The non-hexagonal flux-line lattice in superconductors

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 + 1 2β|ψ |4 + [1/(2m)]|(−ih̄∇−2eA)ψ |2 + ∫ (B/μ0 − Mions) · dB − (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.