Remarks on small superconducting specimens in magnetic field and measurements of the lower critical field

We shall discuss the magnetic behaviors associated with the boundary effects for type-II superconductors in general orientations. Using previous results, we speculate that the relation among the lower critical field H_c1, the thermodynamic critical field H_c and the upper critical field H_c2, namely H²_c ∼ H_c1 H_c2, is still approximately valid for general experimental orientations. More precisely, the magnitudes of H_c1, H_c, and H_c2 are consistent with the formulae given for bulk superconductors when the typical size of the superconducting specimen is greater than the coherence length ξ, provided the penetration depth λ is substituted by a modified value λ_m. Consequently, the criterion for observing type-II superconducting magnetic behaviors also becomes λ_m > ξ, although the London equation is still governed by λ. In the second part of the paper, we shall also suggest an experiment, based on the fact of H_c1 of superconducting thin films in parallel magnetic field being much higher than that of bulk superconductors, to measure H_c1 precisely, especially for extreme type-II superconductors, without influence of the penetration barrier.