Study of the vortex dynamic in MgB₂ by harmonic susceptibility measurements

In order to investigate the flux line dynamic in the recently discovered MgB₂ superconductor, we have measured the ac magnetic susceptibility as a function of the temperature T and the ac field frequency f on a bulk sample. In particular we have analysed the fundamental and the third harmonics X1,3(T) = ⁱX′1,3(T) + ⁱX′′(T) by comparison of the experimental data with both analytical and numerical results. We show that in the temperature range below Tp(X′′1) (i.e. the peak temperature of the imaginary part for the fundamental harmonic) the measured curves for X3(T) do not agree with the curves predicted by the Bean model for the critical state, and that the shape of the third harmonic, both in the real and the imaginary part, is strongly affected by the frequency f, as a consequence of the thermally activated vortex motion in a non linear flux diffusion regime. The evidence of this behaviour allows one to estimate the value of the pinning barrier for the analysed sample.