Square vortex lattices for two component superconducting order parameters

I investigate the vortex lattice structure of the Ginzburg Landau free energy for a two component order parameter in the weak-coupling clean-limit when the field is along the high symmetry axis in a tetragonal crystal. It is shown that the vortex lattice phase diagram as a function of the Ginzburg Landau free energy parameters includes phases with a hexagonal, centered rectangular, rectangular, and square unit cells. It is also shown that the square vortex lattice has the largest region of stability. The field distribution of the square vortex lattice near $H_{c2}$ is determined and the application of this model to Sr$_2$RuO$_4$ is discussed.