Power-law resistivity, magnetic relaxation and ac susceptibility

The nonlinear diffusion of magnetic flux into a superconducting sample can be studied by measuring the relaxation of the magnetisation after application of a step field or by measuring the ac susceptibility, χ₁ and its third harmonic, χ₃, or preferably both methods covering different time scales. Each has been analysed recently for a field-cooled sample of a material whose creep activation energy depends logarithmically on current density, J corresponding to a power-law relation between electric field, E and J. Here, results are compared, using a universal scaling depth. Maximum χ₁″ and |χ₃| values occur, and also the magnetisation has relaxed to half its initial value when the scaling depth is comparable to the sample half-thickness.