Lower critical field of a superconductor with uniaxial anisotropy

Exact transformation of the Ginzburg-Landau free energy with uniaxial anisotropy and a variational procedure are used to calculate accurately the line energy of a single magnetic vortex for arbitrary stiffness ${\mathrm{\kappa }}_{\mathrm{\perp }}$ and anisotropy γ. The lower critical field ${\mathit{H}}_{\mathit{c}1}$(${\mathrm{\theta }}_{\mathit{H}}$) can exhibit a discontinuity, a kink, or be monotonic. Comparisons with experiment are made, and materials likely to exhibit such anomalies are suggested. The effective core cross section in the anisotropic London model is found.