A theoretical comparison of the effects of the shape of the pinning potential and a distribution of pinning energies of the apparent pinning energy as measured by magnetic flux creep

In the analysis of magnetic flux creep experiments, it is assumed that, at a given temperature, the pinning energy, which must be overcome by thermal activation, depends on the magnetic induction and its gradient by U(B,ΔB)≅U_p(B)[1-(ΔB/ΔB_max)] ⁿ, where U_p is the pinning well depth and ΔB _max corresponds to the critical current density with no thermal activation. Customarily, n is assumed to be unity, and any unusual temperature dependence of U_p is then ascribed to a distribution of well depths. However, realistic assumptions about the shape of the pinning potential yield 3/2≲n≲2, which yields an apparent distribution of well depths in the conventional analysis. Simple models are used to illustrate the characteristics of these two quite different origins for the apparent temperature dependence of well depth obtained from magnetic flux creep rates