Lower critical field of an anisotropic type-II superconductor

We consider the Ginzburg-Landau free energy of the anisotropic mass form in the presence of a magnetic field of arbitrary fixed direction. It is shown that the free energy may be transformed into the isotropic Ginzburg-Landau form with a $\kappa$ that depends upon the direction of the magnetic induction $\overrightarrow{\mathrm{B}}$ relative to the crystal lattice. The lower critical field ${\overrightarrow{\mathrm{H}}}_{c1\mathrm{}}$ is then found for arbitrary direction of $\overrightarrow{\mathrm{B}}$. For highly anisotropic crystals the angular dependence of ${\overrightarrow{\mathrm{H}}}_{c1\mathrm{}}$ can exhibit a discontinuity or a cusp. The special case of a crystal with uniaxial symmetry is considered in detail.