Closed Abrikosov vortex in uniaxial superconductor

The structure of a closed Abrikosov vortex in a uniaxial superconductor is investigated. The superconductor anisotropy is described by the electron effective mass tensor. Equations for magnetic field and free energy of the vortex are derived with on arbitrary vortex tilt with respect to the anisotropy axis. A vortex shape is determined for the case of its special orientation. It is shown that in an easy-plane superconductor (m(a) < m(c)), of minimum energy is a vortex lying in the easy plane while in an easy-axis one (m(a) > m(c)) the same is true for a vortex whose plane is parallel to the anisotropy axis, all other things being equal.