Field dependence of the superconductive penetration depth in tin up to the superheating limit

The superconductive penetration depth δ(T, H) has been studied as a function of temperature and field in single tin spheres, 15-30 {μ}m in diameter. A mutual-inductance method was used with the 75-kHz measuring field parallel to the static field. When properly normalized, the variation of the transition signal with T and H is then proportional to d[δ(T, H)×H]dH, where δ is the penetration depth averaged over the sphere surface. The results are independent of sphere diameter, and thus characteristic of bulk tin. In zero field, we find δ(T)=δ₀[1-(TTc)⁴]1/2, with δ₀=520±30 {}. The field dependence was studied for temperatures close to Tc and fields up to the ideal bulk superheating field Hₛₕ2.76Hc, corresponding to a Ginzburg-Landau parameter κ=0.093±0.001. The penetration depth increases sharply as the field approaches Hₛₕ, but stays finite, while its derivative diverges. We find δ(Hₛₕ)δ(H=0)=1.51±0.04. Averaged over the sphere, we have δ(Hₛₕ)δ(H=0)=1.19±0.01. The field dependence is rather well described by one-dimensional Ginzburg-Landau theory in the low-κ limit. The results indicate that the surface order parameter ψₛ is depressed by (30-50)% at Hₛₕ. In "weak" fields, H≤1.5Hc, the data are consistent with the customary quadratic field dependence.