Anti-screening ferromagnetic superconductivity

We consider the Ginzburg-Landau mean field theory of ferromagnetic superconductors with complex order parameter $\psi_i, i=1,2,3$. Below the critical temperature superconductivity is generated by means of a tachyonic term in the free energy $-\alpha |\psi_i|^2$ $(\alpha>0)$, stabilized by a $\psi^4$-term. However, we show that when $\alpha$ becomes negative superconductivity can also be generated spontaneously by the magnetic field through the Zeeman like coupling between the field and the spin of the order parameter, in analogy with what happens in W-meson condensation. We also show that this mechanism leads to a vortex lattice which has anti-screening currents, enhancing the magnetic field instead of counteracting it. The lattice of vortices is a collective phenomenon where the individual elements do not exist in isolated form. If the parameter $\alpha$ vanishes it is possible to obtain an explicit form of the vortex lattice in terms of Weierstrass' p-function.