Magnetization of Dirty Superconductors near the Upper Critical Field

The magnetic behavior of a type-II superconductor with very short electron mean free path (dirty limit) near its upper critical field $B_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ is investigated. A calculation of the magnetization up to the second order in the difference between $B_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ and the external magnetic field is presented which is valid for all temperatures. A triangular and a square lattice of flux lines are considered. A numerical calculation suggests that the triangular lattice remains stable despite the fact that the difference in the thermodynamical potentials between the two lattices decreases due to these second-order terms.