Equivalence of dynamical and conventional magnetic relaxation in high-T_c superconductors

Measurements of the sweep rate dependence of the magnetic moment Script M sign of the high-T_c superconductor Bi₂Sr₂CaCu₂O₈ are shown to provide essentially the same information about the current dependence dU/dj of the activation energy U(j) as measurements of the time decay of Script M sign. However, at very short times the conventional relaxation rate R ≡ -d ln Script M sign/d In t is suppressed due to the existence of a waiting time τ_i and needs to be replaced by measurements of Script M sign at various sweep rates dB_e/dt. For a sufficiently strong relaxation process, the magnetic moment decays non-logarithmically in time. This is caused by the non-linear current dependence of the activation energy. Therefore, it is necessary to evaluate the conventional relaxation rate R and the dynamical relaxation rate Q ≡ d In Script M sign/d ln(d B_e/dt) at the same value of the current density. It is shown that the conventional and dynamical relaxation rates are in good agreement with each other in a wide range of temperature and magnetic field.