0>H_{c2}$ has been observed. Direct measurements of the ac wave form and the exact numerical solution of the Ginzburg-Landau equations, as well
as phenomenological relaxation equation, permit the study of the surface superconducting states dynamics. It is shown, that the low frequency response is defined by transitions between the metastable superconducting states under the action of an ac field. The relaxation rate which determines such transitions dynamics, is found.
We have measured the nonlinear response to the ac magnetic field in the superconducting weak ferromagnet Ru-1222, at different regimes of sample cooling which provides unambiguous evidence of the interplay of the domain structure and the vorticity in
the superconducting state. This is {em direct} proof of coexistence of ferromagnetic and superconductive order parameters in high-$T_c$ ruthenocuprates.
