Magnetization of type-II superconductors in the range of fields H-c1 <= H <= H-c2: Variational method

A variational method is proposed to find the magnetic field dependence of t he magnetization of type-II superconductors in the mixed state by a self-co nsistent technique. This model allows for suppression of the order paramete r to zero at the centers of Abrikosov vortices and also for the magnetic fi eld dependence of the order parameter. The results can be applied to the en tire range of fields H-c1 less than or equal to H less than or equal to H-c 2 for any values of the Ginzburg-Landau parameter kappa > 1/root 2. It is s hown that in weak fields where kappa much greater than 1 the behavior of th e magnetization can be described exactly in the London approximation provid ed that the correct value of H-c1 is used. Near the second critical field t his dependence shows good agreement with the well-known Abrikosov result. I t is also shown that using the concept of isolated vortices and applying th e principle of superposition of the fields and currents generated by these vortices to calculate the magnetization gives inaccurate quantitative resul ts even in fairly weak fields. By going beyond these concepts, it was possi ble to allow more accurately for the influence of the vortex cores on the m agnetization behavior in the intermediate range of fields H-c1 much less th an H much less than H-c2 and to identify the range of validity of various a pproximations used widely in the literature. (C) 2000 MAIK "Nauka/Interperi odica".