Magnetic relaxation in partly penetrated critical states of type-II superconductors

Magnetic relaxation in a thin flat type-II superconductor of arbitrary shape placed in an external magnetic field perpendicular to its plane is analyzed in the general case when flux penetration is not necessarily complete. We derive an expression for the magnetic relaxation rate that generalizes the well-known formula of Beasley et al. obtained for superconductors in the fully penetrated critical state. Our result allows one to extract the effective height of the activation barrier from experimental data even when the critical state has a complicated structure, in particular when the applied magnetic field is less than the field of full flux penetration into the sample.