4 research outputs found
Approximate Ginzburg-Landau solution for the regular flux-line lattice. Circular cell method
A variational model is proposed to describe the magnetic properties of
type-II superconductors in the entire field range between and
for any values of the Ginzburg-Landau parameter . The
hexagonal unit cell of the triangular flux-line lattice is replaced by a circle
of the same area, and the periodic solutions to the Ginzburg-Landau equations
within this cell are approximated by rotationally symmetric solutions. The
Ginzburg-Landau equations are solved by a trial function for the order
parameter. The calculated spatial distributions of the order parameter and the
magnetic field are compared with the corresponding distributions obtained by
numerical solution of the Ginzburg-Landau equations. The comparison reveals
good agreement with an accuracy of a few percent for all values
exceeding . The model can be extended to anisotropic
superconductors when the vortices are directed along one of the principal axes.
The reversible magnetization curve is calculated and an analytical formula for
the magnetization is proposed. At low fields, the theory reduces to the London
approach at , provided that the exact value of is used.
At high fields, our model reproduces the main features of the well-known
Abrikosov theory. The magnetic field dependences of the reversible
magnetization found numerically and by our variational method practically
coincide. The model also refines the limits of some approximations which have
been widely used. The calculated magnetization curves are in a good agreement
with experimental data on high-T superconductors.Comment: 8 pages, RevTex, 6 figures, submitted to Phys. Rev.
Scaling of the Equilibrium Magnetization in the Mixed State of Type-II Superconductors
We discuss the analysis of mixed-state magnetization data of type-II
superconductors using a recently developed scaling procedure. It is based on
the fact that, if the Ginzburg-Landau parameter kappa does not depend on
temperature, the magnetic susceptibility is a universal function of H/H_c2(T),
leading to a simple relation between magnetizations at different temperatures.
Although this scaling procedure does not provide absolute values of the upper
critical fieldH_c2(T), its temperature variation can be established rather
accurately. This provides an opportunity to validate theoretical models that
are usually employed for the evaluation of H_c2(T) from equilibrium
magnetization data. In the second part of the paper we apply this scaling
procedure for a discussion of the notorious first order phase transition in the
mixed state of high temperature superconductors. Our analysis, based on
experimental magnetization data available in the literature, shows that the
shift of the magnetization accross the transition may adopt either sign,
depending on the particular chosen sample. We argue that this observation is
inconsistent with the interpretation that this transition always represents the
melting transition of the vortex lattice.Comment: 18 pages, 12 figure