A generalized form of Ginzburg-Landau theory is proposed which
explains the non-hexagonal flux-line lattice found both in metallic
and magnetic superconductors without invoking any anisotropic
material-dependent properties. The Gibbs energy density postulated
for magnetic superconductors (g) is of the form g(B,T) = α|ψ|2 + ½β|ψ|4 + [1/(2m)]|(- i ℏ ∇-2eA)ψ|2 + ∫(B/µ0-Mions)· d B-(B/µ0-Mions)·(µ0M + µ0Hext) where M is the total local magnetization, Mions is the local magnetization of the magnetic ions and Hext is the externally applied field strength. The macroscopic
Gibbs energy density and magnetization close to the upper critical
field have been calculated for all possible periodic flux-line
lattice structures, for high and low values of the Ginzburg-Landau
constant (κ) in both metallic and magnetic superconductors.
The generalized theory is consistent with standard theory for
high-κ metallic superconductors. However, for low-κ
and/or strongly paramagnetic superconductors for which (1 + χ')/2<κ2<3.45(1 + χ')2/(1-χ')2, where χ' is the differential susceptibility of the
paramagnetic ions in the normal state, non-hexagonal flux-line
lattice structures occur. When the flux-line lattice is
non-hexagonal, (∂⟨MSC⟩/∂⟨Hext⟩)Hext≈HC2 = (1-χ')/(3 + χ'). Ferromagnetic and antiferromagnetic
superconductivity occur when χ'>1. Furthermore,
increasingly strong paramagnetism coexisting with superconductivity
can produce a type I-type II phase transition. Experimental
evidence for these phenomena and for a correlation between strong
paramagnetism in magnetic superconductors and re-entrant
superconductivity is discussed.